B. Baumgart, Geometric modeling for computer vision. PhD thesis, Stanford University, 1974. TR AIM-249.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....since the volume estimation allows a more precise classification. SfS is a method of automatic construction of a 3d model of an object based on a sequence of images of the object taken from multiple views, in which the object s silhouette represents the only interesting feature of the image [2, 12]. The object s silhouette in each input image corresponds to a conic volume in the object real world space. A 3d model of the object can be built by intersecting the conic volumes from all views, which is also called Space Carving [7] The method can be applied on objects of arbitrary shapes, ....

B.G. Baumgart. Geometric Modeling for Computer Vision. PhD thesis, Stanford AI, 1974.

....should be able to use the model to determine which parts of the scene to analyze in more detail, and from which viewpoints to take the next images. Most previous research at acquiring 3D scene descriptions from multiple views have dealt with relatively simple scenes in controlled environments [2, 8, 9, 22, 25, 28]. This has led, in some cases, to only utilizing occluding contours in the image to form the 3D description [2, 8, 9, 22] The work of Moravec [23] deals with complex indoor and outdoor scenes, but the 3D descriptions generated by his system consist of sparse sets of feature points. Our system, on ....

....take the next images. Most previous research at acquiring 3D scene descriptions from multiple views have dealt with relatively simple scenes in controlled environments [2, 8, 9, 22, 25, 28] This has led, in some cases, to only utilizing occluding contours in the image to form the 3D description [2, 8, 9, 22]. The work of Moravec [23] deals with complex indoor and outdoor scenes, but the 3D descriptions generated by his system consist of sparse sets of feature points. Our system, on the other hand, generates full, surface based descriptions. 2.2. Overview A flowchart for the 3D Mosaic system, ....

Baumgart, B.G., Geometric modeling for computer vision, Tech. RepL STAN-CS-74-463, Department of Computer Science, Stanford University, Stanford, CA, 1974.

....of an edge in the graph. An adjacency list improves on the space requirements for storing graphs vith fev edges: each vertex of the graph has a list of its adjacent vertices. Once a graph is embedded, the order in vhich edges enter a vertex determines the faces of the graph. The winged edge [7] or quad edge [46] data structures capture this information. Both structures are edge based, meaning that they explicitly store the edges of the graph, and use comparable amounts of storage space. The vinged edge data structure is similar to a doubly linked list. Each edge keeps a reference to ....

B. G. Baumgart. Geometric modeling for computer vision. Technical Report STAN-CS-74463, Dept. Cornput. Sci., Stanford Univ., Stanford, CA, Oct. 1974.

....vertex normals Does not use vertex normals Table 2.1: Differences betveen our boundary representation and Chiyokura s These differences are described in detail in the following sections. 2.1.1 Halfedge Data Structure vs. Winged edge Data Structure Instead of using Winged edge data structures [2], our system uses Halfedge data struc tures to encode the topology of manifold surfaces. This data structure is functionally equivalent to the Winged edge data structure and is described in the Reference Manual of the Computational Geometry Algorithm Library (CGAL) 6] An excerpt from this ....

Baumgart, B., "Geometric modeling for computer vision", Ph.D. dissertation, Com- puter Science Dept., Stanford University (1974).

....zero coefficients. In other words, the fundamental property of # is that #(#(X) 0 (3) and guarantees that the boundary set is one or more closed surfaces sometimes also called shells. Formally, such a set whose boundary is a zero chain is called a 2 cycle [31, 81] For historical reasons [8, 16], a more restrictive model of solidity has often been adapted where topological polyhedra are restricted to the orientable three dimensional manifolds with boundary. With this restriction, the combinatorial boundary, defined as above, is not only a 2 cycle, but also a 2 manifold. This manifold ....

....the cells themselves must remain disjoint as required by the definition of the cell complex [100] 3.3. Boundary representation: a compromise Historically, boundary representation was one of the first computer representations to be used for description of polyhedral three dimensional objects [8, 15], but both its strengths and weaknesses as a representation scheme can be appreciated better when examined in terms of properties of implicit and combinatorial representations. Recall that every solid X has the well defined boundary #X, and the boundary of every three dimensional solid in E ....

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B. G. Baumgart. Geometric modeling for computer vision. Computer science, Stanford University, 1974.

....been an important and active research topic in computer vision. Among the algorithms that were proposed in the last two decades, the method of Visual Hull (VH) construction or Shape From Silhouette (SFS) approximates the shape of an object using silhouette images. Since its first introduction in [1], different variations, representations and applications of SFS have been proposed [14, 15, 10, 11, 2, 4, 9, 21] and it has become a standard and popular method of shape estimation. Estimating 3D shape using SFS has many advantages. Silhouettes are readily and easily obtainable and the ....

B. Baumgart. Geometric Modeling for Computer Vision. PhD thesis, Stanford University, 1974.

....work with any combination of calibrated input viewpoints and make no assumptions about the object shape, e.g. smoothness or topology. One common way to implement volume intersection is to approximate visual cones by polyhedra. The oldest such algorithm dates back to Baumgart s 1974 PhD thesis [2]. In this work, a polyhedral visual hull is constructed by intersecting the viewing cones associated with polygonal approximations to the extracted silhouettes. Since 1974, many volume intersection systems have continued to rely on 3D polyhedral intersections, which can be tricky to implement. The ....

B. Baumgart, "Geometric Modeling for Computer Vision," Ph. D. Thesis (Tech. Report AIM-249), Stanford University, 1974.

....approach. 1. Introduction Most algorithms for surface reconstruction from outlines compute some form of the visual hull [10] or the intersection of solid visual cones formed by back projecting silhouettes found in the input images. The basic approach dates back to Baumgart s 1974 PhD thesis [1], where a polyhedral visual hull is constructed by intersecting the viewing cones associated with polygonal silhouettes. Volume intersection has remained the dominant paradigm for decades, implemented using representations as diverse as octrees [15] and triangular splines [14] More recently, ....

B.G. Baumgart, "Geometric Modeling for Computer Vision", Ph. D. Thesis (Tech. Report AIM-249), Stanford University, 1974.

....when there is a change in the scene geometry. The results and conclusions are given in the two final sections. 2 Construction and Illumination of the Mesh The method produces a DM tree [15] on each surface, where a DM tree is a 2 D BSP tree supported by a winged edge data structure (WEDS)[1]. It proceeds in the following steps. First the polygons are ordered front to back as seen from the light source by means of an augmented BSP tree. In this order they are projected onto the sides of a hemi cube placed around the scene. Polygons whose projections on the cube overlap have a ....

B. G. Baumgart. Geometric modeling for computer vision. AIM-249, STA -CS-74-463, CS Dept, Stanford U., October 1974.

....realizable manufacturing operations used in sheet metal part fabrication. 4.1 ELEMENTARY OPERATORS In the original Euler Poincar equation for manifold solids, the basic topological manipulations complying with the equation are termed Euler operators. They were originally introduced by Baumgart [13] and are discussed in detail by Mantyla [5] Braid et al. [14] and Morenson [12] The same notion can be carried over to analyze sheet metal parts using Eq. 7) By historical convention, the operators are denoted by mnemonic names. The key to the (new and old) names used here is as follows: M = ....

Baumgart, B., 1974, "Geometric modeling for computer vision", Ph.D. dissertation, Stanford University.

....department s Onyx Reality Engine II. SAM IAM consists of roughly 8000 lines of code. 4.1 Object Data Structure 4.1.1 Winged Edge Concepts SAM IAM uses the winged edge polyhedra data structure to represent both the mesh and the tools. Winged edge polyhedra were originally developed by Baumgart [Bau74] to represent solid geometric models. A solid geometric model is generally defined to be a representation of a physically realizable 3D object. As such, solid models have a well defined inside, outside, and surface (or boundary) Winged edge schemes are a very popular type of boundary ....

Bruce G.Baumgart. Geometric modeling for computer vision. Technical Report CS-463, Dept of Computer Science, Stanford University, 1974.

....models placed in a known orientation. Inferring orientation automatically is certainly feasible but seems unnecessary for modeling applications that involve cooperative users. The camera captures an image sequence of the model as it rotates, and a volumetric scan is generated from silhouettes [4]. This approach worked well on the majority of models we scanned, but when significant concavities were present (e.g. the door and windows of the house in Figure 8) the laser striper could be used to refine the shape of the model. 4 The use of silhouettes and laser striping is well suited to ....

B. G. Baumgart. Geometric modeling for computer vision. Technical Report AIM-249, AI Laboratory, Stanford Univ., Oct. 1974.

....union, intersection and difference. To make CSG possible, the data structure must be able to handle solids of any genus and of any number of pieces. 2. 2 Implementation The boundary representation data structure BRep is founded on the edge based winged edge data structure proposed by Baumgart [2]. f 1 f 2 v 2 v 1 e e 12 e 22 e 11 e 21 Figure 2: Winged edge data structure. In the original full winged edge data structure any edge e =#v 1 ;v 2 ;f 1 ;f 2 ;e 11 ;e 12 ;e 21 ;e 22 # consists of pointers to the two connected faces and vertices and to the four edges in clockwise and ....

Bruce G. Baumgart. Geometric modeling for computer vision. AIM-249, STA-CS-74-463, CS Dept, Stanford U., October 1974.

....with polygons of the 3D input model and encode the topological adjacencies of the cells in a data structure enabling output sensitive traversals of sightlines through 3D space. 7 The winged pair data structure is motivated by the well known winged edge data structure described by Baumgart [1]. The difference is that the winged pair describes topological structures one dimension higher than the winged edge. While the winged edge represents a 2 manifold, the winged pair represents a 3 manifold. The reader can think of the winged pair data structure as a set of glued together ....

....statements are often required to check the orientation of each structure before moving to the next. For instance, to find the cell adjacent to another across a given face, the C code looks like this: Cell CellAcrossFace(Face face, Cell cell) return (cell = face#cell[0] face#cell[1] : face#cell[0] We build the winged pair data structure for any 3D model using a Binary Space Partition (BSP) 15] a recursive binary split of 3D space into convex polyhedral regions (cells) separated by planes. To construct the BSP, we recursively split cells by candidate planes selected by ....

Bruce G. Baumgart. Geometric modeling for computer vision. AIM-249, STA-CS-74-463, CS Dept, Stanford U., October 1974.

....The important topological relationships in such graphs include the order of edges around a vertex or around a face, and incidences between vertices, edges, and faces. Connected components of embedded planar graphs can be represented in the computer by data structures, such as the winged edge [5], that store these topological relationships. In our opinion, the most elegant of the topological data structures is the quad edge of Guibas and Stolfi [17] which simultaneously represents both primal and dual (e.g. both the Voronoi and Delaunay) in a symmetric manner. We use the quad edge data ....

B. G. Baumgart. Geometric modeling for computer vision. Technical Report STAN-CS-74463, Dept. Comput. Sci., Stanford Univ., Stanford, CA, Oct. 1974.

....the algorithms and data structures used to implement the features described in the previous chapter. 4.1 Winged Edge Object Representation SAM IAM uses the winged edge polyhedra data structure to represent both the mesh and the tools. Winged edge polyhedra were originally developed by Baumgart [Bau74] to represent solid geometric models. A solid geometric model is generally defined to be a representation of a physically realizable 3D object. As such, solid models have a well defined inside, outside, and surface (or boundary) N.V. P.V. P Clockwise wing N Clockwise wing P face N face wing ....

Bruce G. Baumgart. Geometric modeling for computer vision. Technical Report CS-463, Dept of Computer Science, Stanford University, 1974.

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B. Baumgart, Geometric modeling for computer vision. PhD thesis, Stanford University, 1974. TR AIM-249.

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B. G. Baumgart, Geometric Modeling for Computer Vision, Ph.D. Dissertation, Stanford University, August 1974.

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Bruce G. Baumgart. Geometric Modeling for Computer Vision. PhD thesis, Stanford University, 1974.

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Bruce G. Baumgart. Geometric Modeling for Computer Vision. PhD thesis, Stanford University, 1974.

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BAUMGART B. G.: Geometric modeling for computer vision. PhD thesis, Stanford University, Oct. 1974. 2

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B. G. Baumgart. Geometric modeling for computer vision. PhD thesis, Stanford University, October 1974.

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B. Baumgart, Geometric modeling for computer vision. PhD thesis, Stanford University, 1974. TR AIM-249.

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B.G. Baumgart. Geometric Modeling for Computer Vision. PhD thesis, Stanford University, 1974.

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Baumgart, B. G., "Geometric Modeling for Computer Vision," Ph.D. Dissertation, Stanford University, August 1974.

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