Analysis of fast compression tracking (CT) algorithm

Fast compressive Tracking

(Fast compression tracking)

Although there are many kinds of tracking algorithms at present, the robustness of many algorithms is not good because of the change of attitude, the change of illumination and the existence of obstacles.

At present, there are two kinds of tracking algorithms, generative tracking algorithms (generating tracking algorithm) and Discriminative algorithms (discriminant tracking algorithm).

Generates a tracking algorithm that, as the name implies, generates edge tracking. That is, the sample of this frame to learn, the result of learning as the next frame of the classifier, to learn to track, edge tracking edge learning effect. The disadvantage of this tracking algorithm is that in the first few frames of the video, the sample size is small, so most of the algorithms require that the target in the video changes little in front of the video. If the target changes greatly, it will produce drift phenomenon.

The discriminant algorithm thinks that tracking is a problem of a two classifier, and its purpose is to find a boundary that distinguishes the target from the background. But this algorithm uses only a positive sample and a small number of negative samples to follow the new classifier. Drift occurs when the feature template contains noise or position deviation.

Author's algorithm:

The main steps in the author's thesis are as follows:

1. Get target area features

In order to obtain the multi-scale feature expression of the image, the input image is often convolution with the Gaussian filter in different space. In the actual application process, the Gaussian filter is computationally large, so the rectangular box is generally used instead of the Gaussian filter. It has been proved that this substitution will not affect the performance of feature detection, and it can greatly speed up the detection.

For a w*h sample, the Rectangle box is selected as follows:

The W and h here represent the width and height of the rectangular box, respectively.

The results of the convolution of these rectangles, respectively, and the input image are as follows:

The result of each input picture (W*H) and the different size of the rectangle is still a (w*h) matrix, but in order to facilitate the fusion of these features, the (W*h) matrix is converted to a column vector containing (w*h) elements. and an input sample picture altogether (W*H) The convolution result, joins this (w*h) column vector, becomes a column vector containing (W*H) 2 elements. The length of this column vector can generally reach 106~1010. For such a high-dimensional characteristics, obviously will bring considerable computational capacity, so the author found a good method of dimensionality reduction.

2. Get the Sparse measurement matrix

The theory of compression perception points out that for a compressible signal, such as an original image or video, a small fraction of the randomly generated linear data can retain significant information from the original signal, and can reproduce the original signal well from a small number of random signals . There is also a relatively professional ranking in the theory of compression perception to describe the "compressible signal"--k-sparse signal that is mentioned earlier.

With this theory as a backing, we can first obtain the complex high-dimensional characteristics of the target, and then use the theory of compression perception to reduce the dimension. The method used by the authors is to use sparse random measurement matrix (R) to reduce the original signal. Obviously, for any k-sparse signal, we hope that this sparse matrix R can extract the significant information from it and map the k-sparse signal from high-dimensional to low-dimensional space.

So, how to find this sparse matrix R, so that it can meet our requirements.

In fact, to find this sparse matrix, we must satisfy a property, that is, the constraint equidistant property .

A typical random sparse matrix satisfying constrained equidistant is the Gaussian random matrix.

It has been proved that when ρ=1, 3, the matrix is satisfied with the constraint equidistant. Also, note that when ρ=3, two-thirds of the data is 0, so no calculations are required.

By multiplying this m*n sparse matrix with the original high-dimensional vector (M-dimension), a low-dimensional vector (n-dimensional) can be obtained. This is the result of descending dimension.

3, using sparse measurement matrix to reduce the dimension of the characteristics of the processing

We can see that the random sparse matrix is the process of dimensionality reduction for high dimensional vectors. In the sparse matrix, the black is positive, gray is negative, and white is 0. It can be seen that this sparse matrix is very sparse, less than 0 items, and can obviously reduce the amount of data processing. And the descending dimension of the vector v, wherein each element is a vector x corresponding to R is not 0, and it contains a plurality of local information and.

4. Classification with Bayesian classifier

Here V is the eigenvector, p (y=1) and P (y=0) represent a priori probability of positive and negative samples respectively. actually P (y=1) =p (y=0). It has been proved that stochastic mapping of high-dimensional random vectors always satisfies the load Gaussian distribution. So here P (Vi|y=1) and P (vi|y=0) are in accordance with the Gaussian distribution, whose parameters are (λ>0, are learning parameters):

This is the distribution of the integral plots obtained from three different low-dimensional spatial features.

This is a measurement of positive and negative samples of the integral map distribution map.

Steps in the program:

One, the first frame image come over:

1, manual marking needs to track the area, this area is a rectangular box.

2, according to the information of the marked area, randomly produce a rectangular box, used as a Haar feature extraction template

3, take the current frame target area as the center, take 4 pixels as the radius, remove a total of 45 positive samples, 8 is the inner radius, 30 is the outer radius of the ring randomly selected 50 negative samples.

4, calculate the original image of the integration diagram.

5, according to the integration diagram and the Haar feature extracted from the template, extract the characteristics of positive and negative samples.

6. Update the Bayesian classifier to obtain a new classifier.

Second, non-first frame images come over:

1, the previous frame of the target area is the center, with 25 pixels as a radius, one by one, you can get about 1100 to be classified area.

2, obtain these to classify the area the integral diagram, uses the haar-like characteristic template which the front produces to extract these to divide the area the Haar characteristic. Get the eigenvector.

3, using Bayesian classifier to classify these areas to be classified, select the most likely target of the rectangle, as the current tracking results.

4, repeat step one of 3, 4, 5, 6

Analysis of fast compression tracking (CT) algorithm