We were discussing Signature verification methods. We reviewed the stages involved with Signature verification. Then we also enumerated the feature extraction techniques. After that, we compared online and offline verification techniques. We also discussed the limitations of image processing and the adaptations for video processing. Today let us discuss image embedding in general.
In this case, we discuss CNN Image Purification techniques from the Li et al paper on Joint Embeddings. CNN stands for Convolutional Neural Network.It purifies images by muting distracting factor The purpose of the embedding is to map an image to a point in the embedding space so that it is close to a point attributed to a 3D model of a similar object. A large amount of training data consisting of images synthesized from 3D shapes is used to train the CNN.
In order to play up the latent objects in images, similar objects were often used in dissimilar images. The dissimilarity was based on viewpoint, lighting, background differences, partial hiding and so on. 3D object representations do not suffer from these dissimilarities and are therefore much easier to establish similarity.
Images and 3D shapes share the embedded space. In that space, both can be measured as if their 3D form was directly available. This embedded space is plotted with each object given a co-ordinate comprising of the dimension reduced form of the distances between the underlying shape and the entire set.  This way two neighboring points in the embedded space are likely to represent similar shapes, as they agree to a similar extent, on their similarities with all the other shapes.
A set of ground truth co-ordinates in the embedding space is required. A large amount of images to train the CNN is also required. Another alternative for obtaining the necessary links between images and their embeddings is to manually link images to similar 3D models. But since this is time-consuming and error prone, the image training set is synthesized based on rendering a rather modest set of annotated shapes from the ShapeNet
This technique of embedding is a novel attempt to correlate 3D shapes and 2D images. The deep embedding is capable of  purifying these images  and interlinking the two domains based on their shared object content This linking then supports querying that was not possible before.
#codingexercise
Minimum removals from array to make max – min <= K
A.sort();
int count = 0;
int i = 0;
int j = A.Length -1;
int GetRemovals(List<int>sorted, int K, int i, int j)
{
if (i >= j) return 0;
if (A[j]-A[i]) <= K) return 0;
return 1 + Math.min(GetRemovals(sorted, K,  i+1, j),
                                  GetRemovals(sorted, K,  i, j -1));
}
if (count  >= A.Length-1) return -1;
1 4 6 8
N = 4
K = 5