An Objective Evaluation of Edge Detection Methods Based on Oriented Half Kernels

Abstract

Easy to use, oriented half kernels are reliable in image analysis. These thin filters, rotated in all the desired directions are useful to detect edges, or extract precisely their orientations, even concerning highly noisy images. Usually, the filtering process corresponds to convolutions with Gaussians and their derivatives. Other filters exist and can be implemented in order to build half kernels. However, functions used for the smoothing and derivative parts have not been studied in depth. The goal of this paper is to evaluate different types of half filters as a function of the noise level. The studied kernels have the same spatial support, enabling easier comparisons. To address the robustness of the studied filters against noise, the image quality is gradually worsened. Then, their performances are compared through objective evaluations of both segmentation and gradient direction.

Shape Similarity Measurement for Known-Object Localization: A New Normalized Assessment

“…, k = 2 for [21,22] Symmetric distance [3,5] [29] Γ(G t , D c ) = FP+FN |Gt| 2 · ∑ p∈Dc d 2 Gt (p) None Complete distance measure [6] Ψ(G t , D c ) = FP+FN |Gt| 2 · ∑…”

A New Normalized Method of Object Shape-based Recognition and Localization

“…To summarize, a measure must penalize highly FNs compared to FPs, because the more FNs are present in D c , the more the shape of the desirable object becomes unrecognizable and thus localizable. Therefore, inspired by the Relative Distance Error in [13] and demonstrations in [4,12], for F N >0 or F P >0, the new normalized distance measure formula becomes:…”

Derivative Half Gaussian Kernels and Shock Filter

“…Consequently, the accuracy of the detected edge points decreases strongly at corner points and for non-straight object contour parts. To bypass this undesirable effect, an anisotropic edge detection method is developed in [14] and deeper evaluated in [10]. Indeed, the proposed technique is able to detect crossing edges and corners due to two elongated and oriented filters in two different directions.…”

“…2(b). On the contrary, for a corner point with a π/2 radian angle, the support of the half filter remains 1/2 on both sides of the edge, whereas it is around 1/4 and 3/4 concerning other filter supports [10](cf. Fig.…”

“…Note that the matlab code of the HK is available on mathworks website [11], involving different HK filters. Once |∇I|, θ 1 and θ 2 have been obtained, η corresponds to the gradient orientation i.e., to the bisector between these two directions, thus the oriented second derivative I ηη may be created ( Fig.…”