GEOG 474
Spatial Filtering: Convolution
Discussion and Exercise

Introduction

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")
3 by 3 matrix of coefficients

Set of coefficients used for image smoothing and noise removal:

 1/9 * 1 1 1 1 1 1 1 1 1
Sample image:
 3 3 4 4 5 6 2 3 3 4 4 5 1 2 2 3 3 4 1 1 2 4 4 7 1 2 4 20 20 20 2 3 6 20 20 20 2 3 4 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

• directional first difference that approximates the first derivative between 2 adjacent pixels
• algorithm produces first difference of input image in horizontal, vertical, and diagonal edges

•

Vertical:     BVi,j  =  BVi,j  -  BVi,j+1  +  K

Horizontal:  BVi,j  =  BVi,j  -  BVi-1,j  +  K

NE diagonal:  BVi,j  =  BVi,j  -  BVi+1,j+1  +  K

SE diagonal:  BVi,j  =  BVi,j  -  BVi-1,j+1  +  K

- the subtraction  (BVi,j  -  BVi,j+1) can be either positive or negative, so constant K is added to make all values positive and centered between 0 and 255.

ArcView Spatial Filtering
Images for this exercise are found under ~tracyd/Geog474/images directory on strauss and the files are called:

flevolandradar.img
landsat_tm_manaus.img
landsat_tm_rondonia.img

Examine the spatial filtering enhancement capabilities available with ArcView.  Online Help discusses the spatial enhancement tools under:

Content ---> Extensions ---> Image Analysis --->Working with Image Analysis Themes ---> Smoothing and Image, Sharpening an image

QUESTION: For continuous remotely sensed data, what type and size of convolution kernel is used to apply a smooth filter to an image?  What type and size of convolution kernel is used to sharpen an image?  Do you have an capabilities to alter the convolution kernel?

Smoothing image appearance

Add the flevolanradar.img image analysis data theme to a view.   This theme is a radar image with high degree of speckling typical of most radar data.  Remove the noise by applying a smooth filtering (low pass filter).  To highlight the speckled radar image, select Zoom to Image Resolution from the View menu or click the Zoom to Image Resolution button.  Do the same for the smoothed image.

Describe the resultant smoothed  image in comparison to the original radar image.

Perform the smoothing filter to the Amazon images - landsat_tm_manaus.img or landsat_tm_rondonia.img.

Describe the resultant smoothed  image in comparison to the original image.

Sharpening an image

Apply a sharpening filter to the Amazon image.

Describe the resultant sharpened  images in comparison to the original image.
Erdas Imagine
Take a look at the spatial enhancement capabilities available with Erdas Imagine.  What types of spatial enhancement tools are available with Imagine.  Which s/w has greater capabilities?

To start Imagine, logon to strauss and the bring up an xterm window on Geography's SGI davinci.

strauss% ssh davinci.geog
password:

davinci.geog% imagine

If  you are adventuresome, load an image and apply a spatial filter.
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)

Last revised on November 18, 1999 by Tracy DeLiberty.