Shape Recognition: A Landmark-Based Approach

Shape recognition has applications in computer vision tasks such as industrial automated inspection and automatic target recognition. When objects are occluded, many recognition methods that use global information will fail. To recognize partially occluded objects, we represent each object by a Set of landmarks. The landmarks of an object are points of interest which have important shape attributes and are usually obtained from the object boundary. In this study, we use high curvature points along an object boundary as the landmarks of the object. Given a scene consisting of partially occluded objects, the hypothesis of a model object in the scene is verified by matching the landmarks of an object with those in the scene. A measure of similarity between two landmarks, one from a model and the other from a scene, is needed to perform this matching. One such local shape measure is the sphericity of a triangular transformation mapping the model landmark and its two neighboring landmarks to the scene landmark and its two neighboring landmarks. Sphericity is in general defined for a diffeomorphism. Its invariant properties under a group of transformation, namely, translation, rotation, and scaling are derived. The sphericity of a triangular transformation is shown to be a robust local shape measure in the sense that minor distortion in the landmarks does not significantly alter its value. To match landmarks between a model and a scene, a table of compatibility, where each entry of the table is the sphericity value derived from the mapping of a model landmark to a scene landmark, is constructed. A hopping dynamic programming procedure which switches between a forward and a backward dynamic programming procedure is applied to guide the landmark matching through the compatibility table. The location of the model in the scene is estimated with a least squares fit among the matched landmarks. A heuristic measure is then computed to decide if the model is in the scene

Invariant Reconstruction of Curves and Surfaces with Discontinuities with Applications in Computer Vision

The reconstruction of curves and surfaces from sparse data is an important task in many applications. In computer vision problems the reconstructed curves and surfaces generally represent some physical property of a real object in a scene. For instance, the sparse data that is collected may represent locations along the boundary between an object and a background. It may be desirable to reconstruct the complete boundary from this sparse data. Since the curves and surfaces represent physical properties, the characteristics of the reconstruction process differs from straight forward fitting of smooth curves and surfaces to a set of data in two important areas. First, since the collected data is represented in an arbitrarily chosen coordinate system, the reconstruction process should be invariant to the choice of the coordinate system (except for the transformation between the two coordinate systems). Secondly, in many reconstruction applications the curve or surface that is being represented may be discontinuous. For example in the object recognition problem if the object is a box there is a discontinuity in the boundary curve at the comer of the box. The reconstruction problem will be cast as an ill-posed inverse problem which must be stabilized using a priori information relative to the constraint formation. Tikhonov regularization is used to form a well posed mathematical problem statement and conditions for an invariant reconstruction are given. In the case where coordinate system invariance is incorporated into the problem, the resulting functional minimization problems are shown to be nonconvex. To form a valid convex approximation to the invariant functional minimization problem a two step algorithm is proposed. The first step forms an approximation to the curve (surface) which is piecewise linear (planar). This approximation is used to estimate curve (surface) characteristics which are then used to form an approximation of the nonconvex functional with a convex functional. Several example applications in computer vision for which the invariant property is important are presented to demonstrate the effectiveness of the algorithms. To incorporate the fact that the curves and surfaces may have discontinuities the minimizing functional is modified. An important property of the resulting functional minimization problems is that convexity is maintained. Therefore, the computational complexity of the resulting algorithms are not significantly increased. Examples are provided to demonstrate the characteristics of the algorithm

Sequential Detection of Linear Features in Two-Dimensional Random Fields

The detection of edges, lines, and other linear features in two-dimensional discrete images is a low level processing step of fundamental importance in the automatic processing of such data. Many subsequent tasks in computer vision, pattern recognition, and image processing depend on the successful execution of this step. In this thesis, we will address one class of techniques for performing this task: sequential detection. Our aims are fourfold. First, we would like to discuss the use of sequential techniques as an attractive alternative to the somewhat better known methods of approaching this problem. Although several researchers have obtained significant results with sequential type algorithms, the inherent benefits of a sequential approach would appear to have gone largely unappreciated. Secondly, the sequential techniques reported to date appear somewhat lacking with respect to a theoretical foundation. Furthermore, the theory that is advanced incorporates rather severe restrictions on the types of images to which it applies, thus imposing a significant limitation to the generality of the method(s). We seek to advance a more general theory with minimal assumptions regarding the input image. A third goal is to utilize this newly developed theory to obtain quantitative assessments of the performance of the method. This important step, which depends on a computational theory, can answer such vital questions as: Are assumptions about the qualitative behavior of the method justified? How does signal-to-noise ratio impact its behavior? How fast is it? How accurate? The state of theoretical development of present techniques does not allow for this type of analysis. Finally, a fourth aim is to\u27 extend the earlier results to include correlated image data. Present sequential methods as well as many non-sequential methods assume that the image data is uncorrelated and cannot therefore make use of the mutual information between pixels in real-world images. We would like to extend the theory to incorporate correlated images and demonstrate the advantages incurred by the use of the existing mutual information. The topics to be discussed are organized in the following manner. We will first provide a rather general discussion of the problem of detecting intensity edges in images. The edge detection problem will serve as the prototypical problem of linear feature extraction for much of this thesis. It will later be shown that the detection of lines, ramp edges, texture edges, etc. can be handled in similar fashion to intensity edges, the only difference being the nature of the preprocessing operator used. The class of sequential techniques will then be introduced, with a view to emphasize the particular advantages and disadvantages exhibited by the class. This Chapter will conclude with a more detailed treatment of the various sequential algorithms proposed in the literature. Chapter 2 then develops the algorithm proposed by the author, Sequential Edge Linking or SEL. It begins with some definitions, follows with a derivation of the critical path branch metric and some of its properties, and concludes with a discussion of algorithms. The third Chapter is devoted exclusively to an analysis of the dynamical behavior and performance of the method. \u27 Chapter 4 then deals with the case of correlated random fields. In that Chapter, a model is proposed for which paths searched by the SEL algorithm are shown to possess a well-known autocorrelation function. This allows the use of a simple linear filter to decorrelate the raw image data. Finally, Chapter 5 presents a number of experimental results and corroboration of the theoretical conclusions of earlier Chapters. Some concluding remarks are also included in Chapter 5