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

A Stochastic Modeling Approach to Region-and Edge-Based Image Segmentation

The purpose of image segmentation is to isolate objects in a scene from the background. This is a very important step in any computer vision system since various tasks, such as shape analysis and object recognition, require accurate image segmentation. Image segmentation can also produce tremendous data reduction. Edge-based and region-based segmentation have been examined and two new algorithms based on recent results in random field theory have been developed. The edge-based segmentation algorithm uses the pixel gray level intensity information to allocate object boundaries in two stages: edge enhancement, followed by edge linking. Edge enhancement is accomplished by maximum energy filters used in one-dimensional bandlimited signal analysis. The issue of optimum filter spatial support is analyzed for ideal edge models. Edge linking is performed by quantitative sequential search using the Stack algorithm. Two probabilistic search metrics are introduced and their optimality is proven and demonstrated on test as well as real scenes. Compared to other methods, this algorithm is shown to produce more accurate allocation of object boundaries. Region-based segmentation was modeled as a MAP estimation problem in which the actual (unknown) objects were estimated from the observed (known) image by a recursive classification algorithms. The observed image was modeled by an Autoregressive (AR) model whose parameters were estimated locally, and a Gibbs-Markov random field (GMRF) model was used to model the unknown scene. A computational study was conducted on images having various types of texture images. The issues of parameter estimation, neighborhood selection, and model orders were examined. It is concluded that the MAP approach for region segmentation generally works well on images having a large content of microtextures which can be properly modeled by both AR and GMRF models. On these texture images, second order AR and GMRF models were shown to be adequate

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