Scale Space Radon Transform for Non Overlapping Thick Ellipses Detection

Abstract

Using integral transforms to the end of lines detection in images with complex background, makes the detection a hard task needing additional processing to manage the detection. As an integral transform, the Scale Space Radon Transform (SSRT) suffers from such drawbacks, even with its great abilities for thick lines detection. In this work, we propose a method to address this issue for automatic detection of thick linear structures in gray scale and binary images using the SSRT, whatever the image background content. This method involves the calculated Hessian orientations of the investigated image while computing its SSRT, in such a way that linear structures are emphasized in the SSRT space. As a consequence, the subsequent maxima detection in the SSRT space is done on a modified transform space freed from unwanted parts and, consequently, from irrelevant peaks that usually drown the peaks representing lines. Besides, highlighting the linear structure in the SSRT space permitting, thus, to efficiently detect lines of different thickness in synthetic and real images, the experiments show also the method robustness against noise and complex background.

Pythagorean Centrality for Data Selection

“…To illustrate this, the three means of 1 and x are plotted in Fig. 1 as a function of x ∈ [2,15]. It can be observed that the means are contained in the interval [0, x] and AM > GM > HM.…”

“…Fitting ellipses to given points is a problem that arises in computer graphics, remote sensing, geology, environment, and statistics, among many others. Different ideas have been implemented, including least-squares error minimizing and probability density estimation [39,14,15]. For 2D scatter points, we want to estimate an enclosing ellipse.…”

Scale space radon transform-based inertia axis and object central symmetry estimation

“…They have shown that this transform can be used to detect elegantly and accurately thick lines and ellipses through an embedded kernel tuned by a scale space parameter. When the scale space parameter is an appropriate one, the maximum of SSRT represents the centerlines of the linear/elliptical structures presented in the image [15,16]. In this paper we propose to investigate the ability of the SSRT to provide, through its maximum in the SSRT space, the main axis of inertia of the processed object.…”