The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an n-gon with r reflex vertices in time O(n 1+" +n 8=11+" r 9=11+" ), for any fixed " ? 0, improving the previous best upper bound of O(nr log n). Our algorithm simulates the sequence of collisions between edges and vertices during the shrinking process, using a technique of Eppstein for maintaining extrema of binary functions to reduce the problem of finding successive interactions to two dynamic range query problems: (1) maintain a changing set of triangles in IR 3 and answer queries asking which triangle would be first hit by a query ray, and (2) maintain a changing set of rays in IR 3 and answer queries asking for the lowest intersection of any ray with a query triangle. We also exploit a novel characterization of the straight skeleton as a ...

The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object, is presented. The boundary is segmented at points of maximal positive curvature and a distance map from each of the segments is calculated. The skeleton is then located by applying simple rules to the zero sets of distance maps differences. A framework is proposed for numerical approximation of distance maps that is consistent with the continuous case, hence does not suffer from digitization bias due to metrication errors of the implementation on the grid. Subpixel accuracy in distance map calculation is obtained by using gray level information along the boundary of the shape in the numerical scheme. The accuracy of the resulting efficient skeletonization algorithm is demonstrated by several examples. Keywords: Differential Geometry, Distance Map, Medial Axis Transform, Shape Analysis, S...

This paper deals with the determination of skeletons and conditional bisectors in discrete binary images using the Euclidean metrics. The algorithm, derived from [18], proceeds in two steps: rst, the Centers of the Euclidean Maximal Discs (CMD) included in the set to skeletonize are characterized and robustly identi ed. Second, a refront propagation is simulated starting from the set boundaries, in which pixels which arenotcenters of maximal discs and are not crucial to homotopy preservation are removed. Not only is the resulting algorithm fast and accurate, it allows the computation of a vast variety of skeletons. Furthermore, it can be extended to provide conditional bisectors of any angular parameter. This leads to the introduction of a new morphological transformation, the bisector function, which synthesizes the information contained in all the-conditional bisectors. The interest of all these skeleton-like transformations is illustrated on the segmentation of binary images of glass bers. 1

This report investigates the application of two Computer Vision techniques for characterizing critical regions in digital terrain maps: Skeletonization and Topographical Region Detection. The Navigation Path Planning problem involves nding the optimal path through a digital terrain Map and must minimize a cost function while satisfying the constraints of navigation. This process is computationally expensive and has typically been intractable for in ight planning applications. The aim of this work is to extract representations of digital terrain maps which are relevant to the requirements of the path planning problem. Clustering and Dierential Geometry is used to detect regions which are critical to the cost function. Skeletonization is then used to extract features from these regions in terms of navigational constraints and provides a graph like representation. This allows the grid elements of digital terrain maps (pixels) to be replaced by critical regions (Skeletonized topographic...

The salience of symmetry for patterns in the human visual system has been noted by a number of observers from Mach onwards. Psychophysical studies show that symmetry is important both for shape recognition and for figure-ground segregation. Here, a computational scheme for detecting local symmetry as an aid to detecting significant structures in images is presented. It is based on filtering with Gaussian derivatives. Part of this research was done while the first author was visiting IBM and the second author was a Research Staff Member at IBM Almaden Research Center, San Jose, CA-95120. R. Manmatha's work is supported by in part by the National Science Foundation, Library of Congress and Department of Commerce under cooperative agreement number EEC-9209623, in part by the United States Patent and Trademarks Office and the Defense Advanced Research Projects Agency/ITO under ARPA order number D468, issued by ESC/AXS contract number F19628-95-C-0235 and in part by NSF Multimedia CDA-...

In this thesis, we develop a computational framework for image-based statistical analysis of anatomical shape in different populations. Applications of such analysis include understanding developmental and anatomical aspects of disorders when comparing patients vs. normal controls, studying morphological changes caused by aging, or even differences in normal anatomy, for example, differences between genders. Once a quantitative description of organ shape is extracted from input images, the problem of identifying differences between the two groups can be reduced to one of the classical questions in machine learning, namely constructing a classifier function for assigning new examples to one of the two groups while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data that are captured by the discriminative model. In contrast, interpretation of the statistical model in the original image domain is an important component of morphological analysis. We propose a novel approach to such interpretation that allows medical researchers to argue about the