Alok Gupta

Segmentation of range images as the search for geometric parametric models

Segmentation of range images has long been considered in computer vision as an important but extremely difficult problem. In this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces. Data aggregation is performed via model recovery in terms of variable-order bi-variate polynomials using iterative regression. Model recovery is initiated independently in regularly placed seed regions in the image. All the recovered models are potential candidates for the final description of the data. Selection of the models is defined as a quadratic Boolean problem, and the solution is sought by the WTA (winner-takes-all) technique, which turns out to be a good compromise between the speed of computation and the accuracy of the solution. The overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way. Partial recovery of the models is followed by the selection (optimization) procedure and only the “best” models are allowed to develop further.The major novelty of the approach lies in an effective combination of simple component algorithms, which stands in contrast to methods which attempt to solve the problem in a single processing step using sophisticated means. We present the results on several real range images.

Segmentation as the search for the best description of the image in terms of primitives

A paradigm is presented for the segmentation of images into piecewise continuous patches. Data aggregation is performed via model recovery in terms of variable-order bivariate polynomials using iterative regression. All the recovered models are candidates for the final description of the data. Selection of the models is achieved through a maximization of the quadratic Boolean problem. The procedure can be adapted to prefer certain kinds of descriptions (one which describes more data points, or has smaller error, or has a lower order model). A fast optimization procedure for model selection is discussed. The approach combines model extraction and model selection in a dynamic way. Partial recovery of the models is followed by the optimization (selection) procedure where only the best models are allowed to develop further. The results are comparable with the results obtained when using the selection module only after all the models are fully recovered, while the computational complexity is significantly reduced. The procedure was tested on real range and intensity images.<<ETX>>

Segmentation versus object representation—are they separable?

When vision is used for moving through the environment, for manipulating or for recognizing objects, it has to simplify the visual input to the level that is required for the specific task. To simplify means to partition images into entities that correspond to individual regions, objects and parts in the real world and to describe those entities only in detail sufficient for performing a required task. For visual discrimination, shape is probably the most important property. After all, line drawings of scenes and objects are usually sufficient for description and subsequent recognition. In computer vision literature this partitioning of images and description of individual parts is called segmentation and shape representation. Segmentation and shape representation appear to be distinct problems and are treated as such in most computer vision systems. In this paper we try to disperse this notion and show that there is no clear division between segmentation and shape representation. Solving any one of those two problems separately is very difficult. On the other hand, if any one of the two problems is solved first, the other one becomes much easier. For example, if the image is correctly divided into parts, the subsequent shape description of those parts gets easier. The opposite is also true when the shapes of parts are known, the partitioning of the image gets simpler.

Optimal polyline tracking for artery motion compensation in coronary angiography

We propose a novel solution to the problem of motion compensation of coronary angiographs. As the heart is beating, it is difficult for the physician to observe closely a particular point (e.g. stenosis) on the artery tree. We propose, to rigidly compensate the sequence so that the area around the point of interest appears stable. This is a difficult problem because the arteries deform in a non-rigid manner and only their 2D X-ray projection is observed. Also, the lack of features around the selected point makes the matching subject to the aperture problem. The algorithm automatically extracts a section of the artery of interest, models it as a polyline, and tracks it. The problem is formulated as an energy minimization problem which is solved using a shortest path in a graph algorithm. The motion compensated sequence can be obtained by translating every pixel so that the point of interest remains stable. We have applied this algorithm to many examples in two sets of angiography data and have obtained excellent results.

Quantitative and qualitative measures for the evaluation of the superquadric models

Evaluation criteria for superquadric models recovered from the range data discussed. Arguments are presented to support the authors belief that both quantitative and qualitative measures are required in order to evaluate a superquadric fit. The concept of superquadric contraction and dilation is introduced and used to derive a novel interpretation of the modified superquadric inside-outside function in terms of contraction/expansion factor. The same concept also gives a close initial guess for the numerical procedure computing the minimum Euclidean distance of a point from a superquadric model. The minimum Euclidean distance map is introduced as a qualitative criterion for interpretation of fit. View-dependent qualitative measures like the contour-difference map and the Z-distance map are shown to be essential for the complete evaluation of the models. Analytical solution and techniques for the contour generator on superquadric models are presented. Finally, examples of real objects are given to generate the measures.<<ETX>>

A cooperative framework for segmentation using 2D active contours and 3D hybrid models as applied to branching cylindrical structures

Hybrid models are powerful tools for recovery in that they simultaneously provide a gross parametric as well as a detailed description of an object. However, it is difficult to directly employ hybrid models in the segmentation process since they are not guaranteed to locate the optimal boundaries in cross-sectional slices. Propagating 2D active contours from slice to slice, on the other hand, to delineate an objects boundaries is often effective, but may run into problems when the objects topology changes, such as at bifurcations or even in areas of high curvature. Here, we present a cooperative framework to exploit the positive aspects of both 3D hybrid model and 2D active contour approaches for segmentation and recovery. In this framework the user-defined parametric component of a 3D hybrid model provides constraints for a set of 2D segmentations performed by active contours. The same hybrid model is then fit both parametrically and locally to this segmentation. For the hybrid model fit we employ several new variations on the physically-motivated paradigm which seek to speed recovery while guaranteeing stability. A by-product of these variations is an increased generality of the method via the elimination, of some of its ad hoc parameters. We apply our cooperative framework to the recovery of branching cylindrical structures from 3D image volumes. The hybrid model we employ has a novel parametric component which is a fusion of individual cylinders. These cylinders have spines that are arbitrary space curves and cross-sections which may be any star shaped planar curve.

Part description and segmentation using contour, surface, and volumetric primitives

In this paper we discuss the ongoing research on the problem of shape description, and decomposition of complex objects in range images. We propose a paradigm for part description and segmentation by integration of contour, surface, and volumetric primitives. Unlike previous approaches, we use geometric properties derived from both bpundary-based (surface contours and occluding contours), and primitive-based (biquadratc patches and superquadric models) representations to define and recover part-whole relationships, without a priori knowledge about the objects or the object domain. The descriptions thus obtained are independent of position, orientation, scale, domain and domain properties, and are based purely on geometric considerations. We pose the problem of integration in terms of evaluation of the intermediate descriptions and segmentation of the objects in a closed loop process. We present algorithms for superquadric edge detection and apparent contour generation. The criteria for the evaluation of the superquadric models is discussed and examples of real objects supporting our approach are presented.

Segmentation, Modeling And Classification Of The Compact Objects In A Pile

We discuss the problem of interpreting dense range images obtained from the scene of a heap of man-made objects. We describe a range image interpretation system consisting of segmentation, modeling, verification, and classification procedures. First, the range image is segmented into regions and reasoning is done about the physical support of these regions. Second, for each region several possible 3-D interpretations are made based on various scenarios of the objects physical support. Finally each interpretation is tested against the data for its consistency. We have chosen the superquadric model as our 3-D shape descriptor, plus tapering deformations along the major axis. Experimental results obtained from some complex range images of mail pieces are reported to demonstrate the soundness and the robustness of our approach.

Scene Segmentation in the Framework of Active Perception

It has been widely acknowledged in the Machine Perception community that Scene Segmentation problem is ill defined, and hence difficult! To make our primitives adequately explain our data, we perform feedback on processed sensory data to explore the scene. This is Active Perception, the modeling and control strategies for perception.

Image segmentation as the search for the best description in terms of primitives

A new paradigm is presented for the segmentation of images into piecewise continuous patches. Data aggregation is performed via model recovery in terms of variable-order bi-variate polynomials using iterative regression. All the recovered models are potential candidates for the final description of the data. Selection of the models is achieved through maximization of a quadratic Boolean problem. The major novelty of the approach is in combining model extraction and model selection.<<ETX>>