GEOG 474
Spatial Filtering: Convolution
Discussion and Exercise


Spatial convolution filtering
- based on the use of convolution masks
- used to enhance low and high frequency detail, and edges
Linear spatial filter
output BVij
= function (weighted average of BVs around input pixel (i,j)
Convolution mask or kernel - 2 dimensional window of coefficients
- size of neighborhood is usually 3x3, 5x5, 7x7, 9x9

                                            c1    c2    c3
- mask template =        c4    c5    c6
                                            c7    c8    c9

Input image subset
1,1 1,2 1,3 1,4 1,5
2,1 2,2 2,3 2,4 2,5
3,1 3,2 3,3 3,4 3,5
4,1 4,2 4,3 4,4 4,5
5,1 5,2 5,3 5,4 5,5

                                       1                    1                        1
Mask A =                    1                    1                        1
                                       1                    1                        1

                                        c1 x BV1,1    c2 x BV1,2    c3 x BV1,3
Mask template =        c4 x BV2,1    c5 x BV2,2    c6 x BV2,3
                                        c7 x BV3,1    c8 x BV3,2    c9 x BV3,3

Output pixel BV2,2 = Int [ (c1 x BV1,1 + c2 x BV1,2 + ... c9 x BV3,3) / 9 ]

Spatial moving window begins at pixel (2,2) then shifts to the next pixel (2,3) and repeats for every pixel in input image

Low frequency spatial filtering
Low frequency (low pass) filters - image enhancement that de-emphasize or block the high spatial frequency detail
Low pass filter ("smoothing")
1/9 * 
Sample image:
20  20  20 
20  20  20 
20  20  20 
Image has a low smoothly varying gray scale, except for the bottom right region, which exhibits a sharp brightness change
To eliminate edge effect      - - - > start the overlay of the moving window pixel (2,2) end on pixel (6,5)

Output pixel (2,2) would be________________.

Fill in the table below to determine the output image from the input image subset above applying a 3x3 low-pass filter given above.


High frequency spatial filtering
High pass filtering is applied to imagery to remove the slowly varying components and enhance high frequency local variations.

E.g., output BV2,2 = (2 x BV2,2) - output BV2,2 from low pass filter

High pass filters that accentuate or sharpen edges produced by applying convolution masks shown in 7-14 and 7-15.

Edge enhancement
Edge enhancement delineates edges surrounding objects.

Linear and non linear edge enhancement techniques

Linear edge enhancement

ArcView Spatial Filtering Erdas Imagine Turn in answers to the questions above by Wednesday, November 24, 1999.  You are not required to print any of the original or enhanced images.
Source:  Remote Sensing Core Curriculum Module 6.4 (Faust)

Return to Geog474 Homepage

Last revised on November 18, 1999 by Tracy DeLiberty.