A linear dual-space approach to 3D surface reconstruction from occluding contours using algebraic surfaces

Kang, Kongbin; Tarel, Jean-Philippe; Fishman, R.; Cooper, David B.

doi:10.1109/iccv.2001.937518

Cited by 22 publications

(31 citation statements)

References 10 publications

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“…Some recent SFS algorithms [20][21][22] make use of the duality property between points and planes. Kang et al [21] partitioned 3D scene-space into an array of cubes and estimated a 3D quadric surface patch in the 4 dimensional homogeneous dual space consisting of tangent planes.…”

Section: Previous Workmentioning

confidence: 99%

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Shape from silhouette outlines using an adaptive dandelion model

Liu

Yao

Gao

2007

Computer Vision and Image Understanding

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Section: Previous Workmentioning

confidence: 99%

“…Kang et al [21] partitioned 3D scene-space into an array of cubes and estimated a 3D quadric surface patch in the 4 dimensional homogeneous dual space consisting of tangent planes. Then a single higher degree algebraic surface is fitted to all or many of those quadric patches to obtain an estimation of the complex object surface.…”

Section: Previous Workmentioning

confidence: 99%

Shape from silhouette outlines using an adaptive dandelion model

Liu

Yao

Gao

2007

Computer Vision and Image Understanding

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“…The dual theory introduced in [1] and [2] tackles the problem of reconstructing the original surface r from the tangent plane space sampled from silhouettes with known projection matrices P. An example illustrating the sampling of tangent planes from silhouettes is given in Fig. 1.…”

Section: A Existing Dual Space Theory and Possible Problemsmentioning

confidence: 99%

Robust Recovery of Shapes with Unknown Topology from the Dual Space

Chen

Wong

2007

IEEE Trans. Pattern Anal. Mach. Intell.

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In this paper, we address the problem of reconstructing object surface from silhouettes. Previous works by other authors have shown that, based on the principle of duality, surface points can be recovered, theoretically, as the dual to the tangent plane space of the object. In practice, however, the identification of tangent basis in the tangent plane space is not trivial given a set of discretely sampled data. This problem is further complicated by the existence of bi-tangents to the object surface. The key contribution of this paper is the introduction of epipolar parameterization in identifying a well-defined local tangent basis. This extends the applicability of existing dual space reconstruction methods to handle fairly complicated shape without making any explicit assumption on the object topology. We verify our approach with both synthetic and real-world data, and compare it both qualitatively and quantitatively with other popular reconstruction algorithms. Experiment results demonstrate that our proposed approach produces more accurate estimation, whilst maintains reasonable robustness towards shapes with complex topologies.

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“…Another possibility is to assume that the surface is locally of order 2, thus with a predictable local behavior. It is more or less the assumption made in duality based approaches [13,5,17] where the surface is assumed to be locally a quadric, or where finite differences are used to estimate derivatives. Our approach differs by the fact that we constrain the points we estimate to be inside well defined intervals along viewing rays, namely viewing edges.…”

Section: Contributions Along Viewing Edgesmentioning

confidence: 99%

“…Our work is founded on the same observation that viewing lines along silhouette contours, and thus the visual hull surface, are tangent to the observed object surface. Following also this observation, approaches [9,13,5,17] exploit the duality that exists between points and planes in 3D space, and estimate the dual of the surface tangent planes as defined by silhouette contour points. However, these approaches do not account for the fact that surface points lie on known viewing lines, in known intervals, and suffer therefore from various singularities.…”

Section: Introductionmentioning

confidence: 99%

Visual Shapes of Silhouette Sets

Franco

Lapierre

Boyer

2006

Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)

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Shape from silhouette methods are extensively used to model dynamic and non-rigid objects using binary foreground-background images. Since the problem of reconstructing shapes from silhouettes is ambiguous, a number of solutions exist and several approaches only consider the one with a maximal volume, called the visual hull. However, the visual hull is not always a good approximation of shapes, in particular when observing smooth surfaces with few cameras. In this paper, we consider instead a class of solutions to the silhouette reconstruction problem that we call visual shapes. Such a class includes the visual hull, but also better approximations of the observed shapes which can take into account local assumptions such as smoothness, among others. Our contributions with respect to existing works is first to identify silhouette consistent shapes different from the visual hull, and second to give a practical way to estimate such shapes in real time. Experiments on various sets of data including human body silhouettes are shown to illustrate the principle and the interests of visual shapes.

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A linear dual-space approach to 3D surface reconstruction from occluding contours using algebraic surfaces

Cited by 22 publications

References 10 publications

Shape from silhouette outlines using an adaptive dandelion model

Shape from silhouette outlines using an adaptive dandelion model

Robust Recovery of Shapes with Unknown Topology from the Dual Space

Visual Shapes of Silhouette Sets

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