We present a new type of "snake" in which the dimensionality of the shapes is scaled appropriately for the resolution of the images in which the shapes are embedded. We define shapes as an ordered list of control points and compute the principal components of the shapes in a prior training set. Our energy function is based upon the Mahalanobis distance of a given shape from the mean shape and on the Mahalanobis distance of the image attributes from image attribute values extracted from the training set. We show that the derivative of this energy function with respect to the modal weights is reduced as the image resolution is reduced, and that the derivative of the energy scales with the variance associated with each mode. We exploit this property to determine the subset of the modes which are relevant at a particular level of image resolution thereby reducing the dimensionality of the shapes. We implement a coarse-to-fine search procedure in the image and shape domains simultaneously, and demonstrate this procedure on the identification of anatomic structures in Computed Tomography images.

Junctions are important features for image analysis and form a critical aspect of image understanding tasks such as object recognition. We present a unified approach to detecting, classifying, and reconstructing junctions in images. Our main contribution is a modeling of the junction which is complex enough to handle all these issues and yet simple enough to admit an effective dynamic programming solution. We use a template deformation framework along with a gradient criterium to detect radial partitions of the template. We use the minimum description length principle to obtain the optimal number of partitions that best describes the junction. The Kona detector presented by Parida et al. (1997) is an implementation of this model. We demonstrate the stability and robustness of the detector by analyzing its behavior in the presence of noise, using synthetic/controlled apparatus. We also present a qualitative study of its behavior on real images.

We study the problem of how to detect "interesting objects" appeared in a given image, I. Our approach is to treat it as a function approximation problem based on an over-redundant basis, and also account for occlusions, where the basis superposition principle is no longer valid. Since the basis (a library of image templates) is over-redundant, there are infinitely many ways to decompose I. We are motivated to select a sparse/compact representation of I, and to account for occlusions and noise. We then study a greedy and iterative "weighted L/sup p/ Matching Pursuit" strategy, with O<p<1. We use an L/sup p/ result to compute a solution, select the best template, at each stage of the pursuit.

Reasoning with uncertainty is a field with many different approaches and viewpoints, with important applications to sensor design and autonomous system development. It is important to have calculi for propagating measures of "probability" or "likelihood" even in cases of subjective information, and it is just as important to be able to propagate the "certitude" of this information. By choosing the semantics properly, this information can be handled by keeping track of certain statistics on a different probability space, (which we call the opinion space). The semantics assume that the "likelihood" or "probability numbers" are in fact averages over many (perhaps subjective) opinions and that uncertainty is represented by the spread in these opinions, which can be technically maintained by a covariance matrix. Different calculi result from different design choices consistent with this choice of semantics. It also turns out that certain mechanisms that are frequently considered "non-Bayesian", result from specific choices for representing the statistics and dependency assumptions.

Geometric hashing methods provide an efficient approach to indexing from image features into a database of models. The hash functions that have typically been used involve quantization of the values, which can result in nongraceful degradation of the performance of the system in the presence of noise. Intuitively, it is desirable to replace the quantization of hash values and the resulting binning of hash entries by a method that gives increasingly less weight to a hash table entry as a hashed feature becomes more distant from the hash entry position. In this paper, we show how these intuitive notions can be translated into a well-founded Bayesian approach to object recognition and give precise formulas for the optimal weight functions that should be used in hash space. These extensions allow the geometric hashing method to be viewed as a Bayesian maximum-likelihood framework. We demonstrate the validity of the approach by performing similarity-invariant object recognition using models obtained from drawings of military aircraft and automobiles and test images from real-world grayscale images of the same aircraft and automobile types. Our experimental results represent a complete object recognition system, since the feature extraction process is automated. Our system is scalable and works rapidly and very efficiently on an 8K-processor CM - 2, and the quality of results using similarity-invariant model matching is excellent.

Beginning with digitized volumetric data, we wish to rapidly and efficiently extract and represent surfaces defined as isosurfaces in the interpolated data. The Marching Cubes algorithm is a standard approach to this problem. We instead perform a decomposition of each 8-cell associated with a voxel into five tetrahedra. We guarantee the resulting surface representation to be closed and oriented, defined by a valid triangulation of the surface of the body, which in turn is presented as a collection of tetrahedra. The entire surface is "wrapped" by a collection of triangles, which form a graph structure, and where each triangle is contained within a single tetrahedron. The representation is similar to the homology theory that uses simplices embedded in a manifold to define a closed curve within each tetrahedron. We introduce data structures based upon a new encoding of the tetrahedra that are at least four times more compact than the standard data structures using vertices and triangles. For parallel computing and improved cache performance, the vertex information is stored local to the tetrahedra. We can distribute the vertices in such a way that no tetrahedron ever contains more than one vertex, We give methods to evaluate surface curvatures and principal directions at each vertex, whenever these quantities are defined. Finally, we outline a method for simplifying the surface, that is reducing the vertex count while preserving the geometry. We compare the characteristics of our methods with an 8-cell based method, and show results of surface extractions from CT-scans and MR-scans at full resolution.

A new paradigm for performing realistic object recognition is presented. It is shown how several intuitive notions in the context of geometric hashing can be translated into a well-founded Bayesian approach to object recognition. This interpretation leads to well-justified formulas and gives a precise weighted-voting method for the evidence-gathering phase of geometric hashing. A computational model for performing object recognition in a distributed fashion is described. The validity of the authors' paradigm is demonstrated by presenting a prototype system that has been implemented on a small cluster of nondedicated workstations. The resulting system is scalable and can recognize models subjected to 2-D rotation, translation and scale changes in real-world digital imagery. The performance of the system is superior by a factor of 2 to that obtained for a similar system on the Connection Machine-2 (CM-2).>

The Dempster Sharer theory of evidence concerns the elicitation and manipulation of degrees of belief rendered by multiple sources of evidence to a common set of propositions. Information indexing and retrieval applications use a variety of quantitative means—both probabilistic and quasi-probabilistic—to represent and manipulate relevance numbers and index vectors. Recently, several proposals were made to use the Dempster Shafer model as a relevance calculus in such applications. This paper provides a critical review of these proposals, pointing at several theoretical caveats and suggesting ways to resolve them. The methodology is based on expounding a canonical indexing model whose relevance measures and combinations mechanisms are shown to be isomorphic to Shafer's belief functions and to Dempster's rule, respectively. Hence, the paper has two objectives: (i) to describe and resolve some caveats in the way the Dempster Shafer theory is applied to information indexing and retrieval, and (ii) to provide an intuitive interpretation of the Dempster Shafer theory, as it unfolds in the simple context of a canonical indexing model.

Presented are two methods for the determination of the parameters of motion of a sensor, given the vector flow field induced by an imaging system governed by a perspective transformation of a rigid scene. Both algorithms integrate global data to determine motion parameters. The first (the flow circulation algorithm) determines the rotational parameters. The second (the FOE search algorithm) determines the translational parameters of the motion independently of the first algorithm. Several methods for determining when the function has the appropriate form are suggested. One method involves filtering the function by a collection of circular-surround zero-mean receptive fields. The other methods project the function onto a linear space of quadratic polynomials and measures the distance between the two functions. The error function for the first two methods is a quadratic polynomial of the candidate position, yielding a very rapid search strategy.>

Consider two wire gratings, superimposed and moving across each other. Under certain conditions the two gratings will cohere into a single, compound pattern, which will appear to be moving in another direction. Such coherent motion patterns have been studied for sinusoidal component gratings, and give rise to percepts of rigid, planar motions. In this paper we show how to construct coherent motion displays that give rise to nonuniform, nonrigid, and nonplanar percepts. Most significantly, they also can define percepts with corners. Since these patterns are more consistent with the structure of natural scenes than rigid sinusoidal gratings, they stand as interesting stimuli for both computational and physiological studies. To illustrate, our display with sharp corners (tangent discontinuities or singularities) separating regions of coherent motion suggests that smoothing does not cross tangent discontinuities, a point that argues against existing (regularization) algorithms for computing motion. This leads us to consider how singularities can be confronted directly within optical flow computations, and we conclude with two hypotheses: (1) that singularities are represented within the motion system as multiple directions at the same retinotopic location; and (2) for component gratings to cohere, they must be at the same depth from the viewer. Both hypotheses have implications for the neural computation of coherent motion.

The authors provide a perspective and interpretation regarding the Dempster-Shafer theory of evidence that regards the combination formulas as statistics of the opinions of experts. This is done by introducing spaces with binary operations that are simpler to interpret or simpler to implement than the standard combination formula, and showing that these spaces can be mapped homomorphically onto the Dempster-Shafer theory-of-evidence space. The experts in the space of opinions-of-experts combine information in a Bayesian fashion. Alternative spaces for the combination of evidence suggested by this viewpoint are presented.>

A large class of problems can be formulated in terms of the assignment of labels to objects. Frequently, processes are needed which reduce ambiguity and noise, and select the best label among several possible choices. Relaxation labeling processes are just such a class of algorithms. They are based on the parallel use of local constraints between labels. This paper develops a theory to characterize the goal of relaxation labeling. The theory is founded on a definition of con-sistency in labelings, extending the notion of constraint satisfaction. In certain restricted circumstances, an explicit functional exists that can be maximized to guide the search for consistent labelings. This functional is used to derive a new relaxation labeling operator. When the restrictions are not satisfied, the theory relies on variational cal-culus. It is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality. A procedure nearly identical to the relaxation operator derived under restricted circum-stances serves in the more general setting. Further, a local convergence result is established for this operator. The standard relaxation labeling formulas are shown to approximate our new operator, which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here. Observations about con-vergence and generalizations to higher order compatibility relations are described.

We consider a particular problem which arises when apply-ing the method of gradient projection for solving constrained optimiza-tion and finite dimensional variational inequalities on the convex set formed by the convex hull of the standard basis unit vectors. The method is especially important for relaxation labeling techniques applied to problems in artificial intelligence. Zoutendijk's method for finding feasible directions, which is relatively complicated in general situations, yields a very simple finite algorithm for this problem. We present an extremely simple algorithm for performing the gradient projection and an independent verification of its correctness.

Modern scanning techniques, such as computed tomography, have begun to produce true three-dimensional imagery of internal structures. The first stage in finding structure in these images, like that for standard two-dimensional images, is to evaluate a local edge operator over the image. If an edge segment in two dimensions is modeled as an oriented unit line segment that separates unit squares (i.e., pixels) of different intensities, then a three-dimensional edge segment is an oriented unit plane that separates unit volumes (i.e., voxels) of different intensities. In this correspondence we derive an operator that finds the best oriented plane at each point in the image. This operator, which is based directly on the 3-D problem, complements other approaches that are either interactive or heuristic extensions of 2-D techniques.

A relaxation process is described and is applied to the detection of smooth lines and curves in noisy, real world images. There are nine labels associated with each image point, eight labels indicating line segments at various orientations and one indicating the no-line case. Attached to each label is a probability. In the relaxation process, interaction takes place among the probabilities at neighboring points. This permits line segments in compatible orientations to strengthen one another, and incompatible segments to weaken one another. Similarly, no-line labels are reinforced by neighboring no-line labels and weakened by appropriately oriented line labels. This process converges, in only a few iterations, to a condition in which points lying on long curves have achieved high line probabilities, while other points have high no-line probabilities, There is some tendency, under this process, for curves to thicken; however, a thinning procedure can be incorporated to counteract this. The process is effective even for curves of low contrast, and even when many curves lie close to one another.

Given a set of objects in a scene whose identifications are ambiguous, it is often possible to use relationships among the objects to reduce or eliminate the ambiguity. A striking example of this approach was given by Waltz [13]. This paper formulates the ambiguity-reduction process in terms of iterated parallel operations (i.e., relaxation operations) performed on an array of (object, identification) data. Several different models of the process are developed, convergence properties of these models are established, and simple examples are given.