1. Digital Filters

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

3. 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.

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

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

6.  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

8.  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

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 111 111 1 1 1.25.5.25.51.5.25.25.5 111 121 1 1 19 1-21 -25-2 1 1 -2 abc d e

10.  Linear edge enhancement  Directional  Laplacian  Highlight points, lines, edges, suppress uniform and smooth regions -1 0 1 -1 -1 -1 0 0 0 1 1 1 0 -1 0 -1 4 -1 0 -1 0 0 1 1 -1 0 1 -1 -1 0 1 1 0 1 0 -1 0 -1 -1 Vertical edgesHorizontal edgeNW-SENE-SW -1 -1 -1 -1 8 -1 -1 -1 -1 1 -2 1 -2 4 -2 1 -2 1 directional Laplacian

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

12. Another median filter example.

13. 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.