Detection of Edges Using Two-Way Nested Design

Abstract

Abstract-This paper implements a novel approach of identifying edges in images using a two-way nested design. The test comprises of two steps. First step is based on an F-test. The sums of square (SS) of various effects are used to extract the mean square (MS) effect of respective effects and the unknown effect considered as noise. The mean square value has a chisquare distribution. The ratio of two chi-square distributions has an F-distribution. The final decision is based on testing a hypothesis for the presence or absence of an effect. The second step is based on contrast function (CF). This test identifies the presence or absence of an edge in four directions that are horizontal, vertical, and the two diagonal directions. The test is based on Tukey's T-test. The performance of nested design is compared with the edge detection using Sobel filter. A rigorous testing reveals that the nested design yields comparable results for images that are either free of noise or corrupted with light noise. The nested design however outperforms the Sobel filter in situations where the images are corrupted with heavy noise.