Many algorithms for both identifying and reconstructing a 3-D object are based on the 2-D silhouettes of the object. In general, identifying a nonconvex object using a silhouette-based approach implies neglecting some features of its surface as identification clues. The same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object. This paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette-based image understanding. For this purpose, the geometric concept of visual hull of a 3-D object is introduced. This is the closest approximation of object S that can be obtained with the volume intersection approach; it is the maximal object silhouette-equivalent to S, i.e., which can be substituted for S without affecting any silhouette. Only the parts of the surface of S that also lie on the surface of the visual hull can be reconstructed or identified using silhouette-based algorithms. The visual hull depends not only on the object but also on the region allowed to the viewpoint. Two main viewing regions result in the external and internal visual hull. In the former case the viewing region is related to the convex hull of S, in the latter it is bounded by S. The internal visual hull also admits an interpretation not related to silhouettes. Algorithms for computing visual hulls are presented and their complexity analyzed. In general, the visual hull of a 3-D planar face object turns out to be bounded by planar and curved patches. >

The visual hull concept for silhouette-based image understanding

We present hierarchical occlusion maps (HOM) for visibility culling on complex models with high depth complexity. The culling algorithm uses an object space bounding volume hierarchy and a hierarchy of image space occlusion maps. Occlusion maps represent the aggregate of projections of the occluders onto the image plane. For each frame, the algorithm selects a small set of objects from the modelas occludersand renders them to form an initial occlusion map, from which a hierarchy of occlusion maps is built. The occlusion maps are used to cull away a portion of the model not visible from the current viewpoint. The algorithm is applicable to all models and makes no assumptions about the size, shape, or type of occluders. It supports approximate culling in which small holes in or among occluders can be ignored. The algorithm has been implemented on current graphics systems and has been applied to large models composed of hundreds of thousands of polygons. In practice, it achieves significant speedup in interactive walkthroughs of models with high depth complexity. CR

/pdf/visibility-culling-using-hierarchical-occlusion-maps-45iohkne8z.pdf

Visibility culling using hierarchical occlusion maps

An Empirical-Statistical Agenda for Recognition.- A Formal-Physical Agenda for Recognition.- Shape.- Shape Models and Object Recognition.- Order Structure, Correspondence, and Shape Based Categories.- Quasi-Invariant Parameterisations and Their Applications in Computer Vision.- Shading.- Representations for Recognition Under Variable Illumination.- Shadows, Shading, and Projective Ambiguity.- Grouping.- Grouping in the Normalized Cut Framework.- Geometric Grouping of Repeated Elements within Images.- Constrained Symmetry for Change Detection.- Grouping Based on Coupled Diffusion Maps.- Representation and Recognition.- Integrating Geometric and Photometric Information for Image Retrieval.- Towards the Integration of Geometric and Appearance-Based Object Recognition.- Recognizing Objects Using Color-Annotated Adjacency Graphs.- A Cooperating Strategy for Objects Recognition.- Statistics, Learning and Recognition.- Model Selection for Two View Geometry:A Review.- Finding Objects by Grouping Primitives.- Object Recognition with Gradient-Based Learning.

Shape, Contour and Grouping in Computer Vision

https://www-users.cs.york.ac.uk/~erh/rae/spectemed.pdf

Spectral embedding of graphs

Object and pattern detection is a classical computer vision problem with many potential applications, ranging from automatic target recognition to image-based industrial inspection tasks in assembly lines. While there have been some successful object and pattern detection systems in the past, most such systems handle only specific rigid objects or patterns that can be accurately described by fixed geometric models or pictorial templates. 
This thesis presents a learning based approach for detecting classes of objects and patterns with variable image appearance but highly predictable image boundaries. Some examples of such object and pattern classes include human faces, aerial views of structured terrain features like volcanoes, localized material defect signatures in industrial parts, certain tissue anomalies in medical images, and instances of a given digit or character, which may be written or printed in many different styles. 
The thesis consists of two parts. In part one, we introduce our object and pattern detection approach using a concrete human face detection example. The approach first builds a distribution-based model of the target pattern class in an appropriate feature space to describe the target's variable image appearance. It then learns from examples a similarity measure for matching new patterns against the distribution-based target model. We also discuss some pertinent learning issues, including ideas on virtual example generation and example selection. The approach makes few assumptions about the target pattern class and should therefore be fairly general, as long as the target class has predictable image boundaries. We show that this is indeed the case by demonstrating the technique on two other pattern detection/recognition problems. 
Because our object and pattern detection approach is very much learning-based, how well a system eventually performs depends heavily on the quality of training examples it receives. The second part of this thesis looks at how one can select high quality examples for function approximation learning tasks. Active learning is an area of research that investigates how a learner can intelligently select future training examples to get better approximation results with less data. We propose an active learning formulation for function approximation, and show for three specific approximation function classes, that the active example selection strategy learns its target with fewer data samples than random sampling. Finally, we simplify the original active learning formulation, and show how it leads to a tractable example selection paradigm, suitable for use in many object and pattern detection problems. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Learning and example selection for object and pattern detection

An efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented. The aspect graph is an approach to representing 3-D objects by a set of 2-D views, for the purpose of object recognition. In this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change. The viewing data of an object is the partition of the viewpoint space together with a representative view in each region. The algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection. >

Efficiently computing and representing aspect graphs of polyhedral objects

An algorithm for computing the aspect graph for polyhedral objects is described. The aspects graph is a representation of three-dimensional objects by a set of two-dimensional views. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same. At the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes. It is shown that for polyhedral objects there are two fundamental visual events: (1) the projections of an edge and a vertex coincide; and (2) the projections of three nonadjacent edges intersect at a point. The geometry of the object is reflected in the locus of the accidental viewpoints. The algorithm computes the partition together with a representative view for each region of the partition. >

/pdf/computing-the-aspect-graph-for-line-drawings-of-polyhedral-uqgow7h3kb.pdf

Computing the aspect graph for line drawings of polyhedral objects

The aspect graph is one of the approaches to representing of 3-D shape for the purposes of object recognition. In this approach, the viewing space of an object is partitioned into regions, such that in each region the topology of the line drawing of the object does not change. The viewing data of an object is the partition of the viewing space together with a representative view in each region, We present an efficient algorithm for computing the viewing data for line drawings of polyhedral objects under orthographic projection. For an object of size O(n) whose partition of size O(m), the algorithm runs O(n4 log n t m log m) time. Using a novel data structure, we construct the set of all views in optimal O(m) time and space.

Efficiently Computing And Representing Aspect Graphs Of Polyhedral Objects

J.J. Koenderink and A.J. van Doorn (1979) introduced aspect graphs as a way of representing 3-D shape for object recognition. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same. The viewing data of an object are the partition of the Gaussian sphere together with representative line drawings for each region of the partition. The authors present an algorithm for computing the viewing data of polyhedral objects. In the course of presenting the algorithm, they provide a full catalog of the visual events that occur for this type of object. >

/pdf/computing-the-aspect-graph-for-line-drawings-of-polyhedral-3uu1e388yy.pdf

J.J. Koenderink and A.J. van Doorn (1979) introduced aspect graphs as a way of representing 3-D shape for object recognition. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region, the qualitative structure of the line drawing remains the same. The viewing data of an object are the partition of the Gaussian sphere and representative line drawings for each region of the partition. An algorithm is presented for computing the viewing data of polyhedral objects. A full catalog of the visual events that occur for polyhedral objects is provided. >

/pdf/computing-the-aspect-graph-for-line-drawings-of-polyhedral-3byj6aspxu.pdf

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Efficiently computing and representing aspect graphs of polyhedral objects

Computing the aspect graph for line drawings of polyhedral objects

Efficiently Computing And Representing Aspect Graphs Of Polyhedral Objects

Computing the aspect graph for line drawings of polyhedral objects

Computing the aspect graph for line drawings of polyhedral objects