A computer vision system has been implemented that can recognize threedimensional objects from unknown viewpoints in single gray-scale images. Unlike most other approaches, the recognition is accomplished without any attempt to reconstruct depth information bottom-up from the visual input. Instead, three other mechanisms are used that can bridge the gap between the two-dimensional image and knowledge of three-dimensional objects. First, a process of perceptual organization is used to form groupings and structures in the image that are likely to be invariant over a wide range of viewpoints. Second, a probabilistic ranking method is used to reduce the size of the search space during model based matching. Finally, a process of spatial correspondence brings the projections of three-dimensional models into direct correspondence with the image by solving for unknown viewpoint and model parameters. A high level of robustness in the presence of occlusion and missing data can be achieved through full application of a viewpoint consistency constraint. It is argued that similar mechanisms and constraints form the basis for recognition in human vision. This paper has been published in Artificial Intelligence, 31, 3 (March 1987), pp. 355–395. 1 1

Model-based recognition and motion tracking depends upon the ability to solve for projection and model parameters that will best fit a 3-D model to matching 2-D image features. This paper extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulations, variable dimensions, or surface deformations. Numerical

In this paper we study the ways in which the topology of the image of a polyhedron changes with changing viewpoint. We catalog the ways that the topological appearance, or aspect, can change. This enables us to find maximal regions of viewpoints of the same aspect. We use these techniques to construct the viewpoint space partition (VSP), a partition of viewpoint space into maximal regions of constant aspect, and its dual, the aspect graph. In this paper we present tight bounds on the maximum size of the VSP and the aspect graph and give algorithms for their construction, first in the convex case and then in the general case. In particular, we give bounds on the maximum size of Q(n 2 ) and Q (n 6 ) under an orthographic projection viewing model and of Q(n 3 ) and Q(n 9 ) under a perspective viewing model. The algorithms make use of a new representation of the appearance of polyhedra from all viewpoints, called the aspect representation or asp. We believe that this representation...

We have developed an algorithm for computing the aspect graph for polyhedral objects, The aspect graph is a representation of 3-D objects by a set of 2-D views. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region the quali- tative structure of the line drawing remains the same. At the boundaries between adjacent regions are the accidental viewpoints where the structure of the line drawing changes--a visual event occurs. We show lhat for polyhedral objects there are two fundamental visual events: 1) the projections of an edge and a vertex coincide, and 2) the projections of three nonadjacent edges intersect at a point. The geometry of the object is reflected in the locus of the accidental viewpoints--the boundaries of the partition. The algorithm compute the partition together with a representative view for each region of the partition. In the course of presenting the algorithm, we provide a full catalog of the changes that occur in the views during each fundamental event.

Abstract-This paper introduces an analytical framework for studying some properties of model acquisition and recognition techniques based on indexing. The goal is to demonstrate that several problems previously associated with the approach can be attributed to the low dimensionality of invariants used. These include limited index selectivity, excessive accumulation of votes in the look-up table buckets, and excessive sensitivity to quantization parameters. Theoretical results demonstrate that using high-dimensional, highly descriptive global invariants produces better results in terms of accuracy, false positive suppression, and computation time. A practical example of high-dimensional global invariants is introduced and used to implement a 2-D shape acquisitionhecognition system. The acquisitiodrecognition system is based on a two-step table look-up mechanism. First, local curve descriptors are obtained by correlating image contour information at short range. Then, seven-dimensional global invariants are computed by correlating triplets of local curve descriptors at longer range. This experimental system is meant to illustrate the behavior of a high-dimensional indexing scheme. Indeed, its performance shows good agreement with the analytical model with respect to database size, fault tolerance, and recognition speed. Model acquisition time is linear to cubic in the number of object features. Object recognition time is constant to linear in the number of models in the database and linear to cubic in the number of features in the image. The system has been tested extensively, with more than 250 arbitrary shapes in the database. Unsupervised shape and subpart acquisition is demonstrated. I.

We survey the main ideas behind recent research in model-based object recognition. The survey covers representations for models and images and the methods used to match them. Perceptual organization, the use of invariants, indexing schemes, and match verification are also reviewed. We conclude that there is still much room for improvement in the scope, robustness, and efficiency of object recognition methods. We identify what we believe are the ways improvements will be achieved. ii Contents 1. Introduction .................................................................................................................................... 1 2. Representation ................................................................................................................................ 3 2.1 What makes a good shape representation? ............................................................................ 3 2.2 The choice of coordinate system ..........................................

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...

Ahsrrucr-The two factors that determine the time complexity associated with model-driven interpretation of range maps are: 1) the particular strategy used for the generation of object hypotheses; and 2) the manner in which both the model and the sensed data are organized, data organization being a primary determinant of the efficiency of verification of a given hypothesis. 3D-POLY, a working system for recognizing objects in the presence of occlusion and against cluttered backgrounds is presented. The time complexity of this system is only O ( n *) for single object recognition, where 17 is the number of features on the object. The most novel aspect of this system is the manner in which the feature data are organized for the models; we use a data structure called the feature sphere for the purpose. Efficient constant time algorithms for assigning a feature to its proper place on a feature sphere and for extracting the neighbors of a given feature from the feature sphere representation are present. For hypothesis generation, we use local feature sets, a notion similar to those used before us by Rolles, Shirai and others. The combination of the feature sphere idea for streamlining verification and the local feature sets for hypothesis generation results in a system whose time complexity has a low-order polynomial bound. I.

The systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years. Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpoint. This problem is entirely avoided if the geometric description is unaffected by the imaging transformation. Such invariant descriptions can be measured from images without any prior knowledge of the position, orientation and calibration of the camera. These invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification. Object models can be acquired directly from images, allowing efficient construction of model libraries without manual intervention. A significant part of the paper is a summary of recent results on the construction of ...

Determining the identity and pose of occluded objects from noisy data is a critical part of a system's intelligent interaction with an unstructured environment. Previous work has shown that local measurements of the position and surface orientation of small patches of an object's surface may be used in a constrained search process to solve this problem, for the case of rigid polygonal objects using two-dimensional sensory data, or rigid polyhedral objects using three-dimensional data. This note extends the recognition system to deal with the problem of recognizing and locating curved objects. The extension is done in two dimensions, and applies to the recognition of two-dimensional objects from two-dimensional data, or to the recognition of three-dimensional objects in stable positions from two-dimensional data.