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.
We discussed Convolutional Neural Network (CNN) in image and object embedding in a shared space. We followed this discussion with shape signature and image retrieval.
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.
We now discuss shape retrieval. The methods for shape retrieval mostly operate on input query in 3D domain.  However, CNN proposes a new way of searching both images and shapes by placing them in a shared embedding space. This sharing enables comparision between images and shapes easily since the shapes and images that are similar are co-located in the same neighborhood.
This is a very sought after discipline because it has appeal for many real world applications. Aubry et al proposed a part-based method that focuses on detecting image regions that match parts in 3D models.  A star model is then designed to combine discriminating patches for measuring the similarity. This is helpful for matching shapes from arbitrary images. However this method requires tuning that may change from domain to domain. Instead, the CNN network provides a uniform shared embedding space where image feature extraction is based on shape distance metric.

We discussed the use of a distance metric and clustering techniques but there does not seem any equivalents for softmax in data mining. Neural net algorithms might be implemented with R-package but their use in native data mining techniques seems limited. clustering and reverse clustering could be combined for softmax but this May may be more tedious than inlined neural net method.

#codingexercise

We talked about exponential and normal distribution. Let us state the uniform distribution in the interval range a to b

double GetUniformDistribution(double a, double b, double x)

{
Debug.Assert(b-a > 0);

if (a <= x && x <=b) 

{

   return 1/(b-a);

}

return 0;

}
#codingexercise
int GetFirstIndexInListWithStepSizeAtMostK(List<int> A, int x, int k)
{
int i = 0;
while (i < A.Length)
{
if (A[i] == x)
   return i;
i = i + Math.Max(1, Math.Abs(A[i]-x)/k);
}
return -1;
}