Gaussian Filter

The Gaussian Filter resampling option determines the gray level from the weighted sum of all the pixels in a square or rectangular kernel surrounding the input coordinates and assigns the value to the output coordinates. To filter pixels located near the edges of the image, edge pixel values are replicated to produce sufficient data.

The filter weights are computed using a Gaussian function:

G(i,j) = exp(-((i-u)**2 + (j-v)**2)/(2 * Gaussian SQ))

where 
(i,j) = a pixel within the kernel, and Gaussian SQ is the square of the Gaussian distribution deviation

You control the size of the kernel by typing a value between 1.0 and 32.0 in each of the Gaussian SQ boxes. The filter weights W(i,j) are the normalized values of G(i,j) in the kernel. The sum of all the weights is 1. The gray level of a filtered pixel is the sum of W(i,j) * V(i,j) over all pixels in the kernel, where V(i,j) is the original value at location (i,j).

If only the first Gaussian SQ value is specified, then the Gaussian Filter is a low-pass filter with a square kernel of 2*SQ + 1. As a result, the image will be blurred.

If the second Gaussian SQ value is specified, then the Gaussian Filter is a band-pass filter with a kernel of 2n*1, where "n" is the larger of the two SQ values. The resulting image is the difference of the image produced with the second SQ subtracted from the image produced with the first SQ. As a result, it will detect sudden intensity changes in the image.