- Image Convolution is the process of applying a filter to images
Images can be convolved by applying a function to each pixel of the image. Usually, this function is precalculated inside a small two dimensional array called a kernel.
A More Mathematical Explanation
Most generally, the convolution of two functions f and g is defined as the following:'"`UNIQ--mat [...]
Most generally, the convolution of two functions f and g is defined as the following:
In this formula is a function that represents the image, and is the kernel. In practical situations, the kernel is only defined over a finite set of points, so we can modify our definition as follows:
Where is the width of the kernel and is the height of the kernel. To convolve an image, this formula is evaluated at every point in the image. The following is pseudocode to convolve an image:
for y from 0 to imageHeight for x from 0 to imageWidth sum := 0; for v from y - kernelHeight to y + kernelHeight for u from x - kernelWidth to x + kernelWidth sum := sum + f( x, y ) * g( x - u, y - v ); h( x, y ) := sum;
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