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Title: Image-based reconstruction and visual hull from imprecise input
Author: He, Peng
ISNI:       0000 0004 1918 5447
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2012
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Image-based reconstruction is a series of computer vision processes which takes 2D images of the scene as input and outputs the geometric shape approximate of the scene. It has vast applications in industrial design, manufacture, gaming, filming, heritage protection and many other areas. The visual hull of a polyhedral (or polygonal) scene in R3 (or R2) is the best 3D (or 2D) shape that one can retrieve from its silhouettes. It has great advantage in obstacle avoidance, robotic navigation, 3D model acquisition and human motion tracking. A 3D visual hull is bounded by planes and quadratic surfaces. Classical image-based reconstruction and visual hull methods fail to maintain the exactness and robustness when the input is imprecise. In the solid domain of 3D objects in R3, geometric shapes with imprecision are well modelled and carefully studied. Each partial geometric object is defined by two disjoint open sets : interior and exterior. The interior (respectively, exterior) is an open set that contains all the points definitely known to be inside (respectively, outside) the object. Partial objects, ordered with subset inclusion, form a continuous Scott domain in which each object approximates the target object at a certain level of precision. We study the image-based reconstruction and visual hull in the solid domain which allows the notion of the partial polyhedron and the partial visual hull. They capture the imprecision in the input polyhedral scenes and outputs the exact information about what points are definitely inside or outside the reconstructed scene and the visual hull. The partial image-based reconstruction and the partial visual hull algorithm maintain the same computational complexity as the corresponding classical methods. The outputs of the algorithms are partial objects or partial visual hulls which converge to their classical counterparts as the input converges to an exact value. For the image-based reconstruction and the 2D visual hull, we show that their construction processes with imprecise input are Hausdro and the Scott continuity. For the 3D visual hull algorithm, we show its Hausdro and the Scott continuity of the domain-theoretic construction in the Solid domain of the projective 3 space P3. Furthermore, we prove the computability of the image-based reconstruction, the 2D and the 3D visual hull.
Supervisor: Welton, Tom Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral