第三章 空域图像增强(2016C).ppt

Convolution (1D) 1 1 2 2 1 1 2 2 1 1 1 2 1 Convolution (1D) 1 1 2 2 1 1 2 2 1 1 1 2 1 1 1 2 2 1 1 2 2 1 1 1 2 1 Convolution (1D) Convolution (1D) 1 1 2 2 1 1 2 2 1 1 1 2 1 Convolution (1D) 1 1 2 2 1 1 2 2 1 1 1 2 1 This process is called Convolution!! Math of convolution g(x): output, h: filter, “*” means convolution, f(x): input, n = INT[ width of filter/2 ]. INT[ ]: rounds down, for example: INT[1.7]=1. MATLAB code: floor(width/2). 1 2 1 h(-1)=1 h(0)=2 h(1)=1 Formula: for example: filter (h): width = 3 = n = 1 Math of convolution x is the pixel of interest, i.e., the position in the signal/image and the center of the filter. 1 1 2 2 1 1 2 2 1 1 1 2 1 f(x) i =-1 = f(x+1) =2 i = 0 = f(x) = 1 i = 1 = f(x-1) = 1 f(x+1) f(x-1) Formula: Math of convolution 1 1 2 2 1 1 2 2 1 1 1 2 1 f(x) Correlation (1D) 1 1 2 2 1 1 2 2 1 1 1 2 1 Normalized filter response filter Input signal/Image-row Output signal/Image-row Filter coefficients Correlation vs. Convolution 1 1 2 2 1 1 2 2 1 1 1 2 1 1 1 2 2 1 1 2 2 1 1 1 2 1 Corr. Conv. In image processing we use CORRELATION but (nearly) always call it CONVOLUTION!!!!! Note: When the filter is symmetric: correlation = convolution! Convolution/correlation on images The filter is now 2D Kernel (mask), kernel coefficients Size: 3x3, 5x5, 7x7, …. 1 1 1 1 1 1 1 1 1 0 2 1 2 1 2 1 2 5 3 1 3 2 2 0 1 1 2 0 2 1 4 1 0 1 Input Output Normalization 1 1 1 1 1 1 1 1 1 0 2 1 2 1 2 1 2 5 3 1 3 2 2 0 1 1 2 0 2 1 4 1 0 1 Input Output Convolution/correlation on images Convolution/correlation on images 0 2 1 2 1 2 1 2 5 3 1 3 2 2 0 1 1 2 0 2 1 4 1 0 1 1 1 1 1 1 1 1 1 1 Input Output Convolution/correlation on images 0 2 1 2 1 2 1 2 5 3 1 3 2 2 0 1 1 2 0 2 1 4 1 0 1 1 1 1 1 1 1 1 1 1 Input ... ... ... ... ... ... ... Output Math. of 2D Convolution/Correlation 1 1 1 1 1 1 1 1 1 Convolution: Correlation: Note: When the filter is symmetric: correlation = convolution ! 2 3 2 -1 0 -1 2 3 2 Problems at the borders 0 2 1 2 1 2 1 2 5 3 1 3 2 2 0 1 1 2 0 2 1 4 1