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;
}

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. Then we mentioned shape signature.
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.
Each shape is given a signature. This makes it easy to perform shape matching, organization and retrieval.  The shape signatures are computed using Light Field Descriptor. By re-using projections or views, the shape signature computation does not need any generalization.
Next we read about image retrieval in this framework.
The content-based image retrieval involves searching for an image that is similar to the query. Similarity can be low-level such as color and texture or high-level such as latent objects. In this scheme, both images and shapes are embedded into the same space.This space then leverages the robust distance metric for 3D shapes and trains a CNN for purifying and mapping real world images into this pre-built embedding space. Since the space is constructed already, there is a separation between that process and the image embedding process so that this becomes tractable. Moreover some synthesized images with annotations are used thereby eliminating the need for manual work in gaining annotations.

Object embedding in images used neural net. word embedding in documents used neural net  As such we don't yet have a technique that determines cohesive and adhesive properties other than vector space clustering. Is it possible to transform the embedding into a data mining problem ?

#codingexercise
How do you get the z-score in a normal probability distribution ?
double GetZScore(double X, double mu, Double sigma)
{
Debug.assert(sigma != 0);
return (X-mu)/sigma;
}

A step array is an array of integer where each element has a difference of atmost k with its neighbor. Given a key x, we need to find the index value of k if multiple element exist return the index of any  occurrence of key.
Input : arr[] = {4, 5, 6, 7, 6}
           k = 1
           x = 6
Output : 2

int GetIndex(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;
}
If we were to return only the first element, we could scan the elements at positions before the index from where we exit the loop.

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);
}

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.
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.

#codingexercise
A step array is an array of integer where each element has a difference of atmost k with its neighbor. Given a key x, we need to find the index value of k if multiple element exist return the index of any  occurrence of key.
Input : arr[] = {4, 5, 6, 7, 6}
           k = 1
           x = 6
Output : 2

int GetIndex(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;
}

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

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. Yesterday we discussed the limitations of image processing and the adaptations for video processing. Today we continue with the discussion on relevant improvements for signature processing.

Unlike earlier, when image processing was confined to research labs and industrial automations, there are now software libraries, packages and applications available. Moreover, services for image processing are no longer restricted in compute and storage because they can now be hosted in the cloud. Many cloud providers now also provide libraries for image processing. For example, Microsoft and Google both provide image processing libraries. Perhaps Clarifai has a dedicated offering in this discipline.

The reason I bring out these companies is that this area of study also benefits from a multidisciplinary approach. For example, Microsoft's machine learning algorithms and R-package covered earlier in this post may also be relevant to image processing after images are transformed to a vector space model. Similarly Google's application of word2vec to perform word embeddings may provide insight into object embedding in images. Clarifai provides an api library and makes image processing just as commercial to develop as it is fun to experiment in Matlab.

Signature processing benefits incredibly with the right choice of algorithms. We don't need to perform edge segmentation since the data may already be smoothed and made clear in the preprocessing step. Gaussian smoothing helps in this regard because it adjusts the value of the current pixel based on the values of the surrounding pixels. After the pre-processing, the offline verification of signature becomes straightforward as we rely on a choice of algorithms from the previously covered list to perform this verification. If we have the luxury of performing these comparisions simultaneously, we can then perform a collaborative filtering of the given sample as a valid or invalid in a serverless computing paradigm. This is a break from the previously mentioned software for signature verification.

Technically this does not seem impossible but as we fine tune the algorithm and user acceptance may determine the success of such a venture. Signatures unlike passwords are handwritings. They are susceptible to the mood and circumstance. Since the input may change each time, the verification has to give such latitude to the user.

We were discussing Signature verification methods. We reviewed the stages involved with Signature verification yesterday. We also enumerated the feature extraction techniques. Then we compared online and offline verification techniques.

One of the reasons offline image processing is preferred is that good image processing algorithms are often computationally expensive and require more time than say network roundtrip for packets. This makes it costly to include as an interactive web page analysis widget.  Time taken to execute image processing algorithms have taken even eight seconds. That is why image processing finds it difficult to keep up with the frame rate of a video. However, significant advances have been made that improve processing for streaming of images to be processed. For example, Active contour model can help track movement of object in images for a frame rate that matches the rate used for video. Signatures are considered a lot simpler to work with in image processing. They are generally small sized, binary color and easy to capture and process.  As long as the image processing can tell apart a real signature from forged specimens, an image processor can work in the backend for a signature pad widget in the front-end.

We talked about the acceptance criteria for an image processing technique that is largely measured by the precision and recall. By training the processor on a signature dataset, these processors become highly effective in determining even forged from real specimens. Today we will take a closer look at how this verification is done. Since we read how classifiers work in text processing to convert the document into a vector space model and then classify the document based on euclidean distance between feature vectors, the signature verification should also be familiar. The features extracted from the image as described in the previous posts is transformed into the vector space and then compared with the master. If the euclidean distance is within tolerance threshold, the signature is accepted. Since the image processor is already trained and tested on a variety of images and measured with precision and recall, it is reliable to convert the given specimen into a representative feature vector. This concludes the signature verification technique.


#codingexercise

We were discussing combinations with duplicates and that too in a greedy manner. instead of enumerating combinations to the whole length, we can leverage stars and bars theorem to be more efficient. With this theorem, we already know the number of combinations that can exist with duplicates and therefore do not enumerate them but directly count them towards the goal such as the price of the accessories shopped. The theorem mentioned used a binomial coefficient.