A Symbolic Representation for 3-D Object Feature Detection Pamela J. Neal Department of Electrical Engineering U.S. Air Force Academy, Colorado pamela.neal@usafa.af.mil Linda G. Shapiro Department of Computer Science University of Washington Seattle, Washington shapiro@cs.washington.edu Abstract In this paper we define a spatial symbolic model that can be used to describe classes of 3-D objects (anatomical and man-made) and a method for finding correspondences be- tween the features of the symbolic models and point sets of 3-D mesh data. An abstract symbolic model is used to de- scribe spatial object classes in terms of parts, boundaries, and spatial associations. A working model is a mechanism to link the symbolic model to geometric information found in a sensed instance of the class, represented by a 3D mesh data set. Matching is performed in a three-step procedure that first finds working sets of points in the mesh, then fits constructed features to these sets, and finally selects a sub- set of these constructed features that best correspond to the features of the working model. 1. Introduction The goal of this paper is to develop a new method to match a symbolic 3D object model that represents a generic class of objects to sensed 3D data from an instance of that class. Even if the identity of the object is already known, identifying the occurrence of the features that are known to be present in such an object can be useful for locating the object in 3D space and for providing named landmarks to be used in further processing. Location and identification of such features can be used in a variety of applications, such as object reconstruction, telerobotic operations, and medi- cal informatics. Use of symbolic models of 3-D objects is often found in the field of artificial intelligence. The models are generally used in reasoning, and sometimes lack a real connection to a physically existing object [4]. Our model has two levels; a purely symbolic level that is useful for reasoning about an object and an intermediate level which contains physi- cal constraints that enable us to tie real object data to the high-level model. In this way, we are able to use reason- ing about the object to identify the real features in the mesh representation of the object. In computer vision, parameterized models are most of- ten the model of choice. Ideal parameters are stored in the model database. The range information is processed in a prescribed manner to produce similar parameters, then the data and model parameters are matched. This an oversim- plification of the process, but is sufficient to illustrate one of the main problems with this type of representation: a differ- ent model must be generated and stored for each individual object desired to be recognized. In our methodology, only one model is needed for each class of object. Our goal is twofold: 1) to design a symbolic representa- tion of three-dimensional object classes that can be used to represent generic objects in a variety of applications, and 2) to design and implement a matching procedure that can find correspondences between symbolic model features and 3D mesh data. To accomplish these goals, we develop a sym- bolic model for three-dimensional object classes and use knowledge of an object in a new, two-step, bottom-up/top- down approach to assist in matching a three-dimensional mesh representation of the object to the symbolic model. This information can be useful for many applications, some of which are: 1. More accurate and aesthetically pleasing reconstruc- tion of an object. 2. Reconstruction from incomplete data. 3. Identification of features in medical images. 4. Recognition of objects in a limited environment. Our new methodology uses symbolic models to repre- sent 3-dimensional object classes. Symbolic representation of spatial information is not new. In [4], Hernandez presents an entire system based on qualitative spatial knowledge to describe 2D spatial objects and relationships. He proposes a way to extend his system to describe 3D objects based on volumetric primitives. He also provides a comprehensive survey of other work in the area of qualitative spatial repre- sentation. The approaches surveyed in this work have one thing in common; they use the qualitative representation for reasoning about spatial objects, but do not try to tie the qual- itative model to any particular instance of an object. Other