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Laplacian of Gaussian (LOG)

The LOG module performs a Laplacian of Gaussian filter. This filter first applies a Gaussian blur, then applies the Laplacian filter (see convolution) and finally checks for zero crossings (i.e. when the resulting value goes from negative to positive or vice versa). The end result of this filter is to highlight edges.

The first stage of the filter uses a Gaussian blur to blur the image in order to make the Laplacian filter less sensitive to noise. If you run the Laplacian filter on a noisy image the result is an edge image with many many small edges that detract from the larger more meaningful edges. Other blur filters could also used prior to the Laplacian filter but the Gaussian blur is more commonly used for this process.

The Laplacian filter is a convolution filter that is used to detect edges. The following are examples of 3 command Laplacian filters:

0 1 0
1 -4 1
0 1 0
1 1 1
1 -8 1
1 1 1
-1 2 -1
2 -4 2
-1 2 -1

In the case of this module the Laplacian and Gaussian are convoluted together to create a single filter that is applied to the image.

Once the filter has been convoluted with the image the resulting values are negative and positive numbers. The final step detects where these numbers switch signs and marks that point in the image. The end result is an image that indicates edges.

Laplacian of Gaussian Interface

1. Specify the window size of the filter to use. The larger the filter the slower the processing but the less resistant to noise in the images.
2. Specify the Gaussian Theta to use when creating the single LOG filter. Higher thetas result in more rounded or blurring of the image.

For additional information on Laplacian of Gaussian (LOG) see
University of Edinburgh - HyperMedia Image Processing Reference2
Oxford University - Stephen M. Smith

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