Extracting structure from an affine view of a 3D point set with one or two bilateral symmetries

Fawcett, Roger; Zisserman, Andrew; Brady, J. Michael

doi:10.1016/0262-8856(94)90015-9

Cited by 18 publications

(5 citation statements)

References 16 publications

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“…With an arbitrary affine coordinate frame defined on the mirror, affine structure can be recovered. Our approach reported here is different from [4,13] in the following respects: a perspective camera model is used here rather than an affine one as in [4]; the structure recovered in our system is affine rather than projective as in [13].…”

Section: Introductionmentioning

confidence: 99%

“…In Rothwell et al's work [13], projective reconstruction of a set of 3D points is investigated and the rank of the matrix involved is used to verify the class of polyhedral the object belongs (the object itself need not be a polyhedron). Following that, Fawcett et al [4] report an affine reconstruction algorithm for an affine image of objects that have bilateral symmetries. In their work, reconstruction modulo an Euclidean transformation to a three parameter family of symmetric shapes is also discussed.…”

Section: Introductionmentioning

confidence: 99%

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Affine reconstruction from monocular vision in the presence of a symmetry plane

Huynh

1999

Proceedings of the Seventh IEEE International Conference on Computer Vision

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Affine reconstruction from monocular vision in the presence of a symmetry plane

Huynh

1999

Proceedings of the Seventh IEEE International Conference on Computer Vision

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“…There are a few works that use symmetry for grouping [43] and segmentation [13], [14], [25], [27], [54]. The majority of the symmetry-related papers consider either bilateral symmetry [12], [42], [57] or rotational symmetry [5], [16], [55], [34]. Some studies are even more specific, for example [30] suggests a symmetry measure for bifurcating structures, [17] handles tree structures and [16], [53] demonstrate the relation between symmetry and perspectivity on simple geometrical shapes.…”

Section: Introductionmentioning

confidence: 99%

“…There is a mass of work on symmetry and symmetry-axis detection [1], [5], [19], [23], [29], [31], [34], [44], [49]. Recovery of 3D structure from symmetry is explored in [12], [42], [45], [46], [50], [53], [57]. There are a few works that use symmetry for grouping [43] and segmentation [13], [14], [25], [27], [54].…”

Section: Introductionmentioning

confidence: 99%

On Symmetry, Perspectivity, and Level-Set-Based Segmentation

Riklin-Raviv

Sochen

Kiryati

2009

IEEE Trans. Pattern Anal. Mach. Intell.

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We introduce a novel variational method for the extraction of objects with either bilateral or rotational symmetry in the presence of perspective distortion. Information on the symmetry axis of the object and the distorting transformation is obtained as a by-product of the segmentation process.The key idea is the use of a flip or a rotation of the image to segment as if it has been another view of the object. We call this generated image the symmetrical counterpart image. We show that the symmetrical counterpart image and the source image are related by planar projective homography. This homography is determined by the unknown planar projective transformation that distorts the object symmetry.The proposed segmentation method uses a level-set based curve evolution technique. The extraction of the object boundaries is based on the symmetry constraint and the image data. The symmetrical counterpart of the evolving level-set function provides a dynamic shape prior. It supports the segmentation by resolving possible ambiguities due to noise, clutter, occlusions and assimilation with the background.The homography that aligns the symmetrical counterpart to the source level-set is recovered via a registration process carried out concurrently with the segmentation. Promising segmentation results of various images of approximately symmetrical objects are shown.

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“…Broadly speaking, existing methods may be divided into those that are geometrical in nature and those that are based upon photometric models. Turning our attention first to the geometric methods, the main contribution here has been to exploit projective geometry to develop algorithms for 3D object reconstruction [1]. Methodologically, the idea underpinning these algorithms is that of recovering both planar and curved surfaces from multiple views making use of calibration data and correspondance information.…”

Section: Introductionmentioning

confidence: 99%

Surface acquisition from single gray-scale images

Robles-Kelly¹,

Borş²,

Hancock³

Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429)

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In this paper we show how a system for performing automatic surface model acquisition from single object views can be designed. The surface acquisition process is a two step one. Firstly, the surface normals are computed using a shape-from-shading algorithm. Secondly, the field of surface normals is integrated into a 3D surface. For the surface integration step, we have performed experiments with two alternatives. The first of these is a geometric surface integration algorithm. The second alternative comprises a graph-spectral surface integration algorithm. We present results on images of classical statues and provide a preliminary quantitative study. . INTRODUCTIONSurface acquisition provides a route to automatic object and scene modelling that is of potential practical use to the computer graphics community. Broadly speaking, existing methods may be divided into those that are geometrical in nature and those that are based upon photometric models. Turning our attention first to the geometric methods, the main contribution here has been to exploit projective geometry to develop algorithms for 3D object reconstruction [1]. Methodologically, the idea underpinning these algorithms is that of recovering both planar and curved surfaces from multiple views making use of calibration data and correspondance information. For curved surfaces there has been considerable success in using turntable sequences for surface reconstruction from both detected feature points and occluding contours [2]. Photometric methods, on the other hand, aim to recover surface information from shading or texture variations. This is a classical problem in the computer vision community, which has lead to a considerable literature on the development of algorithms for shape-fromshading [3], photometric stereo [4] and shape-from-texture [5]. However, the drawbacks of these algorithms are twofold. Firstly, they tend to oversmooth surface detail. Secondly, they are prone to error due to their numerical inestability.In an effort to overcome the problems, Worthington and Hancock have developed a new framework for shape-from-shading [3] in which the image irradiance equation is treated as a hard constraint. The method delivers fields of surface normals (Gauss maps) at output. From the field of surface normals, the surface height may be recovered by applying a surface integration algorithm as a post-processing step.Our aim in this paper is to show how a surface acquisition system may be designed. We depart from the fact that a complete 3D representation of the object requires the depth information and the £ Supported by CONACYT, under grant No. 146475/151752. surface normals to be at hand. This becomes evident ever since the normals are of capital importance for accelerating complex rendering tasks, while the depth data is essential when a mesh or spline representation is required. Following this rationale, our acquisition system makes use of shape-from-shading algorithms and surface height integration methods for recovering the field of surfa...

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Extracting structure from an affine view of a 3D point set with one or two bilateral symmetries

Cited by 18 publications

References 16 publications

Affine reconstruction from monocular vision in the presence of a symmetry plane

Affine reconstruction from monocular vision in the presence of a symmetry plane

On Symmetry, Perspectivity, and Level-Set-Based Segmentation

Surface acquisition from single gray-scale images

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