About: Convolution (computer science)   Sponge Permalink

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Basically a convolution in digital image processing is a weighted sum, which is computed for each pixel of image: result=sum(k[n,p]*I[x,y]). Important things: 1) form and size of window, which moves over image; 2) numbers k[n,p] in all positions [n,p] inside window, which represent impulse response of filter; 3) numbers I[x,y] under window - intensities of pixels[x,y]. For low frequency filter (sum(k[n,p]) >0; each k[n,p]>=0) numbers k[n,p] must be normalised by dividing on a sum(k[,n,p]) - example 1. For high frequency filter sum(k[n,p]) =0 and some of k[n,p] are negative, whilst others are positive. Sharping filter is like high frequency filter, but sum(k[n,p]) >0.

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  • Convolution (computer science)
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  • Basically a convolution in digital image processing is a weighted sum, which is computed for each pixel of image: result=sum(k[n,p]*I[x,y]). Important things: 1) form and size of window, which moves over image; 2) numbers k[n,p] in all positions [n,p] inside window, which represent impulse response of filter; 3) numbers I[x,y] under window - intensities of pixels[x,y]. For low frequency filter (sum(k[n,p]) >0; each k[n,p]>=0) numbers k[n,p] must be normalised by dividing on a sum(k[,n,p]) - example 1. For high frequency filter sum(k[n,p]) =0 and some of k[n,p] are negative, whilst others are positive. Sharping filter is like high frequency filter, but sum(k[n,p]) >0.
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  • Basically a convolution in digital image processing is a weighted sum, which is computed for each pixel of image: result=sum(k[n,p]*I[x,y]). Important things: 1) form and size of window, which moves over image; 2) numbers k[n,p] in all positions [n,p] inside window, which represent impulse response of filter; 3) numbers I[x,y] under window - intensities of pixels[x,y]. For low frequency filter (sum(k[n,p]) >0; each k[n,p]>=0) numbers k[n,p] must be normalised by dividing on a sum(k[,n,p]) - example 1. For high frequency filter sum(k[n,p]) =0 and some of k[n,p] are negative, whilst others are positive. Sharping filter is like high frequency filter, but sum(k[n,p]) >0. Examples of window: 1) low frequency filter - image smoothing [1 1 1 1 1 1 1 1 1] after normalisation [1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9] 2) high frequency filter - gives horizontal contours (north-south) [1 1 1 0 0 0 -1 -1 -1] 3) sharping filter [-1 -1 -1 -1 9 -1 -1 -1 -1].
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