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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.

[Graphics:Images/Jankowski_ImageProcessing_gr_54.gif]

Here we display the three results.

[Graphics:Images/Jankowski_ImageProcessing_gr_55.gif]

[Graphics:Images/Jankowski_ImageProcessing_gr_56.gif]

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.

[Graphics:Images/Jankowski_ImageProcessing_gr_57.gif]

[Graphics:Images/Jankowski_ImageProcessing_gr_58.gif]

Further reading

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

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