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Proceedings ArticleDOI

Annular symmetry operators: a method for locating and describing objects

20 Jun 1995-pp 1016-1021
TL;DR: A machine vision system in which segmentation is computed in conjunction with a structural description of objects in the scene and results are presented to illustrate the method's performance on several images.
Abstract: We present a machine vision system in which segmentation is computed in conjunction with a structural description of objects in the scene. It is assumed that contrast edges capture all relevant object information. The principles which dictate how edge features are grouped to infer objects are based upon detecting SYMMETRICAL ENCLOSING edge configurations. These are detected using ANNULAR OPERATORS applied at multiple scales to edge data which have been extracted at multiple scales from a gray level image. The subsequent grouping of symmetry points results in a set of PARTS which make it possible to identify the LOCATION of objects within an image. These parts are used as a basis for constructing coarse graph-based DESCRIPTORS for the PERCEPTUALLY SIGNIFICANT objects found in the scene. Results are presented to illustrate the method's performance on several images. >
Citations
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Proceedings ArticleDOI
17 Jun 1997
TL;DR: A real-time system is described for automatically detecting, modeling and tracking faces in 3D, which utilizes structure from motion to generate a 3D model of a face and then feeds back the estimated structure to constrain feature tracking in the next frame.
Abstract: A real-time system is described for automatically detecting, modeling and tracking faces in 3D. A closed loop approach is proposed which utilizes structure from motion to generate a 3D model of a face and then feed back the estimated structure to constrain feature tracking in the next frame. The system initializes by using skin classification, symmetry operations, 3D warping and eigenfaces to find a face. Feature trajectories are then computed by SSD or correlation-based tracking. The trajectories are simultaneously processed by an extended Kalman filter to stably recover 3D structure, camera geometry and facial pose. Adaptively weighted estimation is used in this filter by modeling the noise characteristics of the 2D image patch tracking technique. In addition, the structural estimate is constrained by using parametrized models of facial structure (eigen-heads). The Kalman filter's estimate of the 3D state and motion of the face predicts the trajectory of the features which constrains the search space for the next frame in the video sequence. The feature tracking and Kalman filtering closed loop system operates at 25 Hz.

298 citations


Cites methods from "Annular symmetry operators: a metho..."

  • ...We then propose the use of the dark symmetry transform [3] [7] [9] [6]....

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Journal ArticleDOI
01 Jul 2006
TL;DR: This paper describes a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes and uses the transform to define two new geometric properties, center of symmetry and principal symmetry axes.
Abstract: Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection.

290 citations

Proceedings ArticleDOI
18 Jun 1996
TL;DR: First, subpixel local detectors for finding and classifying shocks are developed to show that shock patterns are not arbitrary but obey the rules of a grammar, and in addition satisfy specific topological and geometric constraints.
Abstract: We confront the theoretical and practical difficulties of computing a representation for two-dimensional shape, based on shocks or singularities that arise as the shape's boundary is deformed. First, we develop subpixel local detectors for finding and classifying shocks. Second, to show that shock patterns are not arbitrary but obey the rules of a grammar, and in addition satisfy specific topological and geometric constraints. Shock hypotheses that violate the grammar or are topologically or geometrically invalid are pruned to enforce global consistency. Survivors are organized into a hierarchical graph of shock groups computed in the reaction-diffusion space, where diffusion plays a role of regularization to determine the significance of each shock group. The shock groups can be functionally related to the object's parts, protrusions and bends, and the representation is suited to recognition: several examples illustrate its stability with rotations, scale changes, occlusion and movement of parts, even at very low resolutions.

172 citations

Proceedings ArticleDOI
13 Oct 1997
TL;DR: The wearable video output and the computer vision system provide an integration of real and virtual environments which enhances the experience of playing and learning the game of billiards without encumbering the player.
Abstract: We propose a practical application of wearable computing and augmented reality which enhances the game of billiards. A vision algorithm is implemented which operates in interactive-time with the user to assist planning and aiming. Probabilistic color models and symmetry operations are used to localize the table, pockets and balls through a video camera near the user's eye. Classification of the objects of interest is performed and each possible shot is ranked in order to determine its relative usefulness. The system allows the user to proceed through a regular pool game while it automatically determines strategic shots. The resulting trajectories are rendered as graphical overlays on a head mounted live video display. The wearable video output and the computer vision system provide an integration of real and virtual environments which enhances the experience of playing and learning the game of billiards without encumbering the player.

116 citations

Journal ArticleDOI
TL;DR: A region-based shape representation that might be particularly useful from a biological perspective because it promotes the localization of objects, and object parts relative to each other is described.

115 citations


Cites methods or result from "Annular symmetry operators: a metho..."

  • ...In spite of the similarity in using annular operators, our local circularity measure provides a detailed description of shapes, not only a rough classification as the Kelly and Levine model....

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  • ...The medial-point representation bears similarities with the annular symmetry representation of Kelly and Levine [25], and with the ‘core’ representation proposed by Burbeck and Pizer [26]....

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  • ...The machine vision system described by Kelly and Levine [25] produces a symmetry categorization on the internal points of a figure, discriminating global center-symmetric points of bloblike shapes, and axial-symmetric points of limb-like shapes....

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References
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Journal ArticleDOI
TL;DR: There is a natural uncertainty principle between detection and localization performance, which are the two main goals, and with this principle a single operator shape is derived which is optimal at any scale.
Abstract: This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.

28,073 citations

Journal ArticleDOI
TL;DR: A new geometry based on the primitive notions of a point and a growth is explored in this article, which leads to new properties and descriptions which are particularly suitable for many biological objects.

1,143 citations

Journal ArticleDOI
TL;DR: The main features of the SLS repre sentation are developed and an implemented algorithm that com putes it is described and illustrated for a set of tools.
Abstract: We introduce a novel representation of two-dimensional shape that we call smoothed local symmetries (SLS). Smoothed local symmetries represent both the bounding contour of a shape fragment and the region that it occupies. In this paper we develop the main features of the SLS repre sentation and describe an implemented algorithm that com putes it. The performance of the algorithm is illustrated for a set of tools. We conclude by sketching a method for deter mining the articulation of a shape into subshapes.

393 citations

Journal ArticleDOI
TL;DR: Classes of “ribbonlike” planar shapes can be defined by specifying an arc or axis, and a geometric figure such as a disk or line segment that “sweeps out” the shape by moving along the spine, changing size as it moves.
Abstract: Classes of “ribbonlike” planar shapes can be defined by specifying an arc, called the spine or axis, and a geometric figure such as a disk or line segment, called the generator, that “sweeps out” the shape by moving along the spine, changing size as it moves. Shape descriptions of this type have been considered by Blum, Brooks, Brady, and others. This paper considers such descriptionsfrom the standpoint of the both generation and recovery (i.e., given a shape generated in this way, to determine the axis and generation rule that gave rise to it), and discusses their relative advantages and disadvantages.

120 citations

Journal ArticleDOI
TL;DR: The authors present the intensity axis of symmetry (IAS) method for describing the shape of structures in grey-scale images, which relies on minimizing an active surface functional that provides coherence in both the spatial and intensity dimensions while deforming into anaxis of symmetry.
Abstract: The authors present the intensity axis of symmetry (IAS) method for describing the shape of structures in grey-scale images. They describe the spatial and intensity variations of the image simultaneously rather than by the usual two-step process of using intensity properties of the image to segment an image into regions and describing the spatial shape of these regions. The result is an image shape description that is useful for a number of computer vision applications. The method relies on minimizing an active surface functional that provides coherence in both the spatial and intensity dimensions while deforming into an axis of symmetry. Shape-based image segmentation is possible by identifying image regions associated with individual components of the IAS. The resulting image regions have geometric coherence and correspond well to visually meaningful objects in medical images. >

52 citations