Shen-Castan Edge Detection

Shen-Castan Edge Detection is one of the edge detection techniques that is used in image processing with noisy input. Edge detection is an image processing technique for finding the boundaries of objects within images. Edge detection is used for image segmentation and data extraction in areas such as image processing, computer vision, and machine vision.

Advantage and Disadvantage

The unique feature of the Shen-Castan Edge Detection is that it can detect the edge of an image with noise. By using an Infinite Symmetric Exponential Filter, the noise will be eliminated. Also, Shen-Castan Edge Detection provides better localization than Canny's operator, because the implementation of Canny's algorithm approximates its optimal filter by the derivative of a Gaussian function, whereas Shen-Castan Edge Detection uses the optimal filter directly. The disadvantage of the Shen-Castan Edge Detection is that the calculation/processing time is longer than other edge detection algorithms.

Algorithms

To implement Shen-Castan Edge Detection, there are three steps:

Input data with Infinite Symmetric Exponential Filter (ISEF). The ISEF will filter out any noise that will affect the quality of the image. The Optimal ISEF function:

$f(x)=(p/2)exp(-p|x|)$

Then find the localization edges by zero crossing of the Laplacian. To get Laplacian approximation, use smoothed image subtract original image. The result will be a band limited Laplacian image. The final step will be to set all positive values to 1 and others to 0 to get binary Laplacian image.

Example

To implement Shen-Castan Edge Detection, we first imported an image as shown in P1. We added noise into the original image as shown in P2.

P1: Original Image

File:Salt and pepper calculator.png

P2: Original Image with noise

File:Finished calculator.png

P3: Edge detection of the image by Shen-Castan Edge Detection

References

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