Computer Vision ----Filtering

1  General

       Binary

       Gray Scale

       Color

2  Discrete Derivative

       df/dx = f(x)-f(x-1) = f'(x)        Backward difference

       df/dx = f(x)-f(x+1) = f'(x)       Forward difference

       df/dx = f(x+1)-f(x-1) = f'(x)    Central difference

      

3  Derivatives of Images

         Derivative masks 

               f'(x) => 1/3 [-1 -1 -1; 0 0 0; 1 1 1]

               f'(y) => 1/3 [-1 0 1; -1 0 1; -1 0 1]

4  Correlation

          f = Kernel

         h = Image

5  Convolution

6  Averages

        Mean

        Weighted mean

7  Gaussian Filter

         Properties of Gaussian

             Most common natural model

             Smooth function, it has infinite number of derivatives

             Fourier Transform of Gaussian is Gaussian

             Convolution of a Gaussion with itself is a Gaussian

             There are cells in eye that perform Gaussian filtering

8  Linear Filtering

          The output is the linear combination of the neighborhood pixels