The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recognition-by-components (RBC), is that a modest set of generalized-cone components, called geons (N ^ 36), can be derived from contrasts of five readily detectable properties of edges in a two-dimensional image: curvature, collinearity, symmetry, parallelism, and cotermmation. The detection of these properties is generally invariant over viewing position and image quality and consequently allows robust object perception when the image is projected from a novel viewpoint or is degraded. RBC thus provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition: The constraints toward regularization (Pragnanz) characterize not the complete object but the object's components. Representational power derives from an allowance of free combinations of the geons. A Principle of Componential Recovery can account for the major phenomena of object recognition: If an arrangement of two or three geons can be recovered from the input, objects can be quickly recognized even when they are occluded, novel, rotated in depth, or extensively degraded. The results from experiments on the perception of briefly presented pictures by human observers provide empirical support for the theory. Any single object can project an infinity of image configura-tions to the retina. The orientation of the object to the viewer can vary continuously, each giving rise to a different two-dimen-sional projection. The object can be occluded by other objects or texture fields, as when viewed behind foliage. The object need not be presented as a full-colored textured image but in-stead can be a simplified line drawing. Moreover, the object can even be missing some of its parts or be a novel exemplar of its

An iterative method for computing shape from shading using occluding boundary information is proposed. Some applications of this method are shown. We employ the stereographic plane to express the orientations of surface patches, rather than the more commonly.used gradient space. Use of the stereographic plane makes it possible to incorporate occluding boundary information, but forces us to employ a smoothness constraint different from the one previously proposed. The new constraint follows directly from a particular definition of surface smoothness. We solve the set of equations arising from the smoothness constraints and the image-irradiance equation iteratively, using occluding boundary information to supply boundary conditions. Good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution. Numerical experiments show that the method is effective and robust. Finally, we analyze scanning electron microscope (SEM) pictures using this method. Other applications are also proposed. 1.

We propose models of 3D shape which may be viewed as deformable bodies composed of simulated elastic material. In contrast to traditional, purely geometric models of shape, deformable models are active--their shapes change in response to externally applied forces. We develop a deformable model for 3D shape which has a preference for axial symmetry. Symmetry is represented even though the model does not belong to a parametric shape family such as (generalized) cylinders. Rather, a symmetry-seeking property is designed into internal forces that constrain the deformations of the model. We develop a framework for 3D object reconstruction based on symmetry-seeking models. Instances of these models are formed from monocular image data through the action of external forces derived from the data. The forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2D silhouette of an object of interest. The effectiveness of our approach is demonstrated using natural images. 1

Understanding how line drawings convey tri-dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too compex to model analytically. We put forward here a computational model for interpreting line drawings as three-dimensional surfaces, based on constraints on local surface orientation along extremal and discontinuity boundaries. Specific techniques are described for two key processes recovering the three-dimensional conformation of a space curve (e.g., a surface boundary) from its two-dimensional projection in an image, and interpolating smooth surfaces from orientation constraints along extremal boundaries. The relevance of the model to a general theory of low-level vision is discussed.

We have studied the mechanism of contour perception by recording from neurons in the visual cortex of alert rhesus monkeys. In order to assess the relationship between neural signals and perception, we compared the responses to edges and lines with the responses to patterns in which human observers perceive a contour where no line or edge is given (anomalous contour), such as the border between gratings of thin lines offset by half a cycle. With only one exception out of 60, orientation-selective neurons in area Vl did not signal the anomalous contour. Many neurons failed to re-spond to this stimulus at all, others responded according to the orientation of the grating lines. In area V2, 45 of 103 neurons (44%) signaled the orientation of the anomalous contour. Sixteen did so without signaling the orientation of the inducing lines. Some responded better to anomalous

Codons are simple primitives for describing plane curves. They thus are primarily image-based descriptors. Yet they have the power to capture important information about the 3D world, such as making part boundaries explicit, The codon description is highly redundant (useful for error-correction). This redundancy can be viewed as a constraint on tile number of possible codon strings, For smooth closed strings that represent the bounding contour (silhouette) of many smooth 3D objects, tile constraints are so strong that sequences containing 6 elements yield only 33 generic shapes as compared with possible number of 15,625 combinations.

this paper, we propose the short-cut rule, which states that, other things being equal, human vision prefers to use the shortest possible cuts to parse silhouettes. We motivate this rule, and the well-known Petters rule for modal completion, by the principle of transversality. We present five psychophysical experiments that test the short-cut rule, show that it successfully predicts part cuts which connect boundary points given by the minima rule, and show that it can also create new boundary points

Line drawings produced by contours traced on a surface can produce a vivid impression of the surface shape. The stability of this perception is notable considering that the information provided by the surface contours is quite ambiguous. We have studied the stability of line drawing perception from psychophysical and computational standpoints. For a given family of simple line drawings, human observers could perceive the drawings as depicting either an elliptic (egg-shaped) or hyperbolic (saddle-shaped) smooth surface patch. Rotation of the image along the line of sight and change in aspect ratio of the line drawing could bias the observer toward either interpretation. The results were modeled by a simple Bayesian observer that computes the probability to choose either interpretation given the information in the image and prior preferences. The model's decision rule is noncommitting: for a given input image its responses are still probabilistic, reflecting variability in the modeled observers' judgements. A good fit to the data was obtained when three observer assumptions were introduced: a preference for convex surfaces, a preference for surface contours aligned with the principal lines of curvature, and a preference for a surface orientation consistent with an object viewed from above. We discuss how these assumptions might reflect regularities of the visual world. 1998 Elsevier Science Ltd. All rights reserved.

We propose a strategy to decompose a polygon, containing zero or more holes, into “approximately convex” pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural features and ignore less significant artifacts such as wrinkles and surface texture. We propose a simple algorithm that computes an ACD of a polygon by iteratively removing (resolving) the most significant non-convex feature (notch). As a by product, it produces an elegant hierarchical representation that provides a series of ‘increasingly convex ’ decompositions. A user specified tolerance determines the degree of concavity that will be allowed in the lowest level of the hierarchy. Our algorithm computes an ACD of a simple polygon with n vertices and r notches in O(nr) time. In contrast, exact convex decomposition is NP-hard or, if the polygon has no holes, takes O(nr 2) time. Models and movies can be found on our web-pages at:

Profiles of a sculpture provide rich information about its geometry, and can be used for shape recovery under known camera motion. By exploiting correspondences induced by epipolar tangents on the profiles, a successful solution to motion estimation from profiles has been developed in the special case of circular motion. The main drawbacks of using circular motion alone, namely the difficulty in adding new views and part of the object always being invisible, can be overcome by incorporating arbitrary general views of the object and registering its new profiles with the set of profiles resulted from the circular motion. In this paper, we describe a complete and practical system for producing a 3D model from uncalibrated images of an arbitrary object using its profiles alone. Experimental results on various objects are presented, demonstrating the quality of the reconstructions using the estimated motion.