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.Then we proceeded to discussing image embedding in general.
Today we continue our discussion of Convolutional Neural Network (CNN) in image and object embedding in a shared space.
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.
Each shape is given a signature. This makes it easy to perform shape matching, organization and retrieval.  The notion comes from computer vision and computer graphics. There shape signatures have been associated with geometric properties of the shape such as volume, distance and curvature or 2D projections. They sometimes include graph representations to get a topographical distribution of the shape. In CNN, shape signatures are computed using Light Field Descriptor. In this approach, shapes are indexed via a set of 2D projections or views. This depends directly on the views. A view based distance metric can then be derived from these metrics. The shape signature for each shape then becomes its embedding point in the shared embedding space. By re-using projections or views, the shape signature computation does not need any generalization. Instead its embedding into the robust space is utilized.

#codingexercise
How much time do we need to wait before a given event occurs.
This question is usually answered in the form of exponential probability distribution. The unknown time is represented by a random variable.
If the probability of the event happening in a given interval is proportional to the length of the interval then we have an exponential diatribution.
double GetProbabilityDistribution (double lambda, double x)
{
if (inclusive (x) == false)
     return 0;
return lambda *.math.pow (e, - lambda*x);
}