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Visibility, occlusion, and the aspect graph

Harry Plantinga, Charles R. Dyer
1990 International Journal of Computer Vision  
In this paper we present tight bounds on the maximum size of the VSP and the aspect graph and give algorithms for their construction, first in the convex case and then in the general case.  ...  We use these techniques to construct the viewpoint space partition (VSP), a partition of viewpoint space into maximal regions of constant aspect, and its dual, the aspect graph.  ...  We also presented algorithms for constructing the VSP and the aspect graph for convex and nonconvex polyhedra, under orthographic and perspective projection.  ... 
doi:10.1007/bf00054919 fatcat:n5h3y2xtnnavngndiebyqh2u5a

Sparse Arrangements and the Number of Views of Polyhedral Scenes

Mark de Berg, Dan Halperin, Mark Overmars, Marc van Kreveld
1997 International journal of computational geometry and applications  
We also analyze the case of perspective views, point to the potential role of sparse arrangements in obtaining a sharp bound for this case, and present a lower bound construction inducing (n 8 (n)) distinct  ...  Moreover, we show that this bound is almost tight in the worst case, by introducing a lower bound construction inducing (n 5 (n)) distinct views.  ...  Acknowledgement The authors thank Pankaj Agarwal for pointing out an error in Section 3 in an earlier draft of the paper. We also thank two anonymous referees for many helpful comments.  ... 
doi:10.1142/s0218195997000120 fatcat:65v2uco2z5clvpjmglydky2hde

On the number of views of translates of a cube and related problems

Boris Aronov, Robert Schiffenbauer, Micha Sharir
2004 Computational geometry  
In addition, we present constructions inducing (n 4 ) combinatorially different orthographic views and (n 6 ) combinatorially different perspective views, thus showing that these bounds are nearly tight  ...  In this paper we show that, for the special case of scenes consisting of a collection of n translates of a cube, these bounds improve to O(n 4+ε ) and O(n 6+ε ), for any ε > 0, respectively.  ...  convex polyhedra with total complexity n.  ... 
doi:10.1016/j.comgeo.2003.10.001 fatcat:uqeu6abj2nayphyao2bqbawuei

Wrapping the cube and other polyhedra

T. Tarnai, F. Kovacs, P. W. Fowler, S. D. Guest
2012 Proceedings of the Royal Society A  
Removing the symmetry constraint leads to wrappings of other eight-vertex convex polyhedra.  ...  When the strands of a wrapping correspond to the CCs of a four-regular graph that includes faces of size greater than 4, non-convex 'crinkled' wrappings are generated.  ...  Graph-theory-based approach A more general perspective on the wrapping of cubes (and other polyhedra) comes from a graph-theoretical approach.  ... 
doi:10.1098/rspa.2012.0116 fatcat:f6uy6q73vnhwnnxjjryhmrwxcy

Interpreting Pictures of Polyhedral Scenes

Alan K. Mackworth
1973 International Joint Conference on Artificial Intelligence  
The method is primarily based on general coherence rules that the orientations of the surfaces and edges must satisfy, thereby dispensing with predetermined interpretations of particular categories of  ...  The paper also comments on the relationship of this program to four other scene analysis programs.  ...  can be systematically exploited to construct a perspective interpretation of the line drawing.  ... 
dblp:conf/ijcai/Mackworth73 fatcat:lgpv7dylhjb3pf73o6gwoxnbr4

Formalizing the Face Lattice of Polyhedra [article]

Xavier Allamigeon, Ricardo D. Katz, Pierre-Yves Strub
2022 arXiv   pre-print
This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps.  ...  Faces play a central role in the combinatorial and computational aspects of polyhedra. In this paper, we present the first formalization of faces of polyhedra in the proof assistant Coq.  ...  We warmly thank Kazuhiko Sakaguchi for his help on integrating the ordered structures of MathComp, and Quentin Canu for discussions on the formalization of affine hulls.  ... 
arXiv:2104.15021v4 fatcat:f7axjmr7wjbnznxsniy35nehve

What defines a view?

Michael J Tarr, David J Kriegman
2001 Vision Research  
Using objects with known aspect graphs, five experiments examined whether the perception of orientation is sensitive to the qualitative features that define aspect graphs.  ...  Cybernet. 32 (1979) 211.) geometric method for enumerating complete sets of stable views as aspect graphs.  ...  We would like to thank Jean Ponce of the University of Illinois with whom the methods for computing aspect graphs from object models were developed.  ... 
doi:10.1016/s0042-6989(01)00024-4 pmid:11412888 fatcat:yzqtwbb7n5d3xdg552vu5tpy4q

Formalizing the Face Lattice of Polyhedra

Xavier Allamigeon, Ricardo D. Katz, Pierre-Yves Strub
2022 Logical Methods in Computer Science  
This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps.  ...  Faces play a central role in the combinatorial and computational aspects of polyhedra. In this paper, we present the first formalization of faces of polyhedra in the proof assistant Coq.  ...  We warmly thank Kazuhiko Sakaguchi for his help on integrating the ordered structures of MathComp, and Quentin Canu for discussions on the formalization of affine hulls.  ... 
doi:10.46298/lmcs-18(2:10)2022 fatcat:2u4rcni2dzagrcxxs6apwtg67m

Repetitive Hidden Surface Removal for Polyhedra

Marco Pellegrini
1996 Journal of Algorithms  
+ =m 1=2 g), when the scene is composed of c-oriented polyhedra.  ...  Afterwards, the data structure is accessed repeatedly with view-points given on-line and the portions of the polyhedra visible from each view-point are produced on-line.  ...  number of nodes and edges in the aspect graph.  ... 
doi:10.1006/jagm.1996.0038 fatcat:gxu7rvkqdjdqhihmw4tvie4fjm

Computing exact aspect graphs of curved objects: Algebraic surfaces [chapter]

Jean Ponce, Sylvain Petitjean, David J. Kriegman
1992 Lecture Notes in Computer Science  
Indeed, approximate aspect graphs of polyhedra have been successfully used in recognition tasks [7, 18, 20] , and several algorithms have been proposed for computing the exact aspect graph of these objects  ...  This paper presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface and observed under orthographic projection.  ...  We are investigating the case of perspective projection: the (families of) surface curves that delineate the visual events under orthographic projection also delineate perspective projection visual events  ... 
doi:10.1007/3-540-55426-2_64 fatcat:otevwn57cvhjpdhgj2coydufea

Computing exact aspect graphs of curved objects: Algebraic surfaces

Sylvain Petitjean, Jean Ponce, David J. Kriegman
1992 International Journal of Computer Vision  
Indeed, approximate aspect graphs of polyhedra have been successfully used in recognition tasks [7, 18, 20] , and several algorithms have been proposed for computing the exact aspect graph of these objects  ...  This paper presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface and observed under orthographic projection.  ...  We are investigating the case of perspective projection: the (families of) surface curves that delineate the visual events under orthographic projection also delineate perspective projection visual events  ... 
doi:10.1007/bf00133703 fatcat:sympbpcquvcqroyhwbhcdph6ue

Retrieval of Shape from Silhouette [chapter]

Andrea Bottino, Aldo Laurentini
2006 Advances in Imaging and Electron Physics  
The parallel aspect graph is a sub-graph of the perspective aspect graph, since not any perspective aspect is also a parallel aspect.  ...  Finally, observe that the VE active patches are parts of the VE surfaces considered in the theory of the aspect graphs of polyhedra (Gigus et al. 1991 ). b) Lines making three contacts.  ... 
doi:10.1016/s1076-5670(05)39001-x fatcat:te3jedjhevbxtelbir7buzknhy

The visual hull of smooth curved objects

A. Bottino, A. Laurentini
2004 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We show that the visual hull can be constructed using patches of the surfaces that partition the viewpoint space of the aspect graph.  ...  This is performed by relating the surface of the visual hull of the object to its aspect graph.  ...  Algorithms for constructing the aspect graphs have been given for polyhedra, articulated objects, solids of revolution and various categories of curved objects under parallel and perspective projection  ... 
doi:10.1109/tpami.2004.130 pmid:15573822 fatcat:fyyy3tkrj5elxhhrr4zmfw4vh4

Finite-resolution aspect graphs of polyhedral objects

I. Shimshoni, J. Ponce
1997 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We address the problem of computing the exact aspect graph of a polyhedral object observed by an orthographic camera with nite resolution, such t h a t t wo image points separated by a distance smaller  ...  We p r e s e n t a catalogue of visual events for polyhedral objects and give an algorithm for computing the aspect graph and enumerating all qualitatively di erent aspects.  ...  Most of it has focused on polyhedra: indeed, several algorithms have been proposed for computing the exact aspect graph of these objects under orthographic 2, 7, 14, 17] and perspective 19, 20, 2 1 ,  ... 
doi:10.1109/34.588001 fatcat:vfowfl3ms5e6zmdqoftyiau2vu

Polygonal Complexes and Graphs for Crystallographic Groups [article]

Daniel Pellicer, Egon Schulte
2013 arXiv   pre-print
on various aspects of the classification of regular polygonal complexes, chiral polyhedra, and more generally, two-orbit polyhedra.  ...  The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular  ...  a linear apeirogon, and the orthogonal projection along its axis gives a finite planar (convex or star-) polygon.  ... 
arXiv:1310.4905v1 fatcat:54dh23ls2rcszjhdlrrsj2qe2e
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