Differential geometry reconstructed


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Online Math: Differential Geometry

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Sign In. Access provided by: anon Sign Out. State-of-the-art camera calibration and 3D reconstruction systems are based on very sparse point features, such as SIFT, and projective geometry, which can only model points and lines or simple curves such as circles and other conic sections.

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These systems suffer from many of the following limitations: sparsity, requirements of simple scene, controlled acquisition, difficulty with non-planar objects, requirement of strong calibration, abundant texture, short baselines, and lack of geometric consistency. We believe these systems are useful but form only a module within a greater structure from motion system. Given two or more views of a fixed space curve, in we have shown how the torsion of the curve can be reconstructed from image measurements pdf.

Two views are necessary and sufficient, and more than 3 views provide an over-constrained solution. This initial study has opened an entire new line of research, where we have extended these results to most types of contours rigid, occluding, nonrigid , and have been modeling many other problems involving curvilinear phenomena in the geometry of multiple views, including camera auto-calibration from tracked curves, the use of surface patches and their shading under different illumination models, and fields of both short and long curve fragments for multiview applications.


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We are also working on a practical and comprehensive application for automatically reconstructing complex 3D objects from a sequence of images, and have completed many modules. One of our systems is based on image curve fragments as obtained from a subpixel edge linker. A simple step in corresponding curve fragments in two views is shown in the following figure, where the epipolar lines are in green:.

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Multiview Differential Geometry of Curves

We tackled the challenges of using linked curve fragments, namely the instabilities in linking and correspondence in the 3D Drawing system. The practicalities around nonrigid curves e. Research on Multiview Differential Geometry of Curves and Surfaces Ricardo Fabbri and Benjamin Kimia This project proposes a paradigm shift for 3D reconstruction from multiple perspective projections, based on differential geometry.

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Differential geometry reconstructed Differential geometry reconstructed
Differential geometry reconstructed Differential geometry reconstructed
Differential geometry reconstructed Differential geometry reconstructed
Differential geometry reconstructed Differential geometry reconstructed
Differential geometry reconstructed Differential geometry reconstructed
Differential geometry reconstructed Differential geometry reconstructed

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