International audienceThe 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 adapted to noisy digital contours. In this paper, we propose a new notion, named Adaptive Tangential Cover, to study noisy digital contours. It relies on the meaningful thickness, calculated at each point of the contour, which permits to locally estimate the noise level. The Adaptive Tangential Cover is then composed of maximal blurred segments with appropriate widths, deduced from the noise level estimation. We present a parameter-free algorithm for computing the Adaptive Tangential Cover. Moreover an application to dominant point detection is proposed. The experimental results demonstrate the efficiency of this new notion

In this paper, we investigate the problem of dominant point detection on digital curves which consists in finding points with local maximum curvature. Thanks to previous studies of the decomposition of curves into sequence of discrete structures [5][6][7], namely maximal blurred segments of width ⌫ [13], an initial algorithm has been proposed in [14] to detect dominant points. However, an heuristic strategy is used to identify the dominant points. We now propose a modified algorithm without heuristics but a simple measure of angle. In addition, an application of polygonal simplification is as well proposed to reduce the number of detected dominant points by associating a weight to each of them. The experimental results demonstrate the e ciency and robustness of the proposed method.

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.