A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.

or example, if you are looking for words in long strings of text, you could use a table accessed by indices that are functions of individual words. The table contains the strings where the word appears and the location of the word in the strings. It would be easy then to locate a word by retrieving all of its appearances from the table. This kind of approach was originally proposed for geometric object recognition, making use of indices based on local geometric features that remained invariant to the object transformation. The features were local to handle partial occlusion, and their indexing function was invariant to the relevant transformation, because unlike words in text, geometric features have both location and orientation. For over a decade now, indexing-based approaches have been gaining ground as the method of choice for building working recognition systems that can Geometric Hashing: An Overview HAIM J. WOLFSON Tel Aviv

Abstract—We present a novel approach to finding a correspondence (alignment) between two curves. The correspondence is based on a notion of an alignment curve which treats both curves symmetrically. We then define a similarity metric based on the alignment curve using two intrinsic properties of the curve, namely, length and curvature. The optimal correspondence is found by an efficient dynamic-programming method both for aligning pairs of curve segments and pairs of closed curves, and is effective in the presence of a variety of transformations of the curve. Finally, the correspondence is shown in application to handwritten character recognition, prototype formation, and object recognition, and is potentially useful in other applications such as registration and tracking. Index Terms—Curve alignment, recognition, dynamic programming, prototypes, correspondence.

In this paper we present a new technique for piecewiselinear surface reconstruction from a series of parallel polygonal cross-sections. This is an important problem in medical imaging, surface reconstruction from topographic data, and other applications. We reduce the problem, as in most previous works, to a series of problems of piecewise-linear interpolation between each pair of successive slices. Our algorithm uses a partial curve matching technique for matching parts of the contours, an optimal triangulation of 3-D polygons for resolving the unmatched parts, and a minimum spanning tree heuristic for interpolating between non simply connected regions. Unlike previous attempts at solving this problem, our algorithm seems to handle successfully any kind of data. It allows multiple contours in each slice, with any hierarchy of contour nesting, and avoids the introduction of counter-intuitive bridges between contours, proposed in some earlier papers to handle interpolation between multi...

The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized/sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of close-range laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results.

We describe a model based recognition system, called LEWIS, for the identification of planar objects based on a projectively invariant representation of shape. The advantages of this shape description include simple model acquisition (direct from images), no need for camera calibration or object pose computation, and the use of index functions. We describe the feature construction and recognition algorithms in detail and provide an analysis of the combinatorial advantages of using index functions. Index functions are used to select models from a model base and are constructed from projective invariants based on algebraic curves and a canonical projective coordinate frame. Examples are given of object recognition from images of real scenes, with extensive object libraries. Successful recognition is demonstrated despite partial occlusion by unmodelled objects, and realistic lighting conditions. 1 Introduction 1.1 Overview In the context of this paper, recognition is defined as the prob...

We study the 3D shape similarity between closed surfaces. We represent a curved or polyhedral 3D object of genus zero using a mesh representation that has nearly uniform distribution with known connectivity among mesh nodes. We define a shape similarity metric based on the L 2 distance between the local curvature distributions over the mesh representations of the two objects. For both convex and concave objects, the shape metric can be computed in time O(n 2 ), where n is the number of tessellation of sphere or the number of meshes which approximate the surface. Experiments show that our method produces good shape similarity measurements. Table of Content 1 Introduction 1 2 Representation of a Closed Surface 6 2.1 Discrete Representation of a Curve ..................................................................................... 6 2.2 Spherical Representation of a 3D Surface........................................................................... 6 2.3 3D Local Curvature:...

In this paper we present an algorithm for detecting and repairing defects in the boundary of a polyhedron. These defects, usually caused by problems in CAD software, consist of small gaps bounded by edges that are incident to only one polyhedron face. The algorithm uses a partial curve matching technique for matching parts of the defects, and an optimal triangulation of 3-D polygons for resolving the unmatched parts. It is also shown that finding a consistent set of partial curve matches with maximum score, a subproblem which is related to our repairing process, is NP-Hard. Experimental results on several polyhedra are presented. Keywords: CAD, polyhedra, gap filling, curve matching, geometric hashing, triangulation. 1 Introduction The problem studied in this paper is the detection and repair of "gaps" in the boundary of a polyhedron. This problem usually appears in polyhedral approximations of CAD objects, whose boundaries are described using curved entities of higher leve...

This paper describes a method to automatically generate the mapping between a completely labeled reference image and the 3D medical image of a patient. Toachieve this, we combined three techniques: the extraction of 3D feature lines, their matching using 3D deformable line models, the extension of the deformation to the whole image space using warping techniques. We present experimental results for the segmentation of structures in Magnetic Resonance images of the brain of different patients; the segmentation of the cortical and ventricle structures. We emphasize the advantages of using crest lines deformable models prior to surface based models. This gives a sparser representation of the data, easier to manipulate, and which makes the convergence of the model much less sensitive to initial positionning. In the future, we hope to use this method to generate anatomical atlases, by the automatic interpretation of large sets of 3D medical images.

In this paper we present a new technique for partial surface and volume matching of images in three dimensions. In this