Equations 1, 2, 3

Mahesh,

these are basically Histograms of Oriented Gradients (HOG) where the histograms are computed form local neighborhood with gaussian weighting (SIFT is defined this way as well). When going from 35x35 pixels to 5x5 HOG, one could just simply divide the 35x35 image into a regular 5x5 grid and sum gradients inside the grid cells. In your case, the approach is similar, with the exception that the Gaussians are used to distribute gradients between surrounding HOGs in a "soft" way. Distance between neighboring HOG centers is 7px and the "size" of the Gaussians must reflect this (e.g. std.dev.~=7px).

You could indeed convolve the 35x35 gradient images with a Gaussian kernel and sample 5x5 HOG from it, but this approach is inefficient. (set the kernel size for example 2x std.dev)

Ideally, you would go through the 35x35 image pixel-by-pixel and distribute the gradients between the 4 neighboring HOGs according to responses of Gaussians centered the the positions of the  corresponding HOGs. In this case you do not have a kernel and do not have to set its size.

thanks for you reply but still i m not so clear for that i have attached a paper which contains yellow comments, which is a point that is not clear to me, at page no 3.

at starting point i got 49x49x32 it applied [1 4 6 4 1] smoothing filter to get 16 out of 32.

but how it happened how smoothing filter reduce the spatial coordinates  

Hello Mahesh, Please go through these points may helpful to you

Gaussian Distribution Feature Extraction Technique

Gaussian processes are excellent approximations to the investigation. A number of processes can be approximated by a Gaussian random process. The multivariate Gaussian distributions are experimentally simpler. One of the most important uses of the Gaussian process is to model and investigate the effects of thermal noise in communication systems.

A d-dimensional Gaussian distribution is given as equation.

1

Mean vector and covariance matrix is represented by μ and Σ respectively. The random vector x satisfies the Gaussian distribution with mean μ and Σ is notated by x N (μ, Σ). The curve (shape) of constant density for the d-dimensional Gaussian distribution is ellipsoids defined by the following equation.

2

The ellipsoids are centered at μ and have axes,

3

where ei is an eigenvector of Σ and λi is the corresponding Eigen value.

Method

Every feature extraction technique for facial expression recognition has its own advantages. So each technique can extract only limited features with redundancy and a limited recognition rate is possible with its own extracted feature. For achieving higher recognition rate different feature extraction techniques are combined into a single combined technique to maximize the features. Using hybrid combinations advantage of different techniques also merged in proposed technique. Following Proposed algorithm extract the features of Gabor Filter and

Gaussian Derivative.

• The Gabor features are calculated by convolution of input image with Gabor filter bank and down-sampling by factor 2. In this experiment we use 3 frequencies and 5 angle. These features are kept in feature vector Fg.

• The 2 D Gaussian distribution is used to generate the mask. Different types of masks can be specified by parameters Dx, Dy. By default the size of the mask is 8*SIGMA, 8*SIGMA. Five dimensional feature vectors are computed at each pixel by convolution with the first derivative (Gx, Gy) of Gaussian in x and y direction and second derivative (Gxx, Gxy, Gyy) is used. This is Gaussian feature vector Fgu.

Equations 1, 2, 3

Sir,, Can You Explain How Much It Is Better Technique Thn Gabor Feature Extraction?

Sir Suresh Merugu

Thank You