Using high-pass filters

High-pass filters emphasize border pixels between contrasting areas and are often referred to as edge detectors. Like speckle filters, they highlight pixel contrasts associated with linear features and edge details. You can apply a high-pass filter to highlight pixel contrasts associated with linear features and edge details.

Gaussian Filter (SIGMSQ = 4)

The Gaussian Filter is used as a band-pass filter to blur an image. This filter uses the following Gaussian function to compute the filter weights:

G (i, j) = exp ( -((i-u)**2 + (j-v)**2) / (2 * SIGSMQ) )

where (i, j) is a pixel within the filter window, (u, v) is the center for the filter window, and SIGMSQ is set to 4.

The filter weights W(i, j) are the normalized values of G(i, j) over the entire filter window; therefore, the sum of all weights is 1.

The gray level of a filtered pixel is the sum of W(i, j) *V(i, j) over all pixels in the filter window, where V(i, j) is the original value at location (i, j).

The filter size for a Gaussian Filter is restricted to 9X9.

Note: In order to filter pixels located near the edges of the image, edge pixel values are replicated to give sufficient data.

Laplacian Edge Detector Filters

Laplacian Edge Detector Filters generate sharp edge definition of an image. These filters can be used to highlight edges that have both positive and negative brightness slopes.

The two Laplacian filters have different weight arrangements, as shown below:

Table 1.
Type 1	Type 2
0 1 0 1 -4 1 0 1 0	-1 -1 -1 -1 8 -1 -1 -1 -1
where the sum of all weights = 0

Note: In order to filter pixels located near the edges of the image, edge pixel values are replicated to give sufficient data.

Sobel Edge Detector Filter

The Sobel Edge Detector Filter creates an image where edges (sharp changes in gray-level values) are shown. Only a 3x3 filter size can be used with this filter.

This filter uses two 3x3 templates to calculate the Sobel gradient as shown below:

Table 2.
-1 0 1 -2 0 2 -1 0 1	1 2 1 0 0 0 -1 -2 -1
X	Y

Table 3. Templates
a1 a2 a3 a4 a5 a6 a7 a8 a9	3x3 filter window
where a1 - a9 are gray levels of each pixel in the filter window

Apply the templates to a 3x3 filter window.

X = -1*a1 + 1*a3 - 2*a4 + 2*a6 - 1*a7 + 1*a9

Y = 1*a1 + 2*a2 + 1*a3 - 1*a7 - 2*a8 - 1*a9

Sobel Gradient = sqrt (X*X + Y*Y)

Note: In order to filter pixels located near the edges of the image, edge pixel values are replicated to give sufficient data.

Prewitt Edge Detector Filter

The Prewitt Edge Detector Filter creates an image where edges (sharp changes in gray-level values) are shown. Only a 3x3 filter size can be used with this filter.

This filter uses two 3x3 templates to calculated the Prewitt gradient value, as shown below:

Table 4.
-1 0 1 -1 0 1 -1 0 1	X
1 1 1 0 0 0 -1 -1 -1	Y

Table 5. Templates
a1 a2 a3 a4 a5 a6 a7 a8 a9	3x3 filter window
where a1 - a9 are gray levels of each pixel in the filter window

Apply the templates to a 3x3 filter window.

X = -1*a1 + 1*a3 - 1*a4 + 1*a6 - 1*a7 + 1*a9

Y = 1*a1 + 1*a2 + 1*a3 - 1*a7 - 1*a8 - 1*a9

Prewitt Gradient = sqrt (X*X + Y*Y)

Note: In order to filter pixels located near the edges of the image, edge pixel values are replicated to give sufficient data.

Edge Sharpening Filter

An Edge Sharpening Filter uses a subtractive smoothing method to sharpen an image. First, an average filter is applied to the image. The averaged image retains all low-spatial frequency information, but has its high-frequency features, such as edges and lines, attenuated. Consequently, the averaged image is subtracted from its original image and the resultant difference image will primarily have the edges and lines remaining. After the edges are deternimed in this manner, the difference image is added back to the original image to give an edge-enhanced image. The resultant image will have clearer high-frequency detail; however, there is a tendency for noise to be enhanced.

Note: In order to filter pixels located near the edges of the image, edge pixel values are replicated to give sufficient data.

To apply a high-pass filter:

In the Maps tree, right-click an image layer and click Filter.
In the Filter window, enter an X- and Y-filter kernel size in the Filter size boxes.
Note: This step does not apply to Gaussian filters, as the filter size will be fixed at 9x9.
Click the High Pass tab.
Select a filter option.
Note: If you chose Gaussian (SIGMSQ = 4), the values in the Filter size X and Y boxes are automatically set to 9.
Click Apply to View. The high-pass filter changes the image in the view pane. You can save a filter view by clicking Apply to File.
The Save New Filtered Image Layer window opens. You can either save the filtered image to a new image layer, or overwrite the existing layer.