High Pass Edge Enhancement Filters (Laplacian Edge Enhancement) : Gradient and Compass Operators (Especially for GATE-Geospatial 2022)

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High pass filters emphasize sudden changes in the values of pixels over distance. Those abrupt differences stand for high spatial frequencies, termed “edges” . In images, edges will be found in point features (random noise) , linear features (road, river) or borders between objects (the border between a field and a forest) .

  • Generally, a high-pass filter will emphasize objects smaller than half the size of the window being used, and blur objects larger than half the window size.
  • Before examining some high-pass filters, it would be fruitful to know the effect known as “Mach bands” .
  • The spatial interaction of the reflected light from an object with its environment creates phenomena called the effect of Mach bands. This effect demonstrates that the brightness of an object is not a simple function of its luminance.
Luminance Versus Brightness
  • The grey bands in the image have a uniform reflectance, but the apparent brightness is not uniform. On the edge between two grey bands, we can see differences in the brightness value.
  • The thin line in the chart demonstrates that effect, with the overshoots and undershoots. Some of the high-pass filters are actually creating such phenomena, creating overshoots and undershoots of pixel values on the edges of different objects.

Example of High Pass Filter

A graphical example of creating a high-pass filter is given in the following figure:

HIGH PASS DIFFERENTIAL
  • The procedure described in the figure is the simplest high-pass filter. It is based on the above-mentioned idea that each image is built of two components, one of a low frequency, the other of a high frequency. By subtracting the low-frequency component from the image, we receive a high frequency. This filter is called High Pass Differential Filters.
  • High-pass filters examine the difference between adjacent pixels. As these differences are usually small, a contrast stretch should be performed on the output filtered image, in order to see better the details. These filters can be used in algorithms for pattern recognition when the frequency of an “edge” in a unit of area can indicate certain objects. The output filtered image can be also used as another band helping in the classification procedure.

Laplacian Edge Enhancement

One of the most known high-pass filters is the Laplacian edge enhancement. Its meaning can be thus understood: We subtract the image from a blurred version of itself created from the averaging of the four nearest neighbours. This enhances edges and isolated pixels with extreme values. However, in the classic version of this filter, very bright values are obtained in dark edges and dark values in bright edges. This is visually confusing; therefore, we can use an alternative, the Modified LaPlacian. There are many other versions of this filter. One of them is given below too, on the right.

LAPLACIAN EDGE ENHANCEMENT

Kinds of Edge Detection Operators

There are two basic kinds of edge detection operators:

  • Gradient operators, working in two orthogonal directions (horizontal and vertical) .
  • Compass operators, working in a user-defined direction.

Gradient Operators

The basic idea of gradient operators is to calculate the slope (that is, the difference in pixel values over a distance) of an image, and then to define a certain cutting value above which a pixel is considered as representing an edge point or an edge line.

  • There are many edge detections filters; one of them is the SOBEL EDGE DETECTOR, that is working in the following way: New value = s where
  • X = the resulting image from applying the kernel Kx (below) to the input image Y = the resulting image from applying the kernel Ky (below) to the input image
The Sobel Edge Detector is a Gradient Operator
  • The Sobel edge detector is a gradient operator. Two high-pass filters are being calculated, one in the horizontal direction, the other in the vertical (their respective kernel values are rotated by 90 degrees the one to the other) . The output images resulting are raised by the power of 2, and then we calculate the square root of their sum. Other gradient operators work basically in a similar way, only having different kernels (the weights given to the pixels, and the window size used) .

Compass Operators

Compass operators measure the slope in the requested direction. The resulting slope images are again used to define a “cutting” value, above which pixels are considered as edges. Below are given the 3 ⚹ 3 kernels of the 8 principal directions; in order to calculate directional edge enhancement in other angles, the moving window size should be enlarged.

SONAR the Pipeline

An example of using a directional edge detector filter will be given, with the same SONAR image of the pipeline, with the chosen direction of North and East (it was performed on the MEAN filtered image, to achieve better results) . Notice the easy detection of the pipeline in the North filter.

The Measurement Units of the Variable

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