Two linear-time algorithms for computing the minimum length polygon of a digital contour

AbstractThe Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one combinatorial, and both definitions lead to two different linear time algorithms to compute them. This paper extends the work presented in Provençal and Lachaud (2009) [26], by detailing the algorithms and providing full proofs. It includes also a comparative experimental evaluation of both algorithms showing that the combinatorial algorithm is about 5 times faster than the other. We also checked the multigrid convergence of the length estimator based on the MLP

Analysis of Noisy Digital Contours with Adaptive Tangential Cover

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 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

2D and 3D Shape Descriptors

The field of computer vision studies the computational tools and methods required for computers to be able to process visual information, for example images and video. Shape descriptors are one of the tools commonly used in image processing applications. Shape descriptors are mathematical functions which are applied to an image and produce numerical values which are representative of a particular characteristic of the image. These numerical values can then be processed in order to provide some information about the image. For example, these values can be fed to a classifier in order to assign a class label to the image. There are a number of shape descriptors already existing in the literature for 2D and 3D images. The aim of this thesis is to develop additional shape descriptors which provide an improvement over (or an alternative to) those already existing in the literature. A large majority of the existing 2D shape descriptors use surface information to produce a measure. However, in some applications surface information is not present and only partially extracted contours are available. In such cases, boundary based shape descriptors must be used. A new boundary based shape descriptor called Linearity is introduced. This measure can be applied to open or closed curve segments. In general the availability of 3D images is comparatively smaller than that of 2D images. As a consequence, the number of existing 3D shape descriptors is also relatively smaller. However, there is an increasing interest in the development of 3D descriptors. In this thesis we present two basic 3D measures which afterwards are modified to produce a range of new shape descriptors. All of these descriptors are similar in their behaviour, however they can be combined and applied in different image processing applications such as image retrieval and classification. This simple fact is demonstrated through several examples.Mexican Science Council (Consejo Nacional de Ciencia y Tecnologia, CONACyT

A comparative Evaluation of Length Estimators of digital Curves

International audienceThe paper compares previously published length estimators in image analysis having digitized curves as input. The evaluation uses multigrid convergence (theoretical results and measured speed of convergence) and further measures as criteria. The paper also suggests a new gradient-based method for length estimation, and combines a previously proposed length estimator for straight segments with polygonalization methods