W. H. Plantinga and C. R. Dyer, An algorithm for constructing the aspect graph, in Proc. 27th IEEE Symp. Foundations of Computer Science, 1986, pp. 123--131.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(qualitatively) different. Koenderink and van Doorn are credited for introducing this concept [15] 16] Since then, aspect graphs have attracted a lot of interest, mainly in the computer vision community, e.g. 5] 6] 14] 17] 24] 25] We also mention the works of Plantinga and Dyer [19] and of Gigus et al. 11] that have a computational geometry flavor. Here we give the basic terminology needed in the sequel. For a broader introduction and a survey of recent research on aspect graphs see, e.g. 4] from which we borrow most of the subsequent terminology. In this paper, we ....

....having the same view and separated by critical surfaces. The term aspect graph originates from a certain representation of the viewing space as a discrete graph where each node of the graph represents a maximal connected component of the space having the same aspect (or view) Plantinga and Dyer [19] have shown that the maximum number of views of a convex polyhedron with n vertices is Theta(n ) for views from infinity and Theta(n ) for perspective views. Later, it has been shown that for a general polyhedron, or more generally, for a collection of n non intersecting triangles in ....

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W. H. Plantinga and C. R. Dyer, An algorithm for constructing the aspect graph, in Proc. 27th IEEE Symp. Foundations of Computer Science, 1986, pp. 123--131.

....for constructing the aspect graph of a convex polygon as viewed from viewpoints in the plane of the polygon, using perspective projection. Stewman and Bowyet [21] describe an algorithm for constructing the viewing data of convex polyhedra under perspective pro jection. Plantinga and Dyer [16] presented the first algorithm for computing the exact viewing data of arbitrary polyhedral objects under orthographic projection. There were two major problems with that algorithm. The authors failed to recognize the visual event that results from the interaction of three nonadjacent edges, and ....

W. H. Plantinga and C. R. Dyer, "An algorithm for constructing the aspect graph," in Proc. 271h Symp. Foundations of Computer Science, IEEE, 1986, pp. 123-131.

....different. Koenderink and van Doom introduced the notion of aspect graphs more than a decade ago [12] 13] Since then, aspect graphs have attracted a lot of interest, mainly in the computer vision community, e.g. 4] 5] 11] 14] 21] 22] We also mention the works of Plantinga and Dyer [16] and of Gigus et al. 9] that have a computational geometry flavor. Here we give the basic terminology needed in the sequel. For a broader introduction and a survey of recent research on aspect graphs see, e.g. 3] from which we borrow most of the subsequent terminology. In this paper, we ....

....having the same view and separated by critical surfaces. The term aspect graph originates from a certain representation of the viewing space as a discrete graph where each node of the graph represents a maximal connected component of the space having the same aspect (or view) Plantinga and Dyer [16] have shown that the maximum number of views of a convex polyhedron with n vertices is O(n 2) for views from infinity and O(n 3) for perspective views. Later, it has been shown that for a general polyhedron, or more generally, for a collection of n non intersecting triangles in space, the maximum ....

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W. H. PLANTINGA AND C. R. DYER, An algorithm for constructing the aspect graph, in Proc. 27th IEEE Syrup. Foundations of Computer Science, (1986) pp. 123-131.

....is partitioned in stable regions, where small changes in the viewpoint do not cause significantly the aspect of an object. The transitions between stable regions individuate accidental views where the aspect changes rapidly. The first applications considered the simple case of polyhedral objects [61], but more recently applications to curved surfaces have been proposed: generalized cylinders have been considered by Eggert and Bowyer [25] and Kriegman and Ponce [46] The major disadvantages of these types of representations are the high construction time, excessive storage requirements for ....

W. Planting and C. Dyer. An algorithm for constructing an aspect graph. In Proc. IEEE Symposium on the Foundations of Computer Science, pages 123--131, New York, 1986. IEEE.

....to attentive processing in general and to his complexity level analysis of visual search and proves that active unbounded visual search is NP Complete. Kirousis and Papadimitriou [4] show that the problem of polyhedral scene labeling is inherently NP Complete. Many other vision researchers ( 3] [6], etc. routinely provide an analysis of the complexity of their proposed algorithms. Complexity level analysis of robotics and vision problems is important because it can reveal basic insights into the structure of the problem and delimit the space of permissible solutions in a formal and ....

W. H. Plantinga and C. R. Dyer. An algorithm for constructing the aspect graph. In 27 Annual Symposium on Foundations of Computer Science, pages 123--131, Toronto, Ontario, 1986.

....points of view on the sphere. 2.3 Aspect Trees Each model feature M i is now characterized by a set of approx. five shape properties. The values of the properties are grouped into aspect trees. This is basically motivated by the aspect idea first proposed by [KvD79] see also [WF90, GCS91, PD86] There an aspect is defined as a set of topological equivalent views. This definition causes some constraints of what kind of objects are to be recognized in real world images [EBD 93] Our definition of an aspect is based on the values of properties of model features in order to overcome ....

W. H. Plantinga and C. R. Dyer. An algorithm for constructing the aspect graph. In Proc. of the 27th Symp. on Foundations of Comp. Science, pages 123--131. IEEE, 1986.

....has focused on computing exact visibility (e.g. 5, 12, 16, 19, 22] that is, computing an exact description of the visible elements of the scene data for every qualitatively distinct region of viewpoints. Such complete descriptions may be combinatorially complex and difficult to implement [16, 18], even for highly restricted viewpoint regions (e.g. viewpoints at infinity) The binary space partition or BSP tree data structure [8] obviates the hidden surface computation by producing a back to front ordering of polygons from any viewpoint. This technique has the drawback that, for an ....

W.H. Plantinga and C.R. Dyer. An algorithm for constructing the aspect graph. In Proc. 
 Annual IEEE Symposium on Foundations of Computer Science, pages 123--131, 1986.

....in time Theta(n 2 ) irrespective of the size of the visibility map. 2 1. 3 The aspect graph approach Traditionally, the problem of efficiently computing an object space representation of the visibility map of a polygonal scene has been tackled using the aspect graph approach [KvD76, KvD79, PD86, GCS91, GM90] The aspect graph of a polyhedral scene is a graph in which each node is associated with a region of R 3 where visibility maps with the same combinatorial structure are visible. Provided that we can store efficiently the visibility maps at the nodes of the graph and that, given a ....

W.H. Plantiga and C.R. Dyer. An algorithm for constructing the aspect graph. In Proceedings of the 27th IEEE Symposium on Foundations of Computer Science, pages 123--131, 1986.

....graph of Sigma. That is, there is a vertex in the aspect graph for each topologically distinct view, and two vertices v 1 ; v 2 are connected by an edge if one can vary the viewing direction continuously so as to pass from a view represented by v 1 directly to a view represented by v 2 ; see [6, 9] for a more formal definition of aspect graphs. One can define an aspect graph for perspective views in an analogous manner. In this case it is the dual graph of a partitioning of 3 space, where the perspective views from all points in any single region are topologically equivalent. As a matter of ....

....a matter of fact, the aspect graph can be defined for any scene in 3 space. In this paper we study the size of the aspect graph (i.e. the number of topologically different views) of a polyhedral terrain. Aspect graphs have applications in computer vision, computer graphics, and object recognition [5, 6, 9]. The notion of aspect graphs was introduced by Koenderink and van Doorn [8] and also by Chakravarty and Freeman [3] Plantinga and Dyer [9] proved that the maximum number of topologically different orthographic and perspective views of a convex polyhedron with n faces are Theta(n 2 ) and ....

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W. Plantinga and C. Dyer, An algorithm for constructing the aspect graph, Proc. 27th IEEE Symp. Foundations of Computer Science, 1986, 123--131. 6 References 7

....of the paper we apply the same approach to the case of general polyhedra thereby improving worst case time storage bounds. 1. 2 The aspect graph approach Traditionally, the problem of efficiently computing the visibility map of a polygonal scene has been tackled using the aspect graph approach [25, 26, 35, 21]. For a survey of results on aspect graphs see [21, 22] The aspect graph of a polyhedral scene is a graph in which each node is associated with a region of R 3 where visibility maps with the same combinatorial 1 structure are visible. Provided that we can store efficiently the visibility maps ....

W. Plantiga and C. Dyer. An algorithm for constructing the aspect graph. In Proceedings of the 27th IEEE Symposium on Foundations of Computer Science, pages 123--131, 1986.

....visibility analytically. A detailed comparison of their method to the one being presented here will take place in Section . source blocker e v critical surface critical curve Figure 1: A VE event. The geometry of shadow boundaries in polygonal scenes was investigated by Plantinga and Dyer [33] [32] 34] who found that quadric shadow boundaries can arise due to multiple occluders. Gigus and his collaborators specified the conditions necessary for such boundaries to occur [18] 17] Algorithms by Heckbert [23] 24] and Lischinski et al. 26] include discontinuity boundaries in the ....

W. H. Plantinga and C. R. Dyer. An algorithm for constructing the aspect graph. In Proceedings of the 27 th Annual IEEE Symposium on Foundations of Computer Science, pages 123--131, 1986.

....inter polygon visibility among the cells associated polygons. Figure 3: Visibility propagation from a source cell S 1 . Figure 4: Visibility propagation from a source cell S 2 . The volume visible to a polygon in the presence of polygonal occluders is, in general, bounded by quadratic surfaces [18]. An algorithm for computing this volume was implemented and described in [21] but is not yet sufficiently robust for use on complex models. Consequently, we have developed a simpler algorithm that computes a polyhedral volume guaranteed to enclose the exact visible region. The algorithm is a ....

Plantinga, W., and Dyer, C. An algorithm for constructing the aspect graph. In Proc. 27 th Annual IEEE Symposium on Foundations of Computer Science (1986), pp. 123\Gamma131.

....some viewpoint. The discontinuity mesh is a set of maximal cells on the faces of the scene such that the backprojection is constant for all viewpoints within each cell. Adjacent cells on a face are divided by discontinuity curves, which are the intersection of the face with discontinuity surfaces [PD86]. Discontinuity curves are line segments or conic sections, whereas discontinuity surfaces are subsets of planes or quadric surfaces. The backprojection in one cell can be efficiently updated to compute that in adjacent cells and hence can be propagated to all other cells of the mesh [GM90, GCS91, ....

....in the region labelled (ac; db) two pieces of the source are visible, one delimited by the endpoints a and c, the other delimited by d and b. computer graphics. He showed [Hec92b] how to use a visibility algorithm to compute the discontinuity mesh. Discontinuity meshes are akin to aspect graphs [PD86], which are used in computer vision. We extend Heckbert s work with (a) a new algorithm based on the plane sweep paradigm to compute the discontinuitymesh and (b) an efficient computation of the backprojection in each cell of the mesh. In the plane, a scene consists of a set of simple, ....

[Article contains additional citation context not shown here]

W. Plantinga and C. Dyer. An algorithm for constructing the aspect graph. In Proc. 27th Symp. Foundations of Computer Science, pages 123--131, 1986.

....algorithm when we use it in Section 4. The visibility complex is a data structure that encodes visibility relationships in the plane and which has been used successfully for a number of applications [Pocch96] The different views of a scene were studied in a data structure called the aspect graph [Plant86, Gigus91]. After some pioneering work in the area of the computation of the shadow boundaries [Nishi85] the area became more mature which resulted in a number of algorithms to compute what is called the discontinuity mesh [Lisch92, Heckb92, Stewa94] and also heuristics based on voxels to compute the ....

W. Plantinga and C. Dyer. An algorithm for constructing the aspect graph. In Proc. 27th Symp. Foundations of Computer Science, pages 123--131, 1986.

....has focused on computing exact visibility (e.g. 5, 12, 16, 19, 22] that is, computing an exact description of the visible elements of the scene data for every qualitatively distinct region of viewpoints. Such complete descriptions may be combinatorially complex and difficult to implement [16, 18], even for highly restricted viewpoint regions (e.g. viewpoints at infinity) The binary space partition or BSP tree data structure [8] obviates the hidden surface computation by producing a back to front ordering of polygons from any viewpoint. This technique has the drawback that, for an ....

W.H. Plantinga and C.R. Dyer. An algorithm for constructing the aspect graph. In Proc. 27 th Annual IEEE Symposium on Foundations of Computer Science, pages 123--131, 1986.

....to attentive processing in general and to his complexity level analysis of visual search and proves that active unbounded visual search is NP Complete. Kirousis and Papadimitriou [4] show that the problem of polyhedral scene labeling is inherently NP Complete. Many other vision researchers ( 3] [6], etc. routinely provide an analysis of the complexity of their proposed algorithms. Complexity level analysis of robotics and vision problems is important because it can reveal basic insights into the structure of the problem and delimit the space of permissible solutions in a formal and ....

W. H. Plantinga and C. R. Dyer. An algorithm for constructing the aspect graph. In 27 Annual Symposium on Foundations of Computer Science, pages 123--131, Toronto, Ontario, 1986.

....to each other constrain the possible views that can generate them. We use the T junctions that arise from self occlusion and non convexity as features in order to determine a region of viewpoints that matches the image. These contour features are precomputed and, unlike the aspect graph [KvD79,PD86,GM90], are organized into a structure that makes inter feature relationships and dynamic feature changes explicit. When the precomputed geometry of the occluding contour, geometry that is dependent on viewpoint, is matched to image features, this relationship globally constrains viewpoint because of ....

W. H. Plantinga and C. R. Dyer. An algorithm for constructing the aspect graph. Proc. IEEE Symp. Foundations of Computer Science, pages 123--131, 1986.

....et al. 11] The result is similar to the VSP for convex polyhedra under orthographic projection. Kender and Freudenstein [12] discuss the meanings of terms such as degenerate view, characteristic view, visual event, and general viewing position. More recently, Plantinga and Dyer [14, 15] show how to construct the aspect graph for convex and non convex polyhedra under orthographic projection. Gigus and Malik concurrently developed an algorithm for the same problem, with the same worst case run time of O(n 6 log n) 16] but their algorithm appears to require much more time for ....

H. Plantinga and C. R. Dyer, "An algorithm for constructing the aspect graph," in Proc. 27th Ann. Symp. on Foundations of Computer Sci., pp. 123-131, 1986.

....at a much faster rate than memory bandwidth, and since memory bandwidth is a major bottleneck in raster graphics performance [1] object space techniques that improve rendering efficiency are increasing in applicability and importance. The aspect representation was introduced by Plantinga and Dyer [2] in the context of constructing the aspect graph for a polyhedron. It also appears in other work [3 5] This approach to animating rotation was first introduced by Plantinga [3] and Plantinga et al. 5] Section 2 of this 3 paper discusses frame coherence and the sorts of events that occur. ....

H Plantinga and C R Dyer, An algorithm for constructing the aspect graph, Proc. 27th IEEE Symp. Foundations of Computer Sci., 123-131 (1986).

....Freudenstein [1986] discuss the meanings of terms such as degenerate view, characteristic view, visual event, and general viewing position. The algorithm of Chapter 3 for constructing the aspect graph has been presented earlier for the convex and general cases under orthographic projection [Plantinga and Dyer, 1986]. It is the first algorithm for constructing the aspect graph in the general case. The definition given there of aspect was slightly different that the definition given in Chapter 3, but the algorithm works under both definitions. Stewman and Bowyer [1987] present an algorithm for constructing the ....

....) time. Recently, Gigus and Malik have presented an algorithm for constructing the aspect graph for non convex polyhedra under orthographic projection [Gigus and Malik, 1988] The definition of aspect used there is the same as the definition given in Chapter 3 and slightly different from that of [Plantinga and Dyer, 1986]. Their algorithm has the same worstcase runtime as the algorithm given in Chapter 3. However, our algorithm has better average case run time for simpler objects; its runtime for convex polyhedra is O(n 2 log n) and the runtime of the algorithm of Gigus and Malik is W(n 3 ) The aspect graph ....

Plantinga, W. H. and C. R. Dyer, "An algorithm for constructing the aspect graph," Proc. 27th IEEE Symp. Foundations of Computer Sci., 1986, pp. 123-131.

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