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, and interpolation. A commonly used smoothing filter has constant coefficients. Convolving an image with such a filter has the effect of smoothing or blurring the image. The second example demonstrates the use of convolution to sharpen an image by a method called unsharp masking. Here we load the package.

This loads an example image.

This shows the original image.

Here we smooth and sharpen the example image.

Here we display the two 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.

This loads a grayscale example image.

This shows the edges in the books image, with the gradient edge detector result on the left and the Laplacian-of-Gaussian on the right.