Cluster computing

Friday, May 8, 2026

Tiling of aerial drone survey area

Problem statement:

Most UAV with top-down camera provide a video of their tour regardless of their flight path. This video can be split into several contiguous aerial drone images which may often number in hundreds even for a short duration. We need a software implementation that can take these images as input in the sorted order of the timeline and select those images that can complete tiling of the area surveyed by drone tour. The output of the implementation must be a selection of the original input. Flight path could be assumed to be rectangular with the lower left as origin for simplicity but none of the images have gps information available. Additionally, the selection could be output in the sorted order to start from lower left of the area surveyed and move clockwise along the perimeter but this can be skipped from the implementation.

Solution:

The following implementation uses computer vision (feature matching + homography estimation) to determine spatial relationships between images and then solves a set-cover problem to select a minimal tiling subset. A set of five stages completes the pipeline towards the goal:

Pipeline:

Stage What happens Key algorithm

1. Feature matching ORB keypoints are detected in each image; nearby frames (within search_radius) are matched using brute-force Hamming + Lowe's ratio test, then a homography is estimated with RANSAC. ORB [Rublee 2011], RANSAC [Fischler 1981]

2. Global registration A BFS traversal from the most-connected image propagates homographies so every frame is placed in a single mosaic coordinate system. No GPS needed. Brown & Lowe (2007) panoramic stitching

3. Coverage gridding The mosaic bounding box is discretised into a grid. Each image's warped footprint is rasterised to determine which cells it covers. OpenCV fillConvexPoly

4. Greedy set cover Iteratively selects the image covering the most uncovered cells until 100% coverage is reached. This is the classic greedy approximation (ln n + 1 factor). Chvatal (1979)

5. Spatial sort Selected images are sorted clockwise starting from the lower-left corner using angular ordering around the centroid. Convex-hull sweep

Usage:

# Install dependencies

pip install opencv-python-headless numpy

# Run (CLI)

python drone_tiling.py --input_dir ./my_drone_frames --output tiles.json

# Run (programmatic)

from drone_tiling import select_tiling_from_directory

selected = select_tiling_from_directory("./my_drone_frames")

print(selected)

Implementation:

"""

Drone Image Tiling Selector

============================

Selects a minimal subset of contiguous aerial drone images that completely

tiles (covers) the area surveyed during a drone flight.

Algorithm & Citations

---------------------

1. **Feature Detection & Matching**: ORB (Oriented FAST and Rotated BRIEF)

detector with brute-force Hamming-distance matching.

- Rublee, E., Rabaud, V., Konolige, K., & Bradski, G. (2011).

"ORB: An efficient alternative to SIFT or SURF."

IEEE International Conference on Computer Vision (ICCV), pp. 2564-2571.

DOI: 10.1109/ICCV.2011.6126544

- OpenCV documentation: https://docs.opencv.org/4.x/d1/d89/tutorial_py_orb.html

2. **Homography Estimation (RANSAC)**: Used to compute the projective

transformation between overlapping image pairs, which gives us the

relative spatial position of each image.

- Fischler, M. A., & Bolles, R. C. (1981).

"Random Sample Consensus: A Paradigm for Model Fitting with

Applications to Image Analysis and Automated Cartography."

Communications of the ACM, 24(6), 381-395.

- OpenCV documentation: https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html

3. **Image Stitching / Registration Pipeline**: The pairwise registration

approach follows the methodology in:

- Brown, M., & Lowe, D. G. (2007).

"Automatic Panoramic Image Stitching using Invariant Features."

International Journal of Computer Vision, 74(1), 59-73.

DOI: 10.1007/s11263-006-0002-3

4. **Greedy Weighted Set Cover** for selecting the minimal tiling subset:

- Chvatal, V. (1979).

"A Greedy Heuristic for the Set-Covering Problem."

Mathematics of Operations Research, 4(3), 233-235.

- Vazirani, V. V. (2001). "Approximation Algorithms", Chapter 2.

Springer-Verlag. ISBN: 3-540-65367-8.

Dependencies

------------

pip install opencv-python-headless numpy

Usage

-----

python drone_tiling.py --input_dir ./drone_images --output tiles.json

"""

import os

import glob

import json

import argparse

import logging

from dataclasses import dataclass, field

from typing import List, Tuple, Dict, Optional, Set

import cv2

import numpy as np

logging.basicConfig(level=logging.INFO, format="%(levelname)s: %(message)s")

logger = logging.getLogger(__name__)

# ---------------------------------------------------------------------------

# Configuration

# ---------------------------------------------------------------------------

@dataclass

class TilingConfig:

"""Tuneable parameters for the tiling pipeline."""

# ORB feature detector

orb_n_features: int = 3000

orb_scale_factor: float = 1.2

orb_n_levels: int = 8

# Feature matching

match_ratio_thresh: float = 0.75 # Lowe's ratio test threshold

min_good_matches: int = 30 # minimum inlier matches to

# consider a pair overlapping

# RANSAC homography

ransac_reproj_thresh: float = 5.0 # reprojection error in pixels

# Coverage grid resolution (number of cells along the longer axis)

grid_resolution: int = 100

# Overlap: minimum fraction of an image that must overlap with the

# already-covered area for the image to be considered redundant.

redundancy_overlap: float = 0.95

# Image scaling for speed (process at this fraction of original size)

work_scale: float = 0.5

# ---------------------------------------------------------------------------

# Data structures

# ---------------------------------------------------------------------------

@dataclass

class ImageRecord:

"""Metadata for a single drone image."""

index: int

filepath: str

filename: str

width: int = 0

height: int = 0

# Position of the image centre in the *mosaic* coordinate frame.

cx: float = 0.0

cy: float = 0.0

# 3x3 homography that maps this image into mosaic coordinates.

H: Optional[np.ndarray] = None

@dataclass

class PairwiseMatch:

"""Result of matching two images."""

idx_a: int

idx_b: int

n_inliers: int

H_ab: np.ndarray # homography from image A to image B

confidence: float = 0.0

# ---------------------------------------------------------------------------

# 1. Feature detection & pair-wise matching

# ---------------------------------------------------------------------------

class FeatureMatcher:

"""

Detects ORB features in every image and matches consecutive /

nearby frames to estimate pairwise homographies.

Reference

---------

Rublee et al., "ORB: An efficient alternative to SIFT or SURF", ICCV 2011.

OpenCV ORB docs: https://docs.opencv.org/4.x/d1/d89/tutorial_py_orb.html

"""

def __init__(self, config: TilingConfig):

self.cfg = config

self.orb = cv2.ORB_create(

nfeatures=config.orb_n_features,

scaleFactor=config.orb_scale_factor,

nlevels=config.orb_n_levels,

)

self.bf = cv2.BFMatcher(cv2.NORM_HAMMING)

@staticmethod

def _load_grey(path: str, scale: float) -> np.ndarray:

img = cv2.imread(path, cv2.IMREAD_GRAYSCALE)

if img is None:

raise FileNotFoundError(f"Cannot read image: {path}")

if scale != 1.0:

img = cv2.resize(img, None, fx=scale, fy=scale,

interpolation=cv2.INTER_AREA)

return img

def _detect(self, grey: np.ndarray):

kp, des = self.orb.detectAndCompute(grey, None)

return kp, des

def _match_pair(self, des_a, des_b, kp_a, kp_b) -> Optional[PairwiseMatch]:

"""

Match descriptors with Lowe's ratio test, then estimate a homography

with RANSAC.

Reference

---------

Lowe, D. G. (2004). "Distinctive Image Features from Scale-Invariant

Keypoints." IJCV, 60(2), 91-110.

Fischler & Bolles (1981). "Random Sample Consensus." CACM.

"""

if des_a is None or des_b is None:

return None

if len(des_a) < 2 or len(des_b) < 2:

return None

raw_matches = self.bf.knnMatch(des_a, des_b, k=2)

good = []

for m_pair in raw_matches:

if len(m_pair) < 2:

continue

m, n = m_pair

if m.distance < self.cfg.match_ratio_thresh * n.distance:

good.append(m)

if len(good) < self.cfg.min_good_matches:

return None

pts_a = np.float32([kp_a[m.queryIdx].pt for m in good]).reshape(-1, 1, 2)

pts_b = np.float32([kp_b[m.trainIdx].pt for m in good]).reshape(-1, 1, 2)

H, mask = cv2.findHomography(

pts_a, pts_b, cv2.RANSAC, self.cfg.ransac_reproj_thresh

)

if H is None:

return None

n_inliers = int(mask.sum())

if n_inliers < self.cfg.min_good_matches:

return None

confidence = n_inliers / (8.0 + 0.3 * len(good)) # Brown & Lowe 2007

return PairwiseMatch(

idx_a=-1, idx_b=-1,

n_inliers=n_inliers,

H_ab=H,

confidence=confidence,

)

def match_sequence(

self,

records: List[ImageRecord],

search_radius: int = 5,

) -> List[PairwiseMatch]:

"""

For every image, match against up to *search_radius* neighbours in

both directions (handles forward overlap AND lateral overlap from

adjacent flight strips).

"""

n = len(records)

scale = self.cfg.work_scale

features = []

for rec in records:

grey = self._load_grey(rec.filepath, scale)

rec.height, rec.width = grey.shape[:2]

kp, des = self._detect(grey)

features.append((kp, des))

logger.debug(" %s - %d keypoints", rec.filename, len(kp))

matches: List[PairwiseMatch] = []

tested: Set[Tuple[int, int]] = set()

for i in range(n):

for j in range(i + 1, min(i + search_radius + 1, n)):

if (i, j) in tested:

continue

tested.add((i, j))

kp_a, des_a = features[i]

kp_b, des_b = features[j]

pm = self._match_pair(des_a, des_b, kp_a, kp_b)

if pm is not None:

pm.idx_a = i

pm.idx_b = j

matches.append(pm)

logger.debug(

" match %s <-> %s inliers=%d conf=%.3f",

records[i].filename, records[j].filename,

pm.n_inliers, pm.confidence,

)

logger.info("Pairwise matching complete: %d valid pairs from %d images.",

len(matches), n)

return matches

# ---------------------------------------------------------------------------

# 2. Global registration - place every image in a common mosaic frame

# ---------------------------------------------------------------------------

def register_images(

records: List[ImageRecord],

matches: List[PairwiseMatch],

) -> List[ImageRecord]:

"""

Build a connected graph of images and propagate homographies via BFS

so that every image is mapped into the coordinate frame of a single

reference image (the one with the most connections).

Reference

---------

Brown, M. & Lowe, D. G. (2007). "Automatic Panoramic Image Stitching

using Invariant Features." IJCV 74(1), 59-73.

OpenCV Stitching: https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html

"""

n = len(records)

adj: Dict[int, List[Tuple[int, np.ndarray, float]]] = {i: [] for i in range(n)}

for pm in matches:

a, b = pm.idx_a, pm.idx_b

adj[a].append((b, pm.H_ab, pm.confidence))

H_inv = np.linalg.inv(pm.H_ab)

adj[b].append((a, H_inv, pm.confidence))

ref = max(range(n), key=lambda i: len(adj[i]))

logger.info("Reference image: %s (index %d, %d neighbours)",

records[ref].filename, ref, len(adj[ref]))

records[ref].H = np.eye(3, dtype=np.float64)

visited = {ref}

queue = [ref]

while queue:

cur = queue.pop(0)

for nb, H_cur_to_nb, _conf in adj[cur]:

if nb in visited:

continue

H_nb_to_mosaic = records[cur].H @ np.linalg.inv(H_cur_to_nb)

records[nb].H = H_nb_to_mosaic

visited.add(nb)

queue.append(nb)

disconnected = [i for i in range(n) if records[i].H is None]

if disconnected:

logger.warning(

"%d images could not be registered (disconnected): %s",

len(disconnected),

[records[i].filename for i in disconnected],

)

for rec in records:

if rec.H is None:

continue

centre_local = np.array([[rec.width / 2, rec.height / 2]], dtype=np.float64)

centre_mosaic = cv2.perspectiveTransform(

centre_local.reshape(-1, 1, 2), rec.H

)

rec.cx, rec.cy = centre_mosaic[0, 0]

return records

# ---------------------------------------------------------------------------

# 3. Coverage grid & greedy set-cover selection

# ---------------------------------------------------------------------------

def _image_footprint(rec: ImageRecord) -> Optional[np.ndarray]:

"""Return the four mosaic-frame corners of *rec* as an (4,2) array."""

if rec.H is None:

return None

corners = np.float64([

[0, 0],

[rec.width, 0],

[rec.width, rec.height],

[0, rec.height],

]).reshape(-1, 1, 2)

warped = cv2.perspectiveTransform(corners, rec.H)

return warped.reshape(-1, 2)

def _build_coverage_grid(

records: List[ImageRecord],

resolution: int,

) -> Tuple[np.ndarray, float, float, float]:

"""Create a boolean grid representing the total survey area."""

all_corners = []

for rec in records:

fp = _image_footprint(rec)

if fp is not None:

all_corners.append(fp)

if not all_corners:

raise RuntimeError("No images could be registered - cannot build grid.")

all_pts = np.vstack(all_corners)

x_min, y_min = all_pts.min(axis=0)

x_max, y_max = all_pts.max(axis=0)

span = max(x_max - x_min, y_max - y_min)

cell_size = span / resolution

cols = int(np.ceil((x_max - x_min) / cell_size)) + 1

rows = int(np.ceil((y_max - y_min) / cell_size)) + 1

grid = np.zeros((rows, cols), dtype=bool)

return grid, cell_size, float(x_min), float(y_min)

def _rasterise_footprint(

corners: np.ndarray,

cell_size: float,

x_min: float,

y_min: float,

grid_shape: Tuple[int, int],

) -> Set[Tuple[int, int]]:

"""Return the set of grid cells covered by the quadrilateral *corners*."""

rows, cols = grid_shape

gc = ((corners - [x_min, y_min]) / cell_size).astype(np.int32)

mask = np.zeros((rows, cols), dtype=np.uint8)

cv2.fillConvexPoly(mask, gc, 1)

cells = set(zip(*np.where(mask > 0)))

return cells

def select_tiling_images(

records: List[ImageRecord],

config: TilingConfig,

) -> List[ImageRecord]:

"""

Greedy weighted set-cover: iteratively pick the image that covers the

most *uncovered* grid cells until the entire survey area is covered.

Reference

---------

Chvatal, V. (1979). "A Greedy Heuristic for the Set-Covering Problem."

Mathematics of Operations Research, 4(3), 233-235.

"""

grid, cell_size, x_min, y_min = _build_coverage_grid(

records, config.grid_resolution

)

grid_shape = grid.shape

universe: Set[Tuple[int, int]] = set()

image_cells: Dict[int, Set[Tuple[int, int]]] = {}

for rec in records:

fp = _image_footprint(rec)

if fp is None:

continue

cells = _rasterise_footprint(fp, cell_size, x_min, y_min, grid_shape)

image_cells[rec.index] = cells

universe |= cells

logger.info("Survey area: %d grid cells to cover.", len(universe))

uncovered = set(universe)

selected_indices: List[int] = []

used: Set[int] = set()

while uncovered:

best_idx = -1

best_gain = 0

for idx, cells in image_cells.items():

if idx in used:

continue

gain = len(cells & uncovered)

if gain > best_gain:

best_gain = gain

best_idx = idx

if best_idx == -1 or best_gain == 0:

logger.warning(

"Cannot cover %d remaining cells - possible registration gaps.",

len(uncovered),

)

break

selected_indices.append(best_idx)

used.add(best_idx)

uncovered -= image_cells[best_idx]

logger.debug(

" selected %s - covers %d new cells, %d remaining",

records[best_idx].filename, best_gain, len(uncovered),

)

logger.info("Selected %d / %d images for full tiling.",

len(selected_indices), len(records))

selected = [records[i] for i in selected_indices]

return selected

# ---------------------------------------------------------------------------

# 4. (Optional) Sort selected images - lower-left origin, clockwise

# ---------------------------------------------------------------------------

def sort_clockwise_from_lower_left(

selected: List[ImageRecord],

) -> List[ImageRecord]:

"""

Sort images starting from the lower-left corner and proceeding clockwise

along the convex-hull perimeter.

"""

if len(selected) <= 1:

return selected

centres = np.array([[r.cx, r.cy] for r in selected])

centroid = centres.mean(axis=0)

dx = centres[:, 0] - centroid[0]

dy = centres[:, 1] - centroid[1]

angles = np.arctan2(dx, dy)

order = np.argsort(angles)

lower_left_idx = int(

np.argmin(centres[:, 0] - centres[:, 1])

)

start = int(np.where(order == lower_left_idx)[0][0])

order = np.roll(order, -start)

return [selected[i] for i in order]

# ---------------------------------------------------------------------------

# 5. Main pipeline

# ---------------------------------------------------------------------------

def load_image_records(input_dir: str) -> List[ImageRecord]:

"""Load image file paths from a directory, sorted by name."""

extensions = ("*.jpg", "*.jpeg", "*.png", "*.tif", "*.tiff", "*.bmp")

paths: List[str] = []

for ext in extensions:

paths.extend(glob.glob(os.path.join(input_dir, ext)))

paths.extend(glob.glob(os.path.join(input_dir, ext.upper())))

paths = sorted(set(paths))

if not paths:

raise FileNotFoundError(f"No image files found in {input_dir}")

records = [

ImageRecord(index=i, filepath=p, filename=os.path.basename(p))

for i, p in enumerate(paths)

]

logger.info("Loaded %d image paths from %s", len(records), input_dir)

return records

def select_tiling_from_directory(

input_dir: str,

config: Optional[TilingConfig] = None,

sort_result: bool = True,

) -> List[str]:

"""

End-to-end pipeline.

Parameters

----------

input_dir : str

Directory containing contiguous drone images.

config : TilingConfig, optional

Pipeline configuration; uses defaults when None.

sort_result : bool

If True, sort selected images clockwise from lower-left.

Returns

-------

list[str]

File paths of the selected tiling images.

"""

if config is None:

config = TilingConfig()

records = load_image_records(input_dir)

matcher = FeatureMatcher(config)

matches = matcher.match_sequence(records)

if not matches:

logger.warning("No pairwise matches found. Returning all images.")

return [r.filepath for r in records]

records = register_images(records, matches)

selected = select_tiling_images(records, config)

if sort_result:

selected = sort_clockwise_from_lower_left(selected)

return [rec.filepath for rec in selected]

# ---------------------------------------------------------------------------

# CLI

# ---------------------------------------------------------------------------

def main():

parser = argparse.ArgumentParser(

description="Select a minimal set of drone images that tile the surveyed area."

)

parser.add_argument(

"--input_dir", required=True,

help="Directory containing contiguous aerial drone images.",

)

parser.add_argument(

"--output", default=None,

help="Optional JSON file to write the selected file list to.",

)

parser.add_argument(

"--grid_resolution", type=int, default=100,

help="Grid resolution for coverage computation (default: 100).",

)

parser.add_argument(

"--work_scale", type=float, default=0.5,

help="Down-scale factor for images during processing (default: 0.5).",

)

parser.add_argument(

"--search_radius", type=int, default=5,

help="Match each image against this many neighbours (default: 5).",

)

parser.add_argument(

"--no_sort", action="store_true",

help="Skip clockwise spatial sorting of the result.",

)

args = parser.parse_args()

config = TilingConfig(

grid_resolution=args.grid_resolution,

work_scale=args.work_scale,

)

selected = select_tiling_from_directory(

args.input_dir, config, sort_result=not args.no_sort

)

print(f"\n{'='*60}")

print(f"Selected {len(selected)} images for tiling:")

print(f"{'='*60}")

for i, path in enumerate(selected, 1):

print(f" {i:>3d}. {os.path.basename(path)}")

if args.output:

with open(args.output, "w") as f:

json.dump({"selected_images": selected}, f, indent=2)

print(f"\nResults written to {args.output}")

if __name__ == "__main__":

main()

Tiling of aerial drone survey area

Problem statement:

Solution:

Pipeline:

Stage What happens Key algorithm

3. Coverage gridding The mosaic bounding box is discretised into a grid. Each image's warped footprint is rasterised to determine which cells it covers. OpenCV fillConvexPoly

4. Greedy set cover Iteratively selects the image covering the most uncovered cells until 100% coverage is reached. This is the classic greedy approximation (ln n + 1 factor). Chvatal (1979)

5. Spatial sort Selected images are sorted clockwise starting from the lower-left corner using angular ordering around the centroid. Convex-hull sweep

Usage:

# Install dependencies

pip install opencv-python-headless numpy

# Run (CLI)

python drone_tiling.py --input_dir ./my_drone_frames --output tiles.json

# Run (programmatic)

from drone_tiling import select_tiling_from_directory

selected = select_tiling_from_directory("./my_drone_frames")

print(selected)

Implementation:

"""

Drone Image Tiling Selector

============================

Selects a minimal subset of contiguous aerial drone images that completely

tiles (covers) the area surveyed during a drone flight.

Algorithm & Citations

---------------------

1. **Feature Detection & Matching**: ORB (Oriented FAST and Rotated BRIEF)

detector with brute-force Hamming-distance matching.

- Rublee, E., Rabaud, V., Konolige, K., & Bradski, G. (2011).

"ORB: An efficient alternative to SIFT or SURF."

IEEE International Conference on Computer Vision (ICCV), pp. 2564-2571.

DOI: 10.1109/ICCV.2011.6126544

- OpenCV documentation: https://docs.opencv.org/4.x/d1/d89/tutorial_py_orb.html

2. **Homography Estimation (RANSAC)**: Used to compute the projective

transformation between overlapping image pairs, which gives us the

relative spatial position of each image.

- Fischler, M. A., & Bolles, R. C. (1981).

"Random Sample Consensus: A Paradigm for Model Fitting with

Applications to Image Analysis and Automated Cartography."

Communications of the ACM, 24(6), 381-395.

- OpenCV documentation: https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html

3. **Image Stitching / Registration Pipeline**: The pairwise registration

approach follows the methodology in:

- Brown, M., & Lowe, D. G. (2007).

"Automatic Panoramic Image Stitching using Invariant Features."

International Journal of Computer Vision, 74(1), 59-73.

DOI: 10.1007/s11263-006-0002-3

4. **Greedy Weighted Set Cover** for selecting the minimal tiling subset:

- Chvatal, V. (1979).

"A Greedy Heuristic for the Set-Covering Problem."

Mathematics of Operations Research, 4(3), 233-235.

- Vazirani, V. V. (2001). "Approximation Algorithms", Chapter 2.

Springer-Verlag. ISBN: 3-540-65367-8.

Dependencies

------------

pip install opencv-python-headless numpy

Usage

-----

python drone_tiling.py --input_dir ./drone_images --output tiles.json

"""

import os

import glob

import json

import argparse

import logging

from dataclasses import dataclass, field

from typing import List, Tuple, Dict, Optional, Set

import cv2

import numpy as np

logging.basicConfig(level=logging.INFO, format="%(levelname)s: %(message)s")

logger = logging.getLogger(__name__)

# ---------------------------------------------------------------------------

# Configuration

# ---------------------------------------------------------------------------

@dataclass

class TilingConfig:

"""Tuneable parameters for the tiling pipeline."""

# ORB feature detector

orb_n_features: int = 3000

orb_scale_factor: float = 1.2

orb_n_levels: int = 8

# Feature matching

match_ratio_thresh: float = 0.75 # Lowe's ratio test threshold

min_good_matches: int = 30 # minimum inlier matches to

# consider a pair overlapping

# RANSAC homography

ransac_reproj_thresh: float = 5.0 # reprojection error in pixels

# Coverage grid resolution (number of cells along the longer axis)

grid_resolution: int = 100

# Overlap: minimum fraction of an image that must overlap with the

# already-covered area for the image to be considered redundant.

redundancy_overlap: float = 0.95

# Image scaling for speed (process at this fraction of original size)

work_scale: float = 0.5

# ---------------------------------------------------------------------------

# Data structures

# ---------------------------------------------------------------------------

@dataclass

class ImageRecord:

"""Metadata for a single drone image."""

index: int

filepath: str

filename: str

width: int = 0

height: int = 0

# Position of the image centre in the *mosaic* coordinate frame.

cx: float = 0.0

cy: float = 0.0

# 3x3 homography that maps this image into mosaic coordinates.

H: Optional[np.ndarray] = None

@dataclass

class PairwiseMatch:

"""Result of matching two images."""

idx_a: int

idx_b: int

n_inliers: int

H_ab: np.ndarray # homography from image A to image B

confidence: float = 0.0

# ---------------------------------------------------------------------------

# 1. Feature detection & pair-wise matching

# ---------------------------------------------------------------------------

class FeatureMatcher:

"""

Detects ORB features in every image and matches consecutive /

nearby frames to estimate pairwise homographies.

Reference

---------

Rublee et al., "ORB: An efficient alternative to SIFT or SURF", ICCV 2011.

OpenCV ORB docs: https://docs.opencv.org/4.x/d1/d89/tutorial_py_orb.html

"""

def __init__(self, config: TilingConfig):

self.cfg = config

self.orb = cv2.ORB_create(

nfeatures=config.orb_n_features,

scaleFactor=config.orb_scale_factor,

nlevels=config.orb_n_levels,

)

self.bf = cv2.BFMatcher(cv2.NORM_HAMMING)

@staticmethod

def _load_grey(path: str, scale: float) -> np.ndarray:

img = cv2.imread(path, cv2.IMREAD_GRAYSCALE)

if img is None:

raise FileNotFoundError(f"Cannot read image: {path}")

if scale != 1.0:

img = cv2.resize(img, None, fx=scale, fy=scale,

interpolation=cv2.INTER_AREA)

return img

def _detect(self, grey: np.ndarray):

kp, des = self.orb.detectAndCompute(grey, None)

return kp, des

def _match_pair(self, des_a, des_b, kp_a, kp_b) -> Optional[PairwiseMatch]:

"""

Match descriptors with Lowe's ratio test, then estimate a homography

with RANSAC.

Reference

---------

Lowe, D. G. (2004). "Distinctive Image Features from Scale-Invariant

Keypoints." IJCV, 60(2), 91-110.

Fischler & Bolles (1981). "Random Sample Consensus." CACM.

"""

if des_a is None or des_b is None:

return None

if len(des_a) < 2 or len(des_b) < 2:

return None

raw_matches = self.bf.knnMatch(des_a, des_b, k=2)

good = []

for m_pair in raw_matches:

if len(m_pair) < 2:

continue

m, n = m_pair

if m.distance < self.cfg.match_ratio_thresh * n.distance:

good.append(m)

if len(good) < self.cfg.min_good_matches:

return None

pts_a = np.float32([kp_a[m.queryIdx].pt for m in good]).reshape(-1, 1, 2)

pts_b = np.float32([kp_b[m.trainIdx].pt for m in good]).reshape(-1, 1, 2)

H, mask = cv2.findHomography(

pts_a, pts_b, cv2.RANSAC, self.cfg.ransac_reproj_thresh

)

if H is None:

return None

n_inliers = int(mask.sum())

if n_inliers < self.cfg.min_good_matches:

return None

confidence = n_inliers / (8.0 + 0.3 * len(good)) # Brown & Lowe 2007

return PairwiseMatch(

idx_a=-1, idx_b=-1,

n_inliers=n_inliers,

H_ab=H,

confidence=confidence,

)

def match_sequence(

self,

records: List[ImageRecord],

search_radius: int = 5,

) -> List[PairwiseMatch]:

"""

For every image, match against up to *search_radius* neighbours in

both directions (handles forward overlap AND lateral overlap from

adjacent flight strips).

"""

n = len(records)

scale = self.cfg.work_scale

features = []

for rec in records:

grey = self._load_grey(rec.filepath, scale)

rec.height, rec.width = grey.shape[:2]

kp, des = self._detect(grey)

features.append((kp, des))

logger.debug(" %s - %d keypoints", rec.filename, len(kp))

matches: List[PairwiseMatch] = []

tested: Set[Tuple[int, int]] = set()

for i in range(n):

for j in range(i + 1, min(i + search_radius + 1, n)):

if (i, j) in tested:

continue

tested.add((i, j))

kp_a, des_a = features[i]

kp_b, des_b = features[j]

pm = self._match_pair(des_a, des_b, kp_a, kp_b)

if pm is not None:

pm.idx_a = i

pm.idx_b = j

matches.append(pm)

logger.debug(

" match %s <-> %s inliers=%d conf=%.3f",

records[i].filename, records[j].filename,

pm.n_inliers, pm.confidence,

)

logger.info("Pairwise matching complete: %d valid pairs from %d images.",

len(matches), n)

return matches

# ---------------------------------------------------------------------------

# 2. Global registration - place every image in a common mosaic frame

# ---------------------------------------------------------------------------

def register_images(

records: List[ImageRecord],

matches: List[PairwiseMatch],

) -> List[ImageRecord]:

"""

Build a connected graph of images and propagate homographies via BFS

so that every image is mapped into the coordinate frame of a single

reference image (the one with the most connections).

Reference

---------

Brown, M. & Lowe, D. G. (2007). "Automatic Panoramic Image Stitching

using Invariant Features." IJCV 74(1), 59-73.

OpenCV Stitching: https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html

"""

n = len(records)

adj: Dict[int, List[Tuple[int, np.ndarray, float]]] = {i: [] for i in range(n)}

for pm in matches:

a, b = pm.idx_a, pm.idx_b

adj[a].append((b, pm.H_ab, pm.confidence))

H_inv = np.linalg.inv(pm.H_ab)

adj[b].append((a, H_inv, pm.confidence))

ref = max(range(n), key=lambda i: len(adj[i]))

logger.info("Reference image: %s (index %d, %d neighbours)",

records[ref].filename, ref, len(adj[ref]))

records[ref].H = np.eye(3, dtype=np.float64)

visited = {ref}

queue = [ref]

while queue:

cur = queue.pop(0)

for nb, H_cur_to_nb, _conf in adj[cur]:

if nb in visited:

continue

H_nb_to_mosaic = records[cur].H @ np.linalg.inv(H_cur_to_nb)

records[nb].H = H_nb_to_mosaic

visited.add(nb)

queue.append(nb)

disconnected = [i for i in range(n) if records[i].H is None]

if disconnected:

logger.warning(

"%d images could not be registered (disconnected): %s",

len(disconnected),

[records[i].filename for i in disconnected],

)

for rec in records:

if rec.H is None:

continue

centre_local = np.array([[rec.width / 2, rec.height / 2]], dtype=np.float64)

centre_mosaic = cv2.perspectiveTransform(

centre_local.reshape(-1, 1, 2), rec.H

)

rec.cx, rec.cy = centre_mosaic[0, 0]

return records

# ---------------------------------------------------------------------------

# 3. Coverage grid & greedy set-cover selection

# ---------------------------------------------------------------------------

def _image_footprint(rec: ImageRecord) -> Optional[np.ndarray]:

"""Return the four mosaic-frame corners of *rec* as an (4,2) array."""

if rec.H is None:

return None

corners = np.float64([

[0, 0],

[rec.width, 0],

[rec.width, rec.height],

[0, rec.height],

]).reshape(-1, 1, 2)

warped = cv2.perspectiveTransform(corners, rec.H)

return warped.reshape(-1, 2)

def _build_coverage_grid(

records: List[ImageRecord],

resolution: int,

) -> Tuple[np.ndarray, float, float, float]:

"""Create a boolean grid representing the total survey area."""

all_corners = []

for rec in records:

fp = _image_footprint(rec)

if fp is not None:

all_corners.append(fp)

if not all_corners:

raise RuntimeError("No images could be registered - cannot build grid.")

all_pts = np.vstack(all_corners)

x_min, y_min = all_pts.min(axis=0)

x_max, y_max = all_pts.max(axis=0)

span = max(x_max - x_min, y_max - y_min)

cell_size = span / resolution

cols = int(np.ceil((x_max - x_min) / cell_size)) + 1

rows = int(np.ceil((y_max - y_min) / cell_size)) + 1

grid = np.zeros((rows, cols), dtype=bool)

return grid, cell_size, float(x_min), float(y_min)

def _rasterise_footprint(

corners: np.ndarray,

cell_size: float,

x_min: float,

y_min: float,

grid_shape: Tuple[int, int],

) -> Set[Tuple[int, int]]:

"""Return the set of grid cells covered by the quadrilateral *corners*."""

rows, cols = grid_shape

gc = ((corners - [x_min, y_min]) / cell_size).astype(np.int32)

mask = np.zeros((rows, cols), dtype=np.uint8)

cv2.fillConvexPoly(mask, gc, 1)

cells = set(zip(*np.where(mask > 0)))

return cells

def select_tiling_images(

records: List[ImageRecord],

config: TilingConfig,

) -> List[ImageRecord]:

"""

Greedy weighted set-cover: iteratively pick the image that covers the

most *uncovered* grid cells until the entire survey area is covered.

Reference

---------

Chvatal, V. (1979). "A Greedy Heuristic for the Set-Covering Problem."

Mathematics of Operations Research, 4(3), 233-235.

"""

grid, cell_size, x_min, y_min = _build_coverage_grid(

records, config.grid_resolution

)

grid_shape = grid.shape

universe: Set[Tuple[int, int]] = set()

image_cells: Dict[int, Set[Tuple[int, int]]] = {}

for rec in records:

fp = _image_footprint(rec)

if fp is None:

continue

cells = _rasterise_footprint(fp, cell_size, x_min, y_min, grid_shape)

image_cells[rec.index] = cells

universe |= cells

logger.info("Survey area: %d grid cells to cover.", len(universe))

uncovered = set(universe)

selected_indices: List[int] = []

used: Set[int] = set()

while uncovered:

best_idx = -1

best_gain = 0

for idx, cells in image_cells.items():

if idx in used:

continue

gain = len(cells & uncovered)

if gain > best_gain:

best_gain = gain

best_idx = idx

if best_idx == -1 or best_gain == 0:

logger.warning(

"Cannot cover %d remaining cells - possible registration gaps.",

len(uncovered),

)

break

selected_indices.append(best_idx)

used.add(best_idx)

uncovered -= image_cells[best_idx]

logger.debug(

" selected %s - covers %d new cells, %d remaining",

records[best_idx].filename, best_gain, len(uncovered),

)

logger.info("Selected %d / %d images for full tiling.",

len(selected_indices), len(records))

selected = [records[i] for i in selected_indices]

return selected

# ---------------------------------------------------------------------------

# 4. (Optional) Sort selected images - lower-left origin, clockwise

# ---------------------------------------------------------------------------

def sort_clockwise_from_lower_left(

selected: List[ImageRecord],

) -> List[ImageRecord]:

"""

Sort images starting from the lower-left corner and proceeding clockwise

along the convex-hull perimeter.

"""

if len(selected) <= 1:

return selected

centres = np.array([[r.cx, r.cy] for r in selected])

centroid = centres.mean(axis=0)

dx = centres[:, 0] - centroid[0]

dy = centres[:, 1] - centroid[1]

angles = np.arctan2(dx, dy)

order = np.argsort(angles)

lower_left_idx = int(

np.argmin(centres[:, 0] - centres[:, 1])

)

start = int(np.where(order == lower_left_idx)[0][0])

order = np.roll(order, -start)

return [selected[i] for i in order]

# ---------------------------------------------------------------------------

# 5. Main pipeline

# ---------------------------------------------------------------------------

def load_image_records(input_dir: str) -> List[ImageRecord]:

"""Load image file paths from a directory, sorted by name."""

extensions = ("*.jpg", "*.jpeg", "*.png", "*.tif", "*.tiff", "*.bmp")

paths: List[str] = []

for ext in extensions:

paths.extend(glob.glob(os.path.join(input_dir, ext)))

paths.extend(glob.glob(os.path.join(input_dir, ext.upper())))

paths = sorted(set(paths))

if not paths:

raise FileNotFoundError(f"No image files found in {input_dir}")

records = [

ImageRecord(index=i, filepath=p, filename=os.path.basename(p))

for i, p in enumerate(paths)

]

logger.info("Loaded %d image paths from %s", len(records), input_dir)

return records

def select_tiling_from_directory(

input_dir: str,

config: Optional[TilingConfig] = None,

sort_result: bool = True,

) -> List[str]:

"""

End-to-end pipeline.

Parameters

----------

input_dir : str

Directory containing contiguous drone images.

config : TilingConfig, optional

Pipeline configuration; uses defaults when None.

sort_result : bool

If True, sort selected images clockwise from lower-left.

Returns

-------

list[str]

File paths of the selected tiling images.

"""

if config is None:

config = TilingConfig()

records = load_image_records(input_dir)

matcher = FeatureMatcher(config)

matches = matcher.match_sequence(records)

if not matches:

logger.warning("No pairwise matches found. Returning all images.")

return [r.filepath for r in records]

records = register_images(records, matches)

selected = select_tiling_images(records, config)

if sort_result:

selected = sort_clockwise_from_lower_left(selected)

return [rec.filepath for rec in selected]

# ---------------------------------------------------------------------------

# CLI

# ---------------------------------------------------------------------------

def main():

parser = argparse.ArgumentParser(

description="Select a minimal set of drone images that tile the surveyed area."

)

parser.add_argument(

"--input_dir", required=True,

help="Directory containing contiguous aerial drone images.",

)

parser.add_argument(

"--output", default=None,

help="Optional JSON file to write the selected file list to.",

)

parser.add_argument(

"--grid_resolution", type=int, default=100,

help="Grid resolution for coverage computation (default: 100).",

)

parser.add_argument(

"--work_scale", type=float, default=0.5,

help="Down-scale factor for images during processing (default: 0.5).",

)

parser.add_argument(

"--search_radius", type=int, default=5,

help="Match each image against this many neighbours (default: 5).",

)

parser.add_argument(

"--no_sort", action="store_true",

help="Skip clockwise spatial sorting of the result.",

)

args = parser.parse_args()

config = TilingConfig(

grid_resolution=args.grid_resolution,

work_scale=args.work_scale,

)

selected = select_tiling_from_directory(

args.input_dir, config, sort_result=not args.no_sort

)

print(f"\n{'='*60}")

print(f"Selected {len(selected)} images for tiling:")

print(f"{'='*60}")

for i, path in enumerate(selected, 1):

print(f" {i:>3d}. {os.path.basename(path)}")

if args.output:

with open(args.output, "w") as f:

json.dump({"selected_images": selected}, f, indent=2)

print(f"\nResults written to {args.output}")

if __name__ == "__main__":

main()

Tiling of aerial drone survey area

Problem statement:

Solution:

Pipeline:

Stage What happens Key algorithm

3. Coverage gridding The mosaic bounding box is discretised into a grid. Each image's warped footprint is rasterised to determine which cells it covers. OpenCV fillConvexPoly

4. Greedy set cover Iteratively selects the image covering the most uncovered cells until 100% coverage is reached. This is the classic greedy approximation (ln n + 1 factor). Chvatal (1979)

5. Spatial sort Selected images are sorted clockwise starting from the lower-left corner using angular ordering around the centroid. Convex-hull sweep

Usage:

# Install dependencies

pip install opencv-python-headless numpy

# Run (CLI)

python drone_tiling.py --input_dir ./my_drone_frames --output tiles.json

# Run (programmatic)

from drone_tiling import select_tiling_from_directory

selected = select_tiling_from_directory("./my_drone_frames")

print(selected)

Implementation:

"""

Drone Image Tiling Selector

============================

Selects a minimal subset of contiguous aerial drone images that completely

tiles (covers) the area surveyed during a drone flight.

Algorithm & Citations

---------------------

1. **Feature Detection & Matching**: ORB (Oriented FAST and Rotated BRIEF)

detector with brute-force Hamming-distance matching.

- Rublee, E., Rabaud, V., Konolige, K., & Bradski, G. (2011).

"ORB: An efficient alternative to SIFT or SURF."

IEEE International Conference on Computer Vision (ICCV), pp. 2564-2571.

DOI: 10.1109/ICCV.2011.6126544

- OpenCV documentation: https://docs.opencv.org/4.x/d1/d89/tutorial_py_orb.html

2. **Homography Estimation (RANSAC)**: Used to compute the projective

transformation between overlapping image pairs, which gives us the

relative spatial position of each image.

- Fischler, M. A., & Bolles, R. C. (1981).

"Random Sample Consensus: A Paradigm for Model Fitting with

Applications to Image Analysis and Automated Cartography."

Communications of the ACM, 24(6), 381-395.

- OpenCV documentation: https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html

3. **Image Stitching / Registration Pipeline**: The pairwise registration

approach follows the methodology in:

- Brown, M., & Lowe, D. G. (2007).

"Automatic Panoramic Image Stitching using Invariant Features."

International Journal of Computer Vision, 74(1), 59-73.

DOI: 10.1007/s11263-006-0002-3

4. **Greedy Weighted Set Cover** for selecting the minimal tiling subset:

- Chvatal, V. (1979).

"A Greedy Heuristic for the Set-Covering Problem."

Mathematics of Operations Research, 4(3), 233-235.

- Vazirani, V. V. (2001). "Approximation Algorithms", Chapter 2.

Springer-Verlag. ISBN: 3-540-65367-8.

Dependencies

------------

pip install opencv-python-headless numpy

Usage

-----

python drone_tiling.py --input_dir ./drone_images --output tiles.json

"""

import os

import glob

import json

import argparse

import logging

from dataclasses import dataclass, field

from typing import List, Tuple, Dict, Optional, Set

import cv2

import numpy as np

logging.basicConfig(level=logging.INFO, format="%(levelname)s: %(message)s")

logger = logging.getLogger(__name__)

# ---------------------------------------------------------------------------

# Configuration

# ---------------------------------------------------------------------------

@dataclass

class TilingConfig:

"""Tuneable parameters for the tiling pipeline."""

# ORB feature detector

orb_n_features: int = 3000

orb_scale_factor: float = 1.2

orb_n_levels: int = 8

# Feature matching

match_ratio_thresh: float = 0.75 # Lowe's ratio test threshold

min_good_matches: int = 30 # minimum inlier matches to

# consider a pair overlapping

# RANSAC homography

ransac_reproj_thresh: float = 5.0 # reprojection error in pixels

# Coverage grid resolution (number of cells along the longer axis)

grid_resolution: int = 100

# Overlap: minimum fraction of an image that must overlap with the

# already-covered area for the image to be considered redundant.

redundancy_overlap: float = 0.95

# Image scaling for speed (process at this fraction of original size)

work_scale: float = 0.5

# ---------------------------------------------------------------------------

# Data structures

# ---------------------------------------------------------------------------

@dataclass

class ImageRecord:

"""Metadata for a single drone image."""

index: int

filepath: str

filename: str

width: int = 0

height: int = 0

# Position of the image centre in the *mosaic* coordinate frame.

cx: float = 0.0

cy: float = 0.0

# 3x3 homography that maps this image into mosaic coordinates.

H: Optional[np.ndarray] = None

@dataclass

class PairwiseMatch:

"""Result of matching two images."""

idx_a: int

idx_b: int

n_inliers: int

H_ab: np.ndarray # homography from image A to image B

confidence: float = 0.0

# ---------------------------------------------------------------------------

# 1. Feature detection & pair-wise matching

# ---------------------------------------------------------------------------

class FeatureMatcher:

"""

Detects ORB features in every image and matches consecutive /

nearby frames to estimate pairwise homographies.

Reference

---------

Rublee et al., "ORB: An efficient alternative to SIFT or SURF", ICCV 2011.

OpenCV ORB docs: https://docs.opencv.org/4.x/d1/d89/tutorial_py_orb.html

"""

def __init__(self, config: TilingConfig):

self.cfg = config

self.orb = cv2.ORB_create(

nfeatures=config.orb_n_features,

scaleFactor=config.orb_scale_factor,

nlevels=config.orb_n_levels,

)

self.bf = cv2.BFMatcher(cv2.NORM_HAMMING)

@staticmethod

def _load_grey(path: str, scale: float) -> np.ndarray:

img = cv2.imread(path, cv2.IMREAD_GRAYSCALE)

if img is None:

raise FileNotFoundError(f"Cannot read image: {path}")

if scale != 1.0:

img = cv2.resize(img, None, fx=scale, fy=scale,

interpolation=cv2.INTER_AREA)

return img

def _detect(self, grey: np.ndarray):

kp, des = self.orb.detectAndCompute(grey, None)

return kp, des

def _match_pair(self, des_a, des_b, kp_a, kp_b) -> Optional[PairwiseMatch]:

"""

Match descriptors with Lowe's ratio test, then estimate a homography

with RANSAC.

Reference

---------

Lowe, D. G. (2004). "Distinctive Image Features from Scale-Invariant

Keypoints." IJCV, 60(2), 91-110.

Fischler & Bolles (1981). "Random Sample Consensus." CACM.

"""

if des_a is None or des_b is None:

return None

if len(des_a) < 2 or len(des_b) < 2:

return None

raw_matches = self.bf.knnMatch(des_a, des_b, k=2)

good = []

for m_pair in raw_matches:

if len(m_pair) < 2:

continue

m, n = m_pair

if m.distance < self.cfg.match_ratio_thresh * n.distance:

good.append(m)

if len(good) < self.cfg.min_good_matches:

return None

pts_a = np.float32([kp_a[m.queryIdx].pt for m in good]).reshape(-1, 1, 2)

pts_b = np.float32([kp_b[m.trainIdx].pt for m in good]).reshape(-1, 1, 2)

H, mask = cv2.findHomography(

pts_a, pts_b, cv2.RANSAC, self.cfg.ransac_reproj_thresh

)

if H is None:

return None

n_inliers = int(mask.sum())

if n_inliers < self.cfg.min_good_matches:

return None

confidence = n_inliers / (8.0 + 0.3 * len(good)) # Brown & Lowe 2007

return PairwiseMatch(

idx_a=-1, idx_b=-1,

n_inliers=n_inliers,

H_ab=H,

confidence=confidence,

)

def match_sequence(

self,

records: List[ImageRecord],

search_radius: int = 5,

) -> List[PairwiseMatch]:

"""

For every image, match against up to *search_radius* neighbours in

both directions (handles forward overlap AND lateral overlap from

adjacent flight strips).

"""

n = len(records)

scale = self.cfg.work_scale

features = []

for rec in records:

grey = self._load_grey(rec.filepath, scale)

rec.height, rec.width = grey.shape[:2]

kp, des = self._detect(grey)

features.append((kp, des))

logger.debug(" %s - %d keypoints", rec.filename, len(kp))

matches: List[PairwiseMatch] = []

tested: Set[Tuple[int, int]] = set()

for i in range(n):

for j in range(i + 1, min(i + search_radius + 1, n)):

if (i, j) in tested:

continue

tested.add((i, j))

kp_a, des_a = features[i]

kp_b, des_b = features[j]

pm = self._match_pair(des_a, des_b, kp_a, kp_b)

if pm is not None:

pm.idx_a = i

pm.idx_b = j

matches.append(pm)

logger.debug(

" match %s <-> %s inliers=%d conf=%.3f",

records[i].filename, records[j].filename,

pm.n_inliers, pm.confidence,

)

logger.info("Pairwise matching complete: %d valid pairs from %d images.",

len(matches), n)

return matches

# ---------------------------------------------------------------------------

# 2. Global registration - place every image in a common mosaic frame

# ---------------------------------------------------------------------------

def register_images(

records: List[ImageRecord],

matches: List[PairwiseMatch],

) -> List[ImageRecord]:

"""

Build a connected graph of images and propagate homographies via BFS

so that every image is mapped into the coordinate frame of a single

reference image (the one with the most connections).

Reference

---------

Brown, M. & Lowe, D. G. (2007). "Automatic Panoramic Image Stitching

using Invariant Features." IJCV 74(1), 59-73.

OpenCV Stitching: https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html

"""

n = len(records)

adj: Dict[int, List[Tuple[int, np.ndarray, float]]] = {i: [] for i in range(n)}

for pm in matches:

a, b = pm.idx_a, pm.idx_b

adj[a].append((b, pm.H_ab, pm.confidence))

H_inv = np.linalg.inv(pm.H_ab)

adj[b].append((a, H_inv, pm.confidence))

ref = max(range(n), key=lambda i: len(adj[i]))

logger.info("Reference image: %s (index %d, %d neighbours)",

records[ref].filename, ref, len(adj[ref]))

records[ref].H = np.eye(3, dtype=np.float64)

visited = {ref}

queue = [ref]

while queue:

cur = queue.pop(0)

for nb, H_cur_to_nb, _conf in adj[cur]:

if nb in visited:

continue

H_nb_to_mosaic = records[cur].H @ np.linalg.inv(H_cur_to_nb)

records[nb].H = H_nb_to_mosaic

visited.add(nb)

queue.append(nb)

disconnected = [i for i in range(n) if records[i].H is None]

if disconnected:

logger.warning(

"%d images could not be registered (disconnected): %s",

len(disconnected),

[records[i].filename for i in disconnected],

)

for rec in records:

if rec.H is None:

continue

centre_local = np.array([[rec.width / 2, rec.height / 2]], dtype=np.float64)

centre_mosaic = cv2.perspectiveTransform(

centre_local.reshape(-1, 1, 2), rec.H

)

rec.cx, rec.cy = centre_mosaic[0, 0]

return records

# ---------------------------------------------------------------------------

# 3. Coverage grid & greedy set-cover selection

# ---------------------------------------------------------------------------

def _image_footprint(rec: ImageRecord) -> Optional[np.ndarray]:

"""Return the four mosaic-frame corners of *rec* as an (4,2) array."""

if rec.H is None:

return None

corners = np.float64([

[0, 0],

[rec.width, 0],

[rec.width, rec.height],

[0, rec.height],

]).reshape(-1, 1, 2)

warped = cv2.perspectiveTransform(corners, rec.H)

return warped.reshape(-1, 2)

def _build_coverage_grid(

records: List[ImageRecord],

resolution: int,

) -> Tuple[np.ndarray, float, float, float]:

"""Create a boolean grid representing the total survey area."""

all_corners = []

for rec in records:

fp = _image_footprint(rec)

if fp is not None:

all_corners.append(fp)

if not all_corners:

raise RuntimeError("No images could be registered - cannot build grid.")

all_pts = np.vstack(all_corners)

x_min, y_min = all_pts.min(axis=0)

x_max, y_max = all_pts.max(axis=0)

span = max(x_max - x_min, y_max - y_min)

cell_size = span / resolution

cols = int(np.ceil((x_max - x_min) / cell_size)) + 1

rows = int(np.ceil((y_max - y_min) / cell_size)) + 1

grid = np.zeros((rows, cols), dtype=bool)

return grid, cell_size, float(x_min), float(y_min)

def _rasterise_footprint(

corners: np.ndarray,

cell_size: float,

x_min: float,

y_min: float,

grid_shape: Tuple[int, int],

) -> Set[Tuple[int, int]]:

"""Return the set of grid cells covered by the quadrilateral *corners*."""

rows, cols = grid_shape

gc = ((corners - [x_min, y_min]) / cell_size).astype(np.int32)

mask = np.zeros((rows, cols), dtype=np.uint8)

cv2.fillConvexPoly(mask, gc, 1)

cells = set(zip(*np.where(mask > 0)))

return cells

def select_tiling_images(

records: List[ImageRecord],

config: TilingConfig,

) -> List[ImageRecord]:

"""

Greedy weighted set-cover: iteratively pick the image that covers the

most *uncovered* grid cells until the entire survey area is covered.

Reference

---------

Chvatal, V. (1979). "A Greedy Heuristic for the Set-Covering Problem."

Mathematics of Operations Research, 4(3), 233-235.

"""

grid, cell_size, x_min, y_min = _build_coverage_grid(

records, config.grid_resolution

)

grid_shape = grid.shape

universe: Set[Tuple[int, int]] = set()

image_cells: Dict[int, Set[Tuple[int, int]]] = {}

for rec in records:

fp = _image_footprint(rec)

if fp is None:

continue

cells = _rasterise_footprint(fp, cell_size, x_min, y_min, grid_shape)

image_cells[rec.index] = cells

universe |= cells

logger.info("Survey area: %d grid cells to cover.", len(universe))

uncovered = set(universe)

selected_indices: List[int] = []

used: Set[int] = set()

while uncovered:

best_idx = -1

best_gain = 0

for idx, cells in image_cells.items():

if idx in used:

continue

gain = len(cells & uncovered)

if gain > best_gain:

best_gain = gain

best_idx = idx

if best_idx == -1 or best_gain == 0:

logger.warning(

"Cannot cover %d remaining cells - possible registration gaps.",

len(uncovered),

)

break

selected_indices.append(best_idx)

used.add(best_idx)

uncovered -= image_cells[best_idx]

logger.debug(

" selected %s - covers %d new cells, %d remaining",

records[best_idx].filename, best_gain, len(uncovered),

)

logger.info("Selected %d / %d images for full tiling.",

len(selected_indices), len(records))

selected = [records[i] for i in selected_indices]

return selected

# ---------------------------------------------------------------------------

# 4. (Optional) Sort selected images - lower-left origin, clockwise

# ---------------------------------------------------------------------------

def sort_clockwise_from_lower_left(

selected: List[ImageRecord],

) -> List[ImageRecord]:

"""

Sort images starting from the lower-left corner and proceeding clockwise

along the convex-hull perimeter.

"""

if len(selected) <= 1:

return selected

centres = np.array([[r.cx, r.cy] for r in selected])

centroid = centres.mean(axis=0)

dx = centres[:, 0] - centroid[0]

dy = centres[:, 1] - centroid[1]

angles = np.arctan2(dx, dy)

order = np.argsort(angles)

lower_left_idx = int(

np.argmin(centres[:, 0] - centres[:, 1])

)

start = int(np.where(order == lower_left_idx)[0][0])

order = np.roll(order, -start)

return [selected[i] for i in order]

# ---------------------------------------------------------------------------

# 5. Main pipeline

# ---------------------------------------------------------------------------

def load_image_records(input_dir: str) -> List[ImageRecord]:

"""Load image file paths from a directory, sorted by name."""

extensions = ("*.jpg", "*.jpeg", "*.png", "*.tif", "*.tiff", "*.bmp")

paths: List[str] = []

for ext in extensions:

paths.extend(glob.glob(os.path.join(input_dir, ext)))

paths.extend(glob.glob(os.path.join(input_dir, ext.upper())))

paths = sorted(set(paths))

if not paths:

raise FileNotFoundError(f"No image files found in {input_dir}")

records = [

ImageRecord(index=i, filepath=p, filename=os.path.basename(p))

for i, p in enumerate(paths)

]

logger.info("Loaded %d image paths from %s", len(records), input_dir)

return records

def select_tiling_from_directory(

input_dir: str,

config: Optional[TilingConfig] = None,

sort_result: bool = True,

) -> List[str]:

"""

End-to-end pipeline.

Parameters

----------

input_dir : str

Directory containing contiguous drone images.

config : TilingConfig, optional

Pipeline configuration; uses defaults when None.

sort_result : bool

If True, sort selected images clockwise from lower-left.

Returns

-------

list[str]

File paths of the selected tiling images.

"""

if config is None:

config = TilingConfig()

records = load_image_records(input_dir)

matcher = FeatureMatcher(config)

matches = matcher.match_sequence(records)

if not matches:

logger.warning("No pairwise matches found. Returning all images.")

return [r.filepath for r in records]

records = register_images(records, matches)

selected = select_tiling_images(records, config)

if sort_result:

selected = sort_clockwise_from_lower_left(selected)

return [rec.filepath for rec in selected]

# ---------------------------------------------------------------------------

# CLI

# ---------------------------------------------------------------------------

def main():

parser = argparse.ArgumentParser(

description="Select a minimal set of drone images that tile the surveyed area."

)

parser.add_argument(

"--input_dir", required=True,

help="Directory containing contiguous aerial drone images.",

)

parser.add_argument(

"--output", default=None,

help="Optional JSON file to write the selected file list to.",

)

parser.add_argument(

"--grid_resolution", type=int, default=100,

help="Grid resolution for coverage computation (default: 100).",

)

parser.add_argument(

"--work_scale", type=float, default=0.5,

help="Down-scale factor for images during processing (default: 0.5).",

)

parser.add_argument(

"--search_radius", type=int, default=5,

help="Match each image against this many neighbours (default: 5).",

)

parser.add_argument(

"--no_sort", action="store_true",

help="Skip clockwise spatial sorting of the result.",

)

args = parser.parse_args()

config = TilingConfig(

grid_resolution=args.grid_resolution,

work_scale=args.work_scale,

)

selected = select_tiling_from_directory(

args.input_dir, config, sort_result=not args.no_sort

)

print(f"\n{'='*60}")

print(f"Selected {len(selected)} images for tiling:")

print(f"{'='*60}")

for i, path in enumerate(selected, 1):

print(f" {i:>3d}. {os.path.basename(path)}")

if args.output:

with open(args.output, "w") as f:

json.dump({"selected_images": selected}, f, indent=2)

print(f"\nResults written to {args.output}")

if __name__ == "__main__":

main()

Alternatives: IaCResolutionsPart565.docx

Thursday, May 7, 2026

This is a summary of the book titled “The AI Factor

How to Apply Artificial Intelligence and Use Big Data to Grow Your Business Exponentially” written by Asha Saxena and published by Post Hill in 2023. Through a range of examples, the book illustrates that companies willing to embrace data-driven thinking and innovation are far more likely to succeed with AI.

One of the clearest demonstrations of this transformation is the rise of Netflix and the fall of Blockbuster. In the 1990s, Blockbuster dominated the home entertainment industry, but it failed to recognize the transformative potential of the internet. Netflix, on the other hand, embraced change early. By focusing on streaming technology and building increasingly sophisticated recommendation algorithms, Netflix leveraged customer data to personalize user experiences. This data-driven approach not only improved customer satisfaction but also guided the company’s decision to produce original content, leading to immense success with shows like *Stranger Things* and *Orange is the New Black*. By 2020, Netflix had fundamentally reshaped the entertainment industry, demonstrating how data and AI can redefine entire sectors.

Starbucks offers another compelling example. Starting as a single coffee shop in Seattle, it grew into a global brand by integrating data and AI into its operations. Through digital ordering systems and loyalty programs, Starbucks collects and analyzes customer preferences, allowing it to deliver personalized experiences and build stronger customer relationships. In both cases, success stems from using data to better understand and anticipate customer needs.

Organizations must first identify the right data to collect. This requires clear business objectives and a deep understanding of customer problems. Companies should combine historical data—what customers have done—with predictive data that anticipates future behavior. This combination enables more informed and strategic decision-making.

AI itself is best understood not as science-fiction robots, but as a set of computational tools that mimic aspects of human intelligence, such as reasoning and pattern recognition. It includes levels such as basic AI, machine learning, and deep learning, each offering increasing capability to learn from data. Alongside AI, data analytics plays a crucial role. Descriptive analytics tells businesses what has happened, diagnostic analytics explains why it happened, and predictive analytics helps forecast what is likely to happen next—arguably the most valuable capability for business leaders.

Big data fuels these systems, defined by its volume, variety, and velocity. When AI systems analyze large datasets, organizations can move beyond intuition-based decision-making and rely on objective, data-driven insights. This shift allows companies to uncover new sources of value—what Saxena calls the “AI Factor”—that exist within their data.

The book illustrates this concept further with the example of Domino’s Pizza. After struggling during the 2008 recession, Domino’s reinvented itself by embracing digital technologies and customer data. By inviting customer feedback through initiatives like its “Think Oven” platform and enabling orders through multiple digital channels, including social media and apps, Domino’s transformed its business model. AI-powered tools, such as virtual assistants, enhanced customer convenience, helping the company become the world’s largest pizza chain.

However, the power of AI and big data also raises serious ethical concerns. Misuse of data can harm individuals, organizations, and even broader societal systems. Companies must ensure transparency in how AI systems operate, respect privacy, and uphold values such as fairness and accountability. Ethical AI requires not only internal frameworks but also external regulation to protect individuals and maintain trust.

For organizations seeking to adopt AI, Saxena emphasizes the need for careful preparation. Companies must assess their readiness for innovation, their willingness to take risks, and their capacity for growth. A successful data-driven strategy depends on leadership commitment, alignment between business and technology teams, and access to both structured and unstructured data. Fortunately, many organizations already possess valuable data—they simply need to recognize and use it effectively.

Once ready, businesses should focus on areas where AI can create the greatest impact, particularly their most significant unsolved problems. Rather than attempting to transform everything at once, companies should begin with one or two high-value initiatives. Early successes can demonstrate the power of data-driven strategies and build momentum across the organization.

Equally important is building the right team. A strong data team typically includes engineers, data scientists, business specialists, and leaders who can champion the initiative. This team must not only analyze and expand data sources but also measure outcomes carefully. Avoiding cognitive biases—such as confusing correlation with causation—is essential to ensuring the accuracy and reliability of insights.

Finally, the book highlights the emerging shift toward Web3 technologies, where data becomes more decentralized and user-controlled through tools like blockchain. While still evolving, these developments signal further changes in how data is managed and leveraged, making it essential for forward-thinking leaders to stay informed.

Wednesday, May 6, 2026

Inflection-point detection in streaming aerial imagery

Detecting structural transitions in continuous visual data streams is a foundational challenge in online video analytics, particularly when the underlying physical process exhibits long periods of repetitive behavior punctuated by brief but critical inflection events. This paper introduces a principled framework for inflection‑point detection in streaming aerial imagery, motivated by the practical requirement of identifying the four corner events in a drone’s rectangular survey flight path using only the video stream itself, without reliance on GPS, IMU, or external telemetry. The problem is challenging because the majority of the flight consists of highly repetitive, low‑variation frames captured along straight edges of the rectangle, while the corner events—though visually distinct—occur over a short temporal span and must be detected with 100% recall to ensure the integrity of downstream spatial reasoning tasks such as survey tiling, mosaic alignment, and trajectory reconstruction.

We propose an online clustering and evolution‑analysis framework inspired by the principles of Ocean (ICDE 2024), which models the streaming feature space using a composite window and tracks the lifecycle of evolving clusters representing stable orientation regimes of the drone. Each frame is transformed into a compact orientation–motion embedding, derived from optical‑flow‑based dominant motion direction, homography‑based rotation cues, and low‑dimensional CNN features capturing scene layout stability. These embeddings form a continuous stream over which we maintain a set of micro‑clusters that summarize local density, cohesion, and temporal persistence. The straight‑line segments of the flight correspond to long‑lived, high‑cohesion clusters with stable centroids and minimal drift, while the corners manifest as abrupt transitions in cluster membership, density, and orientation statistics. We formalize these transitions as cluster‑lifetime inflection points, defined by a conjunction of (i) a sharp change in the dominant orientation component, (ii) a rapid decay in the density of the current cluster, and (iii) the emergence of a new cluster with increasing density and decreasing intra‑cluster variance.

A key contribution of this work is a thresholding strategy that differentiates true corner events from background repetitive conformance. By modeling the temporal evolution of cluster statistics within a sliding composite window, we derive adaptive thresholds that remain robust to noise, illumination changes, and minor camera jitter while guaranteeing that any genuine orientation transition exceeding a minimal angular displacement is detected. We prove that under mild assumptions about the smoothness of motion along straight edges and the bounded duration of corner rotations, the proposed method achieves perfect recall of all four corners. Extensive conceptual analysis demonstrates that even if the drone’s speed varies, the camera experiences minor vibrations, or the rectangular path is imperfectly executed, the cluster‑lifetime inflection signature remains uniquely identifiable.

This framework provides a generalizable foundation for online structural change detection in video streams, applicable beyond drone navigation to domains such as autonomous driving, robotic inspection, and surveillance analytics. The corner‑detection use case serves as a concrete and rigorous anchor for the methodology, ensuring that the proposed approach is both theoretically grounded and practically verifiable. The resulting system is capable of selecting the exact frames corresponding to the four corners from the continuous first‑person video stream, even when the full tiling of the survey area is not attempted, thereby satisfying the validation requirements of real‑world aerial analytics pipelines.

#Codingexercise: Codingexercise-05-06-2026.docx

Tuesday, May 5, 2026

CAS4Drones:

Content‑addressable storage for aerial imagery is a mature topic. We extend it is as a practical lever for turning a high‑volume livestream into a tractable, cost‑aware analytic stream. Replace raw frame retention with a content fingerprinting layer that lets the pipeline treat visually redundant frames as the same “object” for downstream processing, and then use that deduplicated stream to drive importance sampling, selective perception, and observability events. Two technical families make this work in practice: fast perceptual fingerprints for cheap, near‑real‑time deduplication, and richer deep‑feature hashing for semantic deduplication when the scene semantics matter. Both feed the same operational pattern: compute a compact signature per frame, cluster or threshold those signatures to identify repeats, score novelty relative to recent history, and promote only the frames that cross a novelty threshold into expensive perception or archival storage.

The first stage is perceptual hashing because it is cheap, robust to small compression and alignment differences, and easy to index. Perceptual Hashing (pHash): Unlike standard cryptographic hashes (where one pixel change creates a new hash), perceptual hashes like dHash or pHash generate a compact digital fingerprint that remains stable even if the image is slightly rotated, compressed, or shifted. That stability is helpful to a nadir camera on a drone flying straight edges: most consecutive frames will be near‑duplicates and should collapse to the same fingerprint. A simple operational rule is to compute a 64–128 bit pHash per frame and use Hamming distance as the similarity metric. We use clustering thresholds. To identify 'near‑duplicates' (frames with high overlap), systems calculate the Hamming distance between hashes. In practice, we pick a Hamming threshold empirically from a small labeled set of flights; values that work for nadir imagery are typically small (e.g., 2–8 bit differences on a 64‑bit hash) because the viewpoint is stable.

That cheap layer buys us two things. First, it collapses the vast majority of frames along straight edges into a single representative per short interval, which immediately reduces compute and storage cost. Second, it produces a stream of deduplication events—“new fingerprint”, “repeat fingerprint”, “fingerprint expired”—that are perfect observability primitives. Those events are deterministic, small, and easy to correlate with other telemetry (frame index, FlightID, altitude, inferred ground speed). They become the low‑latency signals an agent or rule engine uses to decide whether to run heavier perception.

Semantic sensitivity requires something more. Two frames can be visually similar yet differ in the presence of a new object or a subtle scene change that matters for coverage. Deep hashing or CLIP‑style embeddings is helpful to this case. A practical hybrid pipeline computes both a pHash and a compact deep descriptor per sampled frame. The pHash is used for immediate deduplication and eventing; the deep descriptor is used for semantic clustering and importance scoring on a slower cadence (for example, every N seconds or when a pHash change is observed). Deep descriptors are clustered with density‑aware algorithms such as HDBSCAN so that the system can identify persistent semantic clusters (e.g., “building cluster”, “water cluster”, “open field cluster”) and detect when a frame belongs to a new semantic cluster even if its pHash is close to a previous one.

Operationally, we perform importance sampling with CAS. For each incoming frame compute pHash and a small motion proxy (mean optical flow or translation vector). If the pHash matches the most recent representative within the Hamming threshold and motion is within the expected range for the edge, mark the frame as redundant and emit a low‑priority “repeat” event. If the pHash is new or the motion proxy indicates a directional change, compute the deep descriptor and evaluate a novelty score against a short‑term memory buffer of recent descriptors. The novelty score can be a weighted combination of descriptor distance, motion direction change, and semantic histogram drift. If the novelty score exceeds a configured threshold, promote the frame for full perception (object detection, high‑resolution stitching, Vision‑LLM analysis) and emit a high‑priority “NovelFrame” event into the observability pipeline. The observability agent then correlates that event with other telemetry—dependency calls, inference latencies, catalog insertions—and can trigger verification steps or human review if needed.

The design can be tightened further. First, use a sliding composite window for memory: keep a short, high‑resolution buffer (seconds) for pHash and motion checks and a longer, lower‑resolution buffer (tens of seconds to minutes) for semantic descriptors. This mirrors the composite window idea used in streaming clustering: short windows catch transient noise, long windows capture persistent regimes. Second, make thresholds adaptive: compute baseline Hamming and descriptor distances per flight segment and scale thresholds by a small factor to tolerate environmental variability (lighting, wind). Third, attach deterministic metadata to every CAS event—FlightID, frame index, altitude, estimated ground speed, pHash value, descriptor cluster id—so that downstream agents and auditors can reproduce decisions. Deterministic event generation is essential for verification: the agent’s reasoning can be stochastic, but the underlying CAS events must be reproducible.

CAS events are high-value to observability. They are compact, explainable, and correlate directly with mission semantics: long runs of “repeat” events indicate stable edges; bursts of “NovelFrame” events indicate corners or scene transitions. Those event patterns can be formalized as inflection signatures: a corner is a short burst where pHash churn increases, motion direction changes beyond a threshold, descriptor novelty spikes, and the rate of “NovelFrame” events exceeds a local baseline. An agent can implement a simple rule that requires co‑occurrence of at least two of these signals within a small temporal window to declare a corner, which reduces false positives while preserving recall.

Cost and importance sampling are tightly coupled. Treat the cost of full perception as a budgeted resource and use CAS‑driven novelty scores to allocate it. For example, define a per‑mission budget of heavy inferences (N per flight hour) and spend it on the top‑N novel frames as ranked by the novelty score. Track TCO per square mile and TCO per analytic query as mission metrics and expose them in dashboards; correlate them with corner detection coverage to quantify the trade‑off between cost and mission completeness. Because corners are high‑value for tiling and mosaicking, we can bias the sampling policy to favor frames that are both novel and temporally spaced to maximize geometric coverage.

Evaluation is straightforward. Measure deduplication rate (fraction of frames collapsed by pHash), corner recall (fraction of ground‑truth corners with at least one promoted frame within ±K frames), precision of promoted frames (fraction that are true positives), and cost savings (reduction in heavy inference calls). Use a small labeled corpus of rectangular flights to tune Hamming and novelty thresholds, then validate on held‑out flights with different altitudes and ground textures.

CAS for aerial livestreams is a practical, auditable mechanism for importance sampling. Perceptual hashes provide a cheap, deterministic first pass; deep descriptors provide semantic sensitivity; both feed an observability fabric of structured events that agents use to make selective, cost‑aware decisions. The result is a pipeline that reduces compute and storage, preserves the frames that matter for coverage and corner detection, and produces a transparent evidence trail for verification and cost analysis.

Monday, May 4, 2026

This is a summary of a book titled “Lead With (un)Common Sense: Simple truths great leaders live by — that most leaders miss” written and self-published by David Mead in 2025. The book argues that leadership is far less about authority, titles, or technical expertise than most people assume. Instead, it is grounded in something both simpler and more demanding: who a leader is as a human being and how consistently they live out their values in everyday actions.

Mead begins by challenging the conventional image of an effective leader. Many aspiring leaders focus heavily on developing operational skills—setting goals, managing performance, and driving results. While those capabilities are undeniably important, organizations often elevate them at the expense of something more fundamental: the human side of leadership. True leadership, Mead suggests, requires “dual mastery”—a careful balance between hard skills and soft skills. Leaders must be competent, but they must also be compassionate, principled, and trustworthy.

This view leads to a broader and more meaningful definition of leadership. Rather than seeing it as a position of authority, Mead frames leadership as the daily practice of building one’s character so that one’s influence enables others to thrive. Influence, in this sense, does not come from credentials or hierarchy. People do not follow leaders simply because of their title; they follow those they trust—leaders who demonstrate honesty, humility, and genuine humanity in their actions.

Trust, therefore, becomes the cornerstone of effective leadership. Mead emphasizes that leaders who rely on power or control may achieve short-term gains, but they rarely inspire lasting commitment. When there is a gap between what leaders say and what they do, employees quickly notice. Over time, these inconsistencies erode trust, leaving teams disengaged and unmotivated. People may comply with such leaders, but they will not bring their full energy, creativity, or loyalty to their work.

Research cited in the book reinforces this point. A study by FMI Consulting found that a leader’s effectiveness is driven primarily by character and a focus on others, accounting for the vast majority of what makes a leader successful. Traits such as emotional maturity, self-awareness, empathy, and curiosity far outweigh commonly prized attributes like charisma or intelligence. Leadership, in other words, is not a mysterious formula but a deeply human endeavor rooted in integrity and care for others.

Living in alignment with one’s values is essential to building this trust. Mead underscores that values alone are meaningless if they are not reflected in behavior. Employees and customers alike look for consistency between what leaders claim to stand for and how they actually make decisions. When leaders act in ways that contradict their stated principles—especially during times of pressure or crisis—the damage to credibility can be swift and lasting. A leader who cannot be trusted, Mead notes, is simply someone issuing instructions, not truly leading.

Of course, no leader is perfect. Mead acknowledges that even well-intentioned individuals sometimes fall short of their ideals. The real test of leadership lies not in flawless behavior but in how leaders respond when they recognize a misalignment. Self-aware leaders notice these gaps early, acknowledge their mistakes, and take meaningful steps to correct them. By doing so, they reinforce rather than weaken trust.

Modern work environments introduce additional challenges. In remote and hybrid settings, for example, employees have fewer opportunities to observe their leaders’ behavior firsthand. This makes transparency and communication even more critical. Leaders must be deliberate in explaining their decisions and demonstrating consistency, as silence or ambiguity can quickly give rise to doubt and mistrust.

Another central theme of the book is humility. Far from being a weakness, humility is presented as one of a leader’s greatest strengths. Humble leaders focus on the growth and success of others rather than on their own ego. They acknowledge their limitations, remain open to new ideas, and actively seek input from those closest to the work. This openness not only strengthens relationships but also leads to better decision-making and more innovative teams.

At the same time, humility requires confidence. It means being secure enough to admit when a strategy is not working and to change course when necessary. Leaders who cling to their own expertise or insist on being the smartest person in the room can stifle creativity and hinder progress. By contrast, those who create space for others to contribute foster environments where people feel valued and empowered.

Mead argues that leadership grounded in humanity has a profound impact. When leaders genuinely care about their employees as people—not just as resources—workplaces become places where individuals want to show up and do their best. This sense of belonging and respect transforms compliance into commitment, strengthens collaboration, and drives sustained performance.

Saturday, May 2, 2026

Continuous Replication and network connectivity in Azure for databases.

Problem statement: when Azure creates a replica for Azure MySQL server that has connectivity only through a private endpoint, it does not create the replica with another private endpoint but somehow replicates the database snapshot from primary. Does it need a private endpoint to the replica to facilitate automatic continuous replication?

Solution:

Even experts find themselves in opposite directions when answering this question because replication traffic and operational requirements go hand in hand. The short answer is no — you do not need to create a private endpoint on the replica for replication to function.

When Azure creates a read replica for a MySQL Flexible Server that is reachable only through a private endpoint, the replication traffic never flows through your VNet, your private endpoint, or any customer‑visible network surface. The private endpoint only governs how your clients reach the server. It does not govern how Azure’s internal control plane and data plane communicate with the managed MySQL instances. Azure MySQL Flexible Server is built on a managed compute fabric where the primary and replica servers live inside the same Azure-managed network boundary, even if they are in different regions. The replication channel is established entirely inside that boundary, using Azure’s internal service network, not your VNet. That means the replication protocol — which is MySQL’s native asynchronous binlog-based replication — is carried over an internal, non-customer-routable link. The wire traffic never touches your private endpoint, so the existence or absence of a private endpoint on the replica is irrelevant to the replication channel.

The initial snapshot is not copied through your private endpoint either. Azure uses an internal storage-layer snapshot mechanism to seed the replica. This is not a logical dump and not a network copy through your VNet. It is a block-level clone operation inside Azure’s storage fabric. Because the snapshot is taken and materialized inside the managed service boundary, there is no scenario in which Azure would need to traverse your private endpoint to hydrate the replica.

Once the replica is seeded, continuous replication begins. MySQL’s binlog replication requires the replica to connect to the primary’s replication endpoint. In a self-managed MySQL deployment, that would require network reachability between the two servers. But in Azure’s managed service, the replication endpoint is exposed only inside Azure’s internal network. The primary and replica are placed in a topology where they can reach each other without ever touching customer VNets. Azure enforces isolation at the service boundary, not by routing replication traffic through customer-controlled network constructs. This is why the private endpoint is irrelevant to replication: the private endpoint is a consumer-facing ingress point, not a service-to-service communication path.

The opposing view — that replication should require a private endpoint on the replica — cannot hold because it would imply that Azure routes internal service traffic through customer VNets, which would violate Azure’s network isolation model, break multi-tenant guarantees, and create circular dependencies where replication availability depends on customer-managed routing, NSGs, firewalls, or DNS. Azure’s managed database services are explicitly designed so that internal operations, including replication, backups, failover, and patching, are independent of customer networking. If replication depended on your private endpoint, a misconfigured NSG or DNS zone could break Azure’s ability to maintain replicas, which would contradict the service’s reliability guarantees.

If you inspect the replica’s network configuration, you will see that Azure does not create a private endpoint for it unless you explicitly request one for client access. Replication still works. If you delete the private endpoint on the primary, replication still works. If you isolate your VNet completely, replication still works. The only consistent explanation is that replication is not using your private endpoints at all.

So the answer is no, you do not need to add a private endpoint to the replica. Replication is an internal Azure operation that bypasses customer networking entirely, and the architecture of the service makes the opposite scenario impossible without breaking Azure’s isolation and reliability guarantees. However, you will need a private endpoint for client connections to the replica just like the primary and this is an operational requirement for some deployments.

Friday, May 1, 2026

Minimum Operations to Make Array Non Decreasing

You are given an integer array nums of length n.

In one operation, you may choose any subarray nums[l..r] and increase each element in that subarray by x, where x is any positive integer.

Return the minimum possible sum of the values of x across all operations required to make the array non-decreasing.

An array is non-decreasing if nums[i] <= nums[i + 1] for all 0 <= i < n - 1.

Example 1:

Input: nums = [3,3,2,1]

Output: 2

Explanation:

One optimal set of operations:

• Choose subarray [2..3] and add x = 1 resulting in [3, 3, 3, 2]

• Choose subarray [3..3] and add x = 1 resulting in [3, 3, 3, 3]

The array becomes non-decreasing, and the total sum of chosen x values is 1 + 1 = 2.

Example 2:

Input: nums = [5,1,2,3]

Output: 4

Explanation:

One optimal set of operations:

• Choose subarray [1..3] and add x = 4 resulting in [5, 5, 6, 7]

The array becomes non-decreasing, and the total sum of chosen x values is 4.

Constraints:

• 1 <= n == nums.length <= 105

• 1 <= nums[i] <= 109

class Solution {

public long minOperations(int[] nums) {

long sum = 0;

for (int i = 0; i < nums.length-1; i++) {

if (nums[i] > nums[i+1]) {

long diff = nums[i] - nums[i+1];

for (int l = i+1; l < nums.length; l++) {

nums[l] += diff;

}

sum += diff;

}

return sum;

}

Test cases:

Case 1:

nums=[3,3,2,1]

Expected: 2

Actual: 2

Case 2:

nums=[5,1,2,3]

Expected: 4

Actual: 4