- 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. In this example g is only defined over the points . 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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