Mathematica 9 is now available

Image Processing Using LSI Filters

Many useful image operations are implemented with linear shift-invariant (LSI) filters. A smoothing operation is frequently a first step in operations such as noise reduction, edge detection or interpolation. A commonly used smoothing filter has constant coefficients. The effect of smoothing or blurring an image is achieved by convolving the image with such a filter. The third example will demonstrate the use of convolution to "sharpen" an image by a method called unsharp masking. The simplest form of unsharp masking may be implemented by subtracting a scaled smoothed image from the original.

Here we smooth and sharpen image the "head" example image.


Here we display the three results.



Edge detection is an important step in many shape-based recognition tasks. Edge detection is typically implemented as a convolution operation with appropriately chosen differentiating filters. Two examples of edge detection using two common edge filters, the Sobel gradient edge detector and the Laplacian-of-Gaussian edge detector, conclude this section.



Further reading

User's Guide: Sections 5.2, 5.3, 7.3.

Function Index: DiscreteConvolve, EdgeMagnitude, ImagePlus, LoGFilter, SobelFilter, Threshold, ZeroCrossing.