2004
DOI: 10.1007/978-3-540-24672-5_38
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Structure of Applicable Surfaces from Single Views

Abstract: Abstract. The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propa… Show more

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Cited by 50 publications
(31 citation statements)
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“…This problem can be avoided by computing the 3D shape directly from the correspondences, which amounts to solving a degenerate linear system and requires either reducing the number of degrees of freedom or imposing additional constraints [2]. The first can be achieved by various dimensionality reduction techniques [3], [4] while the second often involves assuming the surface to be either developable [5], [6], [7] or inextensible [8], [9], [10], [4]. These two approaches are sometimes combined and augmented by introducing additional sources of information such as shading or textural clues [11], [12] or physicsbased constraints [13].…”
Section: Introductionmentioning
confidence: 99%
“…This problem can be avoided by computing the 3D shape directly from the correspondences, which amounts to solving a degenerate linear system and requires either reducing the number of degrees of freedom or imposing additional constraints [2]. The first can be achieved by various dimensionality reduction techniques [3], [4] while the second often involves assuming the surface to be either developable [5], [6], [7] or inextensible [8], [9], [10], [4]. These two approaches are sometimes combined and augmented by introducing additional sources of information such as shading or textural clues [11], [12] or physicsbased constraints [13].…”
Section: Introductionmentioning
confidence: 99%
“…From the experimental figure it can be also seen that there is a better effect when the fitting curve is within 6 m and the trend of fitting error is smaller; along with the increasing distance, the fitting effect has shown a certain deviation and the fitting error is increased. So there is a linear relationship of RSSI value between adjacent distances which is less than 10 m, the not-measured RSSI value can be obtained by using the interpolation [33]. It is known that the real RSSI value is close to Gaussian distribution at different distance by analyzing the above section; the place of larger distribution density of RSSI is most likely to be the distance between receiving nodes and projection nodes.…”
Section: Ranging Methods Based Onmentioning
confidence: 99%
“…There are in fact relatively few others that can do this for deformable objects. One of them has been proposed in Gumerov et al (2004) but requires that the whole outline be detected, which severely limits its scope. Another is the tracking of Lin and Liu (2006) that exploits the repeating properties of a near regular texture to discover new texture tiles in new frames.…”
Section: Direct Methodsmentioning
confidence: 99%