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Introduction to Linear Convolution Filters

Linear convolution filters are based on a filter kernel that is convoluted with an image or in the one dimensional case a curve/profile. The filter kernel itself can be considered as an image (or in 1D as a curve) and also viewed as such. The SPIP program makes it easy to modify the filter kernel and display the kernel in 2D, 3D or for one-dimensional filter kernels as curves.

 

The Linear filter kernels provided are divided into the following categories:

- Smoothing (Low Pass, Mean, Gaussian)

- Sharpening (High Pass)

- Edge enhancement & Laplace

- ISO standard filters

 

The mathematical description of a convolution with a filter kernel K of size N x M and an Image I is described below.

Filter Convolution Formula

To avoid a general amplification of the data the sum of products are normally scaled by a factor 1/k , where k is the sum of the kernel coefficients.

Filter Nomalization Factor

The simplest form of a convolution kernel is 1x1. Then the output data depends only on the value of the input data at the position (x,y) and the convolution becomes a gray-level transformation, which is also called mapping.

 

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