gauss

This program calculates weight based on the bell-shaped Gaussian curve. The weight is then applied to an image kernel in such a way as to create a filter that will move a weighted average through the image. The end result is a blurred image with reduced detail and noise. The Gaussian function that determines the weight for all of the values in the kernel is as follows

                                                  /   x^2+y^2   \
                                               - |  -----------  |
                G(x,y) =           1              \ 2(STDDEV)^2 /
      			    --------------- e^
			    2(pi)(STDDEV)^2
  

This formula creates a kernel that then runs through the image. The center of the kernel is at (0,0). This means that a 3x3 boxcar will be of the form

        The kernel coordinates
  (-2,-2) (-1,-2) (0,-2) (1,-2) (2,-2)
  (-2,-1) (-1,-1) (0,-1) (1,-1)	(2,-1)
  (-2, 0) (-1, 0) (0, 0) (1, 0) (2, 0)
  (-2, 1) (-1, 1) (0, 1) (1, 1) (2, 1)
  (-2, 2) (-1, 2) (0, 2) (1, 2) (2, 2)

          The kernel values (approx)
       1   4   7   4   1
       4   16  26  16  4
       7   26  41  26  7     x 1/273
       4   16  26  16  4
       1   4   7   4   1
  

Description

Use this parameter to select the filename. All bands within the file will be filtered.

Type	cube
File Mode	input
Filter	*.cub

Description

This file will contain the results of the filter, a blurred version of the input file.

Type	cube
File Mode	output

Description

This is the user specified size of the boxcar that will move through the image. The boxcar must be square, so the default value of 3 will result in a 3 x 3 boxcar. A value of five would result in a 5 x 5 boxcar moving through the image.

Type	integer
Default	3
Odd	This value must be an odd number

Description

At the most basic level, standard deviation can be thought of in this context as the intensity of the blur being applied to the image. The higher this value, the more noise and detail will be removed. At a deeper level, standard deviation is described as the average distance from any single measurement of a set to the mean of that set.

Type	double
Default	1.0
Minimum	0 (exclusive)

This example shows the use of the default standard deviation (1.0) and the default boxcar size (3). Since the boxcar must be square in this program, this means that a 3 x 3 boxcar will be used.

gauss from= peaks.cub to=gauss3x3.cub size=3 STDDEV= 1.0

gauss gui

Example GUI Screenshot of the GUI with parameters set to perform Gaussian smoothing with a 3 x 3 boxcar.

The image before the filter

Input image before gauss. Parameter Name: FROM This is the image as it was taken originally.

The image after the filter

Output image after gauss Parameter Name: TO This is the image after the gauss filter. Edges of the image are now much softer. Detail and noise has been removed.

This example shows the use of a larger standard deviation (2.0) and the larger boxcar (5). As with the last example, the single value of 5 will be applied to both the line size and sample size of the boxcar.

gauss from= peaks.cub to=bigblur.cub size=5 STDDEV= 2.0

gauss gui

Example GUI Screenshot of the GUI with parameters set to perform Gaussian smoothing with a 5 x 5 boxcar and 2.0 as the standard deviation.

The image before the filter

Input image before gauss. Parameter Name: FROM This is the image as it was taken originally.

The image after the filter

Output image after gauss Parameter Name: TO This is the image after the gauss filter. Edges of the image are now much softer. The blur is much more noticeable on account both of the larger boxcar and the larger standard deviation.