CEE 615: Digital Image Processing
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Lab 6: Spatial and frequency domain filters
I. Filtering in the Spatial Domain
There are several images supplied for use with this exercise:
1. Bird image: This is one of the images that was used
in lecture. It is problematic for two reasons. First, it
has been compressed (jpeg) and it has already been
edge-enhanced. (Look closely ant the leading edge of
the wings.) There are some details that show up well
in this image, but it is probably not the best for
demonstrating the use of filters.
2. The bridge image: This image has also undergone
jpeg compression, but there is no obvious evidence of
edge-sharpening. Given the repeating vertical,
horizontal and angled elements in the image, it is
particularly useful for exploring the use of directional
filters.
3. Ooid Shoals, Bahamas: This is a one-band image of
a shallow region in the Bahamas that shows an area of
sand and sea grass. (The darker areas are largely sea
grass.) The presence of sand waves and the structure
and texture of the sea grass make for interesting
targets for filtering operations. There is also fairly
obvious banding (vertical striping) in this image that
will be sensitive to some of the spatial filters.
4. Ginna: This is a 3-band image of an area in
Rochester, NY near the Ginna power station. Only the
red channel is shown at right. Interesting features to
observe when using the filters are the orchards vs. the
wooded areas. Also note the effect of filters on the
power plant (lower right) and on details in the water
(bottom).
5. Test images
a.
b.
CEE 615: Digital Image Processing
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Lab 6: Spatial and frequency domain filters
A. Convolution Filters
Convolution is a form of filtering that produces an output image in which the brightness value at a
given pixel is a function of some weighted average of the brightness of the surrounding pixels.
Convolution of a user-selected kernel with the image array returns a new, spatially filtered image.
General requirements for configuring and using convolution filters and specifics for each filter type
are described below.
Using Convolution Filters
Convolution of a user-selected kernel with the image array returns a new, spatially filtered image.
You can select the kernel size and values, producing different types of filters. Standard filters
include high pass, low pass, Laplacian, directional, Gaussian, median, Sobel, Roberts, and userdefined. For descriptions of each filter type, see Convolution Filters.
1. Select Filter > Convolutions and Morphology.
The Convolutions and Morphology Tool dialog
appears.
2. Select Convolutions > filter type
· If you select the Directional filter, enter the
filter angle when the Directional Filter Angle
dialog appears. North (up) is zero degrees
and the other angles are measured in the
clockwise direction.
3. Specify the kernel size by clicking the "Kernel Size"
arrow increment buttons.
· Some specialized filters have default sizes that
cannot be changed. If you select filter types
such as Sobel and Roberts, you cannot
change the kernel size.
· The kernel sizes are in odd-number increments. Clicking with the left mouse button
increases/decreases the value by 2, clicking with the middle mouse button
increases/decreases value by 10, and clicking with the right mouse button sets the kernel
size back to 3 x 3.
· By default, the kernel size is set to a square kernel.
· To change to a non-square kernel, select Options > Square kernel:No.
Note - The Median filter is always a square.
· To edit individual kernels, see the Editing Kernels.
4. Enter an add back value in the "Image Add Back (0-100%)" text box.
"Adding back" part of the original image to the convolution filter results helps preserve the
spatial context and is typically done to "sharpen" an image. The Image Add Back value is the
percentage of the original image that is included in the final output image. For example, if you
enter 40%, then 40% of the intensity of the original image is added to 60% of the convolution
filter image to produce the final result.
CEE 615: Digital Image Processing
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Lab 6: Spatial and frequency domain filters
High Pass Filters
High pass filters remove the low frequency components of an image while retaining the high
frequency (local variations). They can be used to enhance edges between different regions as
well as to "sharpen" an image. This is accomplished using a kernel with a high central value,
typically surrounded by negative weights. ENVI's default high pass filter uses a 3 x 3 kernel
with a value of "8" for the center pixel and values of "-1" for the exterior pixels. High pass
filters can only have odd kernel dimensions.
Low Pass Filters
Low pass filtering preserves the low frequency components of an image, which smooths it.
ENVI's default low pass filter contains the same weights in each kernel element, replacing the
center pixel value with an average of the surrounding values. The default kernel size is 3 x 3.
Laplacian Filters
A Laplacian filter is a second derivative edge enhancement filter that operates without regard to
edge direction. Laplacian filtering emphasizes maximum values within the image by using a
kernel with a high central value typically surrounded by negative weights in the north-south and
east-west directions and zero values at the kernel corners. ENVI's default Laplacian filter uses a
3 x 3 kernel with a value of "4" for the center pixel and values of "-1" for the north-south and
east-west pixels. All Laplacian filters must have odd kernel sizes.
Directional Filters
A directional filter is a first derivative edge enhancement filter that selectively enhances image
features having specific direction components (gradients). The sum of the directional filter
kernel elements is zero. The result is that areas with uniform pixel values are zeroed in the
output image, while those that are variable are presented as bright edges.
Gaussian Filters
A Gaussian filter passes a Gaussian convolution function of specified size over the image. The
default is a 3 x 3 kernel and kernel dimensions must be odd.
Median Filters
Median filtering smooths an image, while preserving edges larger than the kernel dimensions
(good for removing salt and pepper noise or speckle). ENVI's Median filter replaces each center
pixel with the median value (not to be confused with the average) within the neighborhood
specified by the filter size. The default is a 3 x 3 kernel.
Sobel Filters
The Sobel filter is a non-linear edge enhancement, special case filter that uses an approximation
of the true Sobel function, and is a preset 3 x 3, non-linear edge enhancement operator. The size
of the filter cannot be changed and no kernel editing is possible.
Roberts Filters
The Roberts filter is a non-linear edge detector filter similar to the Sobel. It is a special case
filter that uses a preset 2 x 2 approximation of the true Roberts function, a simple, twodimensional differencing method for edge-sharpening and isolation. The size of the filter
cannot be changed and no kernel editing is possible.
User-Defined Convolution Filters
You can define custom convolution kernels (including rectangular rather than square filters) by
selecting and editing a user kernel.
CEE 615: Digital Image Processing
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Lab 6: Spatial and frequency domain filters
Editing Kernels
To edit the selected kernel and change any of the weight values:
1. In the Convolutions and Morphology Tool, double-click within the text box of the value to
be edited.
The line cursor appears.
2. Highlight the value, enter a new value, and press the "Return" key.
B. Statistical Filters (Not available in ENVI)
Statistical filters compute first-order statistical properties of the gray values within the filter
window, i.e., mean, standard deviation, variance, skewness, kurtosis, etc. They operate like
convolution filters in that the filter is applied independently at each point in the image, but the
operation is different. The filter itself is simply a mask which denotes which pixels within the filter
will be included and which will be ignored.
C. Rank-order filters (General form not available in ENVI)
Rank-order filters
A rank order filter sorts the pixels within the filter mask and replaces the center pixel based on the
relationship of its gray value to its place in the ordered set. The most common rank-order filter is
the median filter which replaces the center pixel with the median value of the pixels within the filter
window. The median filter (see above) is a special case of rank order filter.
CEE 615: Digital Image Processing
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Lab 6: Spatial and frequency domain filters
D. Morphological Filtering
Mathematical morphology is a non-linear method of processing digital images on the basis of shape.
Its primary goal is the quantification of geometrical structures. A detailed discussion of this topic is
beyond the scope of this manual. See the following reference for additional details.
Haralick, Sternberg, and Zhuang, Image Analysis Using Mathematical Morphology, IEEE
Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-9, No. 4, July 1987, p. 532550.
1. Select Filters > Morphology.
2. Choose one of the types of morphological filters: Dilate, Erode, Opening, or Closing.
Using Morphological Filters
There are several predefined morphological kernels. (Morphological kernels used here are just the
structuring element and should not to be confused with convolution kernels).
1. Select Filters > Morphology
2. When the Morphology Input File dialog appears, select the data to be processed.
File selection procedures are the same as those for convolution filters (see Using
Convolution Filters).
Choosing Morphology Parameters
After the input data has been selected in the file selection dialog:
1. Click "OK".
2. When the Morphology Parameters dialog appears, Enter the kernel size in the text boxes
labeled "Cols" and "Rows."
To edit the kernel
A. Click "Edit Kernel".
B. When the Kernel Edit dialog appears, with each kernel value listed in its own editable
text box, select from the following options.
To change any value, click on the value to be changed and enter the new value.
To reset to the original values, click "Reset".
To save the edited kernel, click "Save Kernel" and enter the output file name into the
appropriate text box
To restore a previously saved kernel, click "Restore Kernel" and select the desired
kernel file.
3. Click "OK"
4. When a second Morphology Parameters dialog appears, select the number of cycles to iterate
the filter by entering the desired value in the "Cycles" text box.
CEE 615: Digital Image Processing
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Lab 6: Spatial and frequency domain filters
5. Select a filter style of "Binary," "Gray", or "Value."
"Binary" causes the output pixels to be either black or white. "Gray" preserves gradients.
"Value" allows the kernel value to be either added (dilate) or subtracted (erode) from the
selected pixels.
6. Select "File" or "Memory" output.
 If output to "File" is selected, enter an output filename.
7. Click "OK" to execute the filter.
A status message will appear showing how much of the operation has been completed. If no
image tiling is required, the status message will not advance gradually but will go abruptly from
0 to 100% after a short wait because the operation is being performed on the entire image array.
When completed, the filtered image is added to the top of the Available Bands list and can be
displayed using standard ENVI procedures.
Dilate
The dilate function, commonly known as "fill," "expand," or "grow," is used to fill holes smaller
than the structural element (kernel) in a binary or grayscale image.
Erode
The erode function, commonly known as "shrink," or "reduce," is used to remove islands of pixels
smaller than the structural element (kernel) in a binary or grayscale image.
Opening
The "opening" of an image is defined as the erosion of the image followed by subsequent dilation
using the same structural element. Opening an image smoothes the contours, breaks narrow
isthmuses, and eliminates small islands and sharp peaks or capes. The same operation can be
performed by using the erode and dilate filters sequentially.
Closing
The "closing" of an image is defined as the dilation of the image followed by subsequent erosion
using the same structural element. Closing an image smoothes the contours, fuses narrow breaks
and long thin gulfs, and eliminates small holes and fills gaps in the contours. The same operation
can be performed by using the dilate and erode filters sequentially.
E. CHALLENGE
Using convolution, median or morphological filters,
1. Design a filter that will remove the horizontal and vertical lines in image 5a.
2. Design a filter that will remove only the vertical (or only the horizontal) lines in image 5b
while leaving the other lines intact.
3. Design a filter that will enhance the thick diagonal lines, minimize the thin diagonal lines,
and leave the horizontal and vertical lines in image 5b,
4. Devise a filter that will enhance the sand waves in image 3.