Digital Filters. What are they?  Local operation (neighborhood operation in GIS terminology) by mask, window, or kernel (different words for the same.

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Presentation transcript:

Digital Filters

What are they?  Local operation (neighborhood operation in GIS terminology) by mask, window, or kernel (different words for the same thing).  Also called “convolution”!

Purposes (1)  Image improvement or restoration  Elimination of problems with lines and/or points (ie. filling in gaps)  Noise suppression  Image enhancement (sharpening)  Edge detection of linear structures.

Purposes (2)  Preprocessing before classification  Averaging of field units  Elimination of local disturbances.  Discover spatial patterns (enhancement)  Better distinguish area, line, and point objects.

Overall….  Trying to enhance low frequency detail (averaging), high frequency detail (sharpening), and edges (areas of rapid change).  All about, as always, reflectance values.

 The size of the neighborhood convolution mask or kernel (n) is usually 3 x 3, 5 x 5, 7 x 7, or 9 x 9.  We will constrain our discussion to 3 x 3 convolution masks with nine coefficients, c i, defined at the following locations:  c 1 c 2 c 3  Mask template = c 4 c 5 c 6  c 7 c 8 c 9

 The coefficients, c 1, in the mask are multiplied by the following individual brightness values (BV i ) in the input image – and then divided by 9 (thereby creating some sort of an average):  c 1 x BV 1 c 2 x BV 2 c 3 x BV 3  Mask template = c 4 x BV 4 c 5 x BV 5 c 6 x BV 6 c 7 x BV 7 c 8 x BV 8 c 9 x BV 9

 Low frequency (pass) filter: block the high spatial frequency detail, left the low-frequency  A kernel with small positive values with the same or a little large central value  High frequency (pass) filter: remove the slowly varying components and enhance the high- frequency local variations.  a kernel with a high central value, typically surrounded by negative weights abc d e

 Linear edge enhancement  Directional  Laplacian  Highlight points, lines, edges, suppress uniform and smooth regions Vertical edgesHorizontal edgeNW-SENE-SW directional Laplacian

Can also do, say, a median or modal (median below, 3x3 and 5x5) filter

Another median filter example.

Review: Properties of filters  Low pass: averaging small fluctuations in image values. Random noise suppression. Smoothing. However, image blurs.  High pass: enhancing details (and noise). Emphasizes edges.