EDGE DETECTION ON GRAYSCALE IMAGES USING THE PYTHAGOREAN THEOREM

Abstract

Edge detection is one of the important task performed in computer vision and image processing as edges that are present in an image in some ways makes it possible to form a very sparse representation of what is actually in the image. In this work, a new method is proposed for edge detection using the universal concept behind the Pythagorean Theorem and the geometric surface two-sheeted hyperboloid. A triangular kernel is used which computes values for every possible direction first, followed by mutually subtracting each resulting image. After this, thresholding is applied in resultant images to generate binary image and to discard any false edges. Morphological operation is also applied as post processing step for refining the edges furthermore. Final results shows that the proposed method has comparatively consistent performance on various test images, which is competitive with traditional edge detecting algorithm like Sobel, Prewitt, Canny operator etc. and also proves how edge detection method strongly depends upon the application domain as well. Evaluation of results for quantitative comparisons was done with two assessment techniques Cohen‘s Kappa and Shannon‘s Entropy and results were shown for a number of test images.