MultiscaleSurfaceOrganizationandDescription forFreeFormObjectRecognition Kim L. Boyer and Ravi Srikantiah Patrick J. Flynn Signal Analysis and Machine Perception Laboratory Department of Computer Science and Engineering The Ohio State University University of Notre Dame kim@ee.eng.ohio-state.edu flynn@nd.edu Abstract We introduce an efficient, robust means to obtain reliable surface descriptions, suitable for free form object recogni- tion, at multiple scales from range data. Mean and Gaussian curvatures are used to segment the surface into four saliency classes of based on curvature consistency as evaluated in a robust multivoting scheme. Contiguous regions consis- tent in both mean and Gaussian curvature are identified as the most homogeneous segments, followed by those consis- tent in mean curvature but not Gaussian curvature, followed by those consistent in Gaussian curvature only. Segments at each level of the hierarchy are extracted in the order of size, large to small, such that the most salient features of the surface are recovered first. This has potential for effi- cient object recognition by stopping once a just sufficient description is extracted. I. Introduction We have built a multiscale recognition system that de- scribes objects at successively higher resolutions until a suitable degree of discrimination is obtained 1 . This paper focuses on the surface organization technique. Mokhtar- ian et al. [1] and Zhang and Hebert [2] propose multiscale description techniques, both of which are computationally intensive. We propose a (pseudo)multiscale analysis based on curvature consistency criterion. Most prior work in region-based range image segmenta- tion, such as [3, 4, 5, 6, 7, 8], endeavors to classify surface regions into canonical types. The notion of curvature con- sistency has been explored by Sander and Zucker [9] and Ferrie, et al. [10]. Our approach differs in that we simply group contiguous patches of the surface having consistent curvature characteristics. This lends a measure of robust- ness and stability not heretofore attainable with free form objects. Attempts to segment these surfaces using standard models or surface types often leaves large regions either un- modeled, or broken into many small pieces conveying little or no real information about the surface. NB: The resolution of the range image is fixed; it is the resolution of our description of the surface that is adjusted. II. SurfaceOrganization Our algorithm extends the voting technique developed by Wuescher and Boyer [11] for extracting constant curva- ture segments in 2D edge maps. We partition the surface into four types of primitives in descending order of con- straint and saliency: 1. Segments having (nearly) constant mean and Gaus- sian curvatures ( – segments). These are the most homogeneous and, therefore, most salient of the seg- ment classes, for a given size. 2. Segments of (nearly) constant mean curvature only ( – segments). These are the next most salient seg- ments. 3. Segments of (nearly) constant Gaussian curvature only ( – segments). The saliency of these segments is essentially identical to those of constant mean cur- vature, except that the calculation of mean curvature is less noise-sensitive and, therefore, more reliable. 4. Segments for which both curvatures change rapidly ( – segments). These segments aren’t homogeneous; they are the “leftovers.” For a given hierarchical level, significance is ranked in decreasing order of segment size, i.e., largest segment first. A. CurvatureVoting: -Consistency With the mean and Gaussian curvatures ( and , re- spectively) calculated at each surface point, we next turn our attention to extracting contiguous regions that are con- sistent in both these measures. We begin by defining toler- ance windows and for the two curvatures such that, if: (1) then the points and on the surface may be grouped into the same constant curvature bin (a –bin). 1051-4651/02 $17.00 (c) 2002 IEEE