Analysis of Noisy Digital Contours with Adaptive Tangential Cover

Abstract

The notion of tangential cover, based on maximal segments, is a well-known tool to study the geometrical characteristics of a discrete curve. However, it is not robust to noise, while extracted contours from digital images typically contain noise and this makes the geometric analysis tasks on such contours difficult. To tackle this issue, we investigate in this paper a discrete structure, named Adaptive Tangential Cover (ATC), which is based on the notion of tangential cover and on a local noise estimator. More specifically, the ATC is composed of maximal segments with different widths deduced from the local noise values estimated at each point of the contour. Furthermore, a parameter-free algorithm is also presented to compute ATC. This study leads to the proposal of several applications of ATC on noisy digital contours: dominant point detection, contour length estimator, tangent/normal estimator, detection of convex and concave parts. An extension of ATC to 3D curves is also proposed in this paper. The experimental results demonstrate the efficiency of this new notion.

A Discrete Approach for Polygonal Approximation of Irregular Noise Contours

“…In other words, ν-tangential cover is inadequate in case of noise varying differently on the curve. To over come this issue, a discrete structure, called adaptive tangential cover (ATC), is presented in [18]. Such a structure is designed to capture the local noise on curve by adjusting the thickness of maximal blurred segments in accordance with the amount of noise present along the curve.…”

“…The ATC is a good tool for analyzing noisy digital curves [18]. However, when using ACT, we often observe that there are the MBS of big thickness encompassing the significant details of the curve; See Fig.…”

“…The principle for computing the MATC is described in Algorithm 1. It is similar to the one in [18] except for the labeling step as described above. It should be mentioned that the computation of MATC has no parameter to set, or only two values related to MT estimator [10].…”

“…Polygonal approximation is often involved in many applications of computer vision, graphics, image processing and data compression. In [18,20], ATC is used as a tool to study digital curves as the sequence of MBS composing ATC provides important information about the geometrical structure of the curve. In particular, it is involed in detecting points of local maximum curvature, called dominant points [3].…”

“…The sequence of blurred segments of thickness ν along a digital curve C is called a ν-tangential cover of C and can be computed in quasi-linear time [6]. It is used in many different contexts to study and analyze the geometrical characteristics of noisy curves such as length, tangent, curvature estimators (e.g., [14,18]).…”