Image derivative

Image derivatives can be computed by using small convolution filters of size 2 × 2 or 3 × 3, such as the <a href="/facts/Discrete_Laplace_operator/w3fdFNC4">Laplacian</a>, <a href="/facts/Sobel_operator/LDCvBBTJ">Sobel</a>, <a href="/facts/Roberts_cross/vTRND4Uy">Roberts</a> and <a href="/facts/Prewitt_operator/abrBLgVN">Prewitt</a> operators. However, a larger mask will generally give a better approximation of the derivative and examples of such filters are <a href="/facts/Gaussian_filter/L7Y7MLQE">Gaussian</a> derivatives and <a href="/facts/Gabor_filter/GyWW4j45">Gabor filters</a>. Sometimes high frequency noise needs to be removed and this can be incorporated in the filter so that the Gaussian kernel will act as a band pass filter. The use of Gabor filters in image processing has been motivated by some of its similarities to the perception in the human visual system.
The pixel value is computed as a <a href="/facts/Convolution/PVPrdz9J">convolution</a>

p
          
            u
          
          ′
        
        =
        
          d
        
        ∗
        G
      
    
    {\displaystyle p'_{u}=\mathbf {d} \ast G}

where 
 
 
 
 
 d
 
 
 
 {\displaystyle \mathbf {d} }
 
 is the derivative kernel and 
 
 
 
 G
 
 
 {\displaystyle G}
 
 is the pixel values in a region of the image and 
 
 
 
 ∗
 
 
 {\displaystyle \ast }
 
 is the operator that performs the <a href="/facts/Convolution/PVPrdz9J">convolution</a>.

Image derivative open-in-new

Image derivative