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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 17, NO. 5, MAY 1995 539 Silhouette-Based Isolated Object Recognition through Curvature.Scale Space Farzin Mokhtarian Abstrac-A complete, fast and practical isolated object recognition sys- tem has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deforma- tions of shape (due to perspective projection, segmentation errors and non- rigid material used in some objects). The system has been tested on a wide variety of three-dimensional objects with different shapes and material and surface properties. A light-box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave. Convex curves are recognized using their four high-scale curvature extrema points. Curvature Scale Space (CSS) Representations are computed for concave curves. The CSS represen- tation is a multi-scale organization of the natural, invariant features of a curve (curvature zero-crossings or extrema) and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects. A three-stage, coarse-to-fine matching algorithm prunes the search space in stage one by applying the CSS aspect ratio test. The maxima of contours in CSS representations of the surviving models are used for fast CSS matching in stage two. Finally, stage three verifies the best match and resolves any ambiguities by determining the distance be- tween the image and model curves. Transformation parameter optimization is then used to find the best fit of the input object to the correct model. Zndex Term- Object recognition system, light-box setup, boundary contours, curvature scale space representation, maxima of curvature zero- crossing contours, coarse-to-fine matching strategy, transformation pa- rameter optimization. I. INTRODUCTION Object representation and recognition is one of the central problems in computer vision. Normally, a reliable, working vision system must be able to I) effectively segment the image and 2) recognize objects in the image using their representations. This paper describes a complete, working vision system [8] which segments the image effectively using a light-box setup and recognizes isolated objects in the image reliably using their curvature scale spk (CSS) representations [6], [7]. The CSS representation is based on the scale space image concept intro- duced in [lo] and popularized by Witkin [14]. It is an organization of curvature zero-crossing points on a contour at multiple scales. Note that an earlier CSS matching algorithm was implemented and tested in [6]. That algorithm was designed for both open and closed contour matching, made assumptions about the CSS image which were not always valid and was relatively slow. The CSS matching algorithm described in this paper in an improved, more efficient version of the earlier algorithm which has been designed specifically for closed con- tour matching. It is assumed that the recognition system developed here may be used for recognition of isolated 3D objects. In particular, it is assumed that objects are placed one at a time on a light-box in front of a camera (by a robot arm, for example) and that the task is to recognize each object. This particular task is believed to be interesting for the following reasons: 1) Despite the constraints placed on the environment, no constraints have been placed on object shapes or types. Furthermore, envi- ronment constraints are not difficult to satisfy in many object rec- ognition tasks (such as in industrial settings). 2) Every 3D object, when placed on a flat surface and viewed by a fixed camera, has a limited number of stable positions, each of Manuscript received June 7,1993; revised April 28,1994. F. Mokhtarian is with the Department of Electronic and Electrical Engineer- ing, University of Surrey, Guildford, Surrey, GU2 5XH, United Kingdom; e- mail: [email protected]. IEEECS Log Number P95054. which can be modeled using a 2D contour. 3) Even with only one object present on the light-box at a time, rec- ognition can become challenging due to arbitrary shapes of ob- jects, noise, and local deformations of shape which can be caused by perspective projection, segmentation errors and the non-rigid material used in some objects. 4) By considering only complete contour matching, a matching al- gorithm has been developed which is believed to be optimal for that particular task. The existing literature on shape representation and recognition is quite large. Many methods are intended to be utilized on occluded scenes. There are also techniques designed for isolated object recogni- tion. Examples are Fourier descriptors [9], [12], the circular harmonic expansion [l] and moment invariants [2], [3], [l 11. One shortcoming of those techniques is that noise is not removed prior to the feature extrac- tion process. As a result, only the first few low-frequency coefficients (or low-order moments) may be reliable for matching. This results in a coarse shape discrimination ability but would make it difficult to distin- guish between objects with relatively small differences in shape. Fur- thermore, all techniques mentioned above compute global features of the input shapes and have no local support. Therefore local shape dis- tortions cause global changes in the computed coefficients or moments. Another shortcoming is the difficulty of recovering the transformation parameters and point correspondences on the original contours. These would be useful to register those contours and verify that the correct match has been found or to choose between two or more close matches. The following is the organization of the remaining sections of this paper. Section I1 explains the preprocessing carried out before matching starts. Section 111 describes a fast CSS matching algorithm. Section IV describes the verification steps taken after CSS matching. Section V gives an overall view of the implemented recognition system. Section VI presents the results and an evaluation of the system. Section VI1 contains the concluding remarks. 11. PREPROCESSING This section describes the computations carried out by the system before matching begins. It consists of image segmentation, the curva- ture


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UT CS 395T - Lecture notes

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