Scale Resolution

Analytics also help with distance and area calculation from aerial drone images from disparate points of time and real-world GPS coordinates.

The following prompts and responses explain these:

Case 1:

Prompt:

Given the attached aerial drone image and its Estimated Coordinates: Latitude = 42.3736, Longitude = -71.1097 and its scale resolution as 2cm in image=50feet in actual distance, find the square footage occupied by the building with a circular structure.

Response:

The square footage occupied by the building with the circular structure in the attached aerial image is approximately 81,300 square feet.frame5.jpg

Calculation Method

• The circular structure was located and its size was estimated using the image's pixel dimensions and known scale: 2 cm in image = 50 feet actual.frame5.jpg

• The circle's diameter was estimated visually based on the image dimensions, and this scale was used to convert pixel measurements into real-world feet.

• The area was then calculated using the formula for the area of a circle: πr2\pi r^2πr2, with the radius converted to feet.frame5.jpg

Assumptions

• The building's central circular feature fully encompasses the occupied area (overestimating the whole structure if non-circular parts extend the actual footprint).

• Image DPI was assumed to be 96 if metadata was missing, which is standard for web images.frame5.jpg

• Manual visual estimation introduces possible error, but provides a close real-world approximation given the described scale and visible features.

• frame5.jpg

Case 2:

Prompt:

Given the bounding box locations of the nearest (Latitude 42.37043, Longitude: -71.12165) and the farthest (Latitude: 42.37125, Longitude: -71.11733) points on the rectangular area covered by the drone in its tour and a scale resolution of 2cm on image = 50 feet on ground, what was the total area in square miles surveyed by the drone.

Response:

Ground area covered: 0.012494 square miles

This can be confirmed with:

from math import radians, cos, sin, asin, sqrt

# Step 1: Haversine function to compute distances in meters

def haversine(lat1, lon1, lat2, lon2):

    R = 6371000 # Earth's radius in meters

    dlat = radians(lat2 - lat1)

    dlon = radians(lon2 - lon1)

    a = sin(dlat/2)**2 + cos(radians(lat1))*cos(radians(lat2))*sin(dlon/2)**2

    c = 2 * asin(sqrt(a))

    return R * c

# Bounding rectangle corners (nearest and farthest)

lat_min, lon_min = 42.37043, -71.12165

lat_max, lon_max = 42.37125, -71.11733

# Compute east-west (width) and north-south (height) ground distances, in meters

height_m = haversine(lat_min, lon_min, lat_max, lon_min)

width_m = haversine(lat_min, lon_min, lat_min, lon_max)

# Step 2: Area in square meters

area_m2 = width_m * height_m

# Step 3: Convert to square feet (1 m = 3.28084 ft)

area_ft2 = area_m2 * (3.28084 ** 2)

# Step 4: Convert to square miles (1 sq mile = 27,878,400 sq ft)

area_miles2 = area_ft2 / 27878400

print(f"Ground area covered: {area_miles2:.6f} square miles")