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12.3.2 The Convolution Operation

The convolution operation is a mathematical operation which takes two functions f(x) and g(x) and produces a third function h(x). Mathematically, convolution is defined as:
 equation4309
g(x) is referred to as the filter. The integral only needs to be evaluated over the range where tex2html_wrap_inline11306 is nonzero (called the support of the filter).[18]

In spatial domain image processing, you discretize the operation. f(x) becomes an array of pixels F[x]. The kernel g(x) is an array of values G[0...(width-1)] (assume finite support). Equation 7 becomes:
 equation4318