H.H. Baker (1989). Building Surfaces of Evolution: The Weaving Wall. International Journal of Computer Vision, 3:51-71.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....begin with some initial cell(s) and track the surface by selectively propagating new cells; this technique is known as numerical continuation [AG90] 1. 3 Cubical Cell Polygonization Most tiling methods developed to date partition space into cubical (or rectilinear) cells [WMW86] LC87] Blo88] [Bak89][Wal91] The regularity of the cubical lattice is particularly appropriate for both discrete and continuous data. For discrete data, the regular grid is compatible with most scanning hardware used to gather samples. For continuous data, the regular grid permits a simple integer indexing scheme for ....

.... direction of contours in ambiguous faces may be chosen based on the polarity of the four face vertices; i.e. one may elect to always separate the positives (and join the negatives) or always separate the negatives (and join the positives) This is effectively the result of algorithms in [Blo88][Bak89][WJ90] In [Blo88] WJ90] a polygon tracing technique is employed that connects one edge intersection to the next by turning clockwise along a face s boundary, with an initial direction towards the positive end of that edge. It can be shown that this rule always separates the positive vertices in ....

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H.H. Baker, "Building Surfaces of Evolution: The Weaving Wall," International Journal of Computer Vision, vol. 3, pp. 51-71, 1989.

....in lists of extracted edges remains a process of O(n 2 ) complexity. Snake like approaches ( 15] 7] 10] eschew list searching, but need intelligent initialization and cannot deal with emerging and vanishing, splitting and merging edge segments. Starting with the works of Baker et al. 8] [2], 3] 4] the spatiotemporal surface (STS) was introduced in the computer vision literature. Informally, the STS is the 2 d object spanned by the temporal development of a 1 d edge in a sequence consisting of a stack of 2 d image frames. However, up to now the topological structure of the ....

....which are stable singularities of the mappings of the object surface onto the image plane. Due to the stability they will keep their appearance from 2 frame, hence only the first type (edges) corresponds to a 2 d closed manifold, let al..one to a Jordan surface, as is assumed in [21] and [2]. A cusp, observed in a sequence of successive frames, corresponds to a bounded 2 d manifold. An evolving T junction is not a 2 d manifold, since three faces meet at the junction point. Not even the 2 d images of these singularities are 1 d manifolds in the 2 d image. The visual events of ....

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H. H. Baker. Building surfaces of evolution: The weaving wall. International Journal of Computer Vision, 3(1):51--72, 1989.

....Terms: Algorithms, Graphics. 1 INTRODUCTION The signal processing approach described in this paper was originally motivated by the problem of how to fair large polyhedral surfaces of arbitrary topology, such as those extracted from volumetric medical data by iso surface construction algorithms [21, 2, 11, 15], or constructed by integration of multiple range images [36] Since most existing algorithms based on fairness norm optimization [37, 24, 12, 38] are prohibitively expensive for very large surfaces a million vertices is not unusual in medical images , we decided to look for new algorithms ....

H. Baker. Building surfaces of evolution: The weaving wall. International Journal of Computer Vision, 3:51--71, 1989.

....the detector outputs. Alternatively, one could try to find the best spatial scale or range of scales to describe structure at every region of the image and only use the detector outputs within that range. Stable bandpass filter output zero crossings across scale may indicate important size regimes [114, 9]. An approachsuchas[9]may be used to mark the preferred spatial scales. 78 stoppedness computation contourness computation Processing block diagram linear filter bank (all orientations) energy measures lateral gain control 1st and 2nd derivatives taken along and against ....

....one could try to find the best spatial scale or range of scales to describe structure at every region of the image and only use the detector outputs within that range. Stable bandpass filter output zero crossings across scale may indicate important size regimes [114, 9] An approachsuchas[9]may be used to mark the preferred spatial scales. 78 stoppedness computation contourness computation Processing block diagram linear filter bank (all orientations) energy measures lateral gain control 1st and 2nd derivatives taken along and against orientation squared ....

H. H. Baker. Building surfaces of evolution: the weaving wall. Intl. J. Comp. Vis., 3:51--71, 1989.

....uses the open star of a point. The open star of a point is the point itself, the 6 lines, the 12 faces, and the 8 voxels bounded by the point, as depicted in figure 1. This processing scheme is known from the famous Marching Cubes algorithm ( 10] and from the similar Weaving Wall algorithm ([1]) but differs from them in a fundamental way. The former algorithms construct isosurfaces (namely zero sets) of scalar 3D functions, which are 2D manifolds, namely Jordan surfaces. The algorithms consider the sign of the function value in the 8 voxels bounded by the point. This leaves 2 8 ....

H. H. Baker. Building surfaces of evolution: The weaving wall. Int. J. of Computer Vision, 3(1):51--72, 1989.

....each cell based on a precomputed table of 15 topologically distinct plus minus patterns of cell corners. In the original implementation, marching cubes did not recognize ambiguities. As pointed out by Durst [Dur88] that method could yield a discontinuity between cells. Later researchers [Bak89, Nat91, Kal91] as well as the original authors, described modifications that ensured continuity. Some variants are discussed in Section 4.1. Gallagher and Nagtegaal [GN89] generalized the above approaches to irregular lattices that frequently occur in finite element analysis, and considered ....

....differs) UA90] Positive values are considered to represent the objects . In the cited paper R u = R 1 corresponds to our label UA R1 , etc. the UA gives the authors initials. UA R1 Always connect negative diagonals (often associated with corrected versions of marching cubes [LC87, Bak89, Kal91] UA R2 Always connect positive diagonals (often associated with cuberilles [AFH81, HU83, CHRU85] UA R3 Connect negative diagonals if the face is parallel to the xy plane; otherwise, connect positive diagonals. 1 Policy UA R3 originates in the cited paper. Typically, CT volumes have ....

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H. H. Baker. Building surfaces of evolution: The weaving wall. International Journal of Computer Vision, 3:51--71, 1989.

....Dale and Sereno[3] determined the orientation of points on the surface of the brain by reconstructing the surface of a volume produced from MRI data, and used these orientations to constrain their expressions for the brain s electric and magnetic fields. In another interesting application, Baker[1] phrased the motion tracking problem, important in computer vision, as a surface reconstruction problem. In this section, a surface reconstruction algorithm is introduced that produces surfaces that can be used for visualization or as input to an active contour algorithm. The necessary properties ....

H. Harlyn Baker. Building surfaces of evolution: The weaving wall. International Journal of Computer Vision, 3:51--71, 1989.

....start new tracks if there is a sufficiently large (2 pixel wide) gap between successive samples on the contour. While we do not operate directly on the spatiotemporal volume, our tracking and contour linking processes form a virtual surface similar to the weaving wall technique of Harlyn Baker [Bak89]. Unlike Baker s technique, however, we do not assume a regular and dense sampling in time. 3 Reconstructing surface patches The surface being reconstructed from a moving camera can be parametrized in a natural way by two families of curves [GW87, CB90] one family consists of the critical sets ....

H. H. Baker. Building surfaces of evolution: The weaving wall. International Journal of Computer Vision, 3(1):50--71, 1989.

....motion is concerned with using these low level motion descriptions in order to recover a coordinated sequence of events that can then be used to index into models of high level motion. Using spatiotemporal surfaces, Bolles and Baker [Boll87, Bake88b] examined how to recover camera motion. Baker [Bake88a] showed how to construct these spatiotemporal surfaces. Most of this work has concentrated on recovering camera motion rather than a description of high level motion in the scene. Badler and Smoliar [Badl79] presented a survey of representations of human movement. They reviewed: 1) human movement ....

....results in the lower left part of the left object and the top of the right object in Figure 3.8. These errors were caused because edge points from separate ST surfaces were recovered as one surface. In general, the problem of segmenting edge points into coherent ST surfaces is a difficult problem [Bake88a] which we have not focused on in this research. Gray level images are preferable in this respect since the intermediate steps of detecting edge points and segmenting them into ST surfaces are avoided. a) b) Figure 3.7: a) Middle frame from a 9 frame sequence of a doll translating down at 2 ....

H. H. Baker. Building surfaces of evolution: the weaving wall. Image Understanding Workshop, pages 1031--1040, 1988.

....the simplest case, the spacing between adjacent sections allows unambiguous solution of the correspondence problem by examining overlap between contours on adjacent sections. Many current methods solve the correspondence problem by making the assumption that the available data allow this approach [Bak89, LC87, WA86, ZJH87] If the available data are not sampled densely enough so that contours of the same object from adjacent slices overlap when projected onto the same plane, those methods will find multiple objects where only one is present. When available data are insufficient to allow an ....

H.Harlyn Baker. Building surfaces of evolution: The weaving wall. Int. J. Comput. Vision, 3:51--71, 1989.

....surface, oblique views with elevation keyed surface pseudocolors, and shaded surface rendering. For volume data of the form w = f(x; y; z) extensive attention has been paid to the 3D analogs of 2D contour plots and pseudocolor maps: see, for example, various methods for constructing isosurfaces [11, 1], viewing color coded density data [14, 12, 6] making easily visible pseudocolor maps [13] and exploiting transport theory [10] However, except for some exploratory efforts (see, e.g. 4, 9] the analogs of elevation maps for 3D scalar fields have not been pursued to their logical ....

....data and visualizing the values of the elevations in various ways with this constraint. Analogs of each of these depictions can be constructed for 3D scalar fields as well. For example, contour lines for 3D scalar fields are basically nested shells produced by an isosurface construction algorithm [11, 1]. If we add pseudocolor to indicate where the level sets are located within the volume, we can use the tiny cubes algorithm of Nielson et al. 13] to make the interior voxels of the cube visible. 3.1 Pseudocolor 4D Hemisphere We can easily define a 4D analog of the hemisphere we used for ....

H.H. Baker, "Building surfaces of evolution: the weaving wall," International Journal of Computer Vision, Vol. 3, No. 1, pp. 51--71, 1989.

....start new tracks if there is a sufficiently large (2 pixel wide) gap between successive samples on the contour. While we do not operate directly on the spatiotemporal volume, our tracking and contour linking processes form a virtual surface similar to the weaving wall technique of Harlyn Baker [Baker, 1989]. Unlike Baker s technique, however, we do not assume a regular and dense sampling in time. 3 Reconstructing surface patches The surface being reconstructed from a moving camera can be parametrized in a natural way by two families of curves [Giblin and Weiss, 1987; Cipolla and Blake, 1990] one ....

H. H. Baker. Building surfaces of evolution: The weaving wall. International Journal of Computer Vision, 3(1):50--71, 1989.

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H.H. Baker (1989). Building Surfaces of Evolution: The Weaving Wall. International Journal of Computer Vision, 3:51-71.

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Baker, Harlyn, "Building surfaces of evolution : The Weaving Wall," International Journal of Computer Vision, Volume 3:1, 1989.

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Baker, H. H. "Building Surfaces of Evolution: The Weaving Wall," IJCV, 3:51-71, 1989.

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