This thesis introduces novel algorithms for 3D shape recovery under multiple viewpoints and single viewpoint. Surface of a 3D object is reconstructed by either graph-cuts using images under multiple viewpoints, depth from reflection under a fixed viewpoint, or depth from refraction under a fixed viewpoint. The first part of this thesis revisits the graph-cuts based approach for solving the multi-view stereo problem and proposes a novel foreground / background energy. Unlike traditional graph-cuts based methods which focus on the photo-consistency energy, this thesis targets at deriving a robust and unbiased foreground / background energy which depends on data. It is shown that by using the proposed foreground / background energy, it is possible to recover the object surface from noisy depth maps even in the absence of the photo-consistency energy, which demonstrates the effectiveness of the proposed energy. In the second part of this thesis, a novel method for shape recovery is proposed based on reflection of light using a spherical mirror. Unlike other existing methods which require the prior knowledge of the position and the radius of the spherical mirror, it is shown in this thesis that the object can be reconstructed up to an unknown scale using an unknown spherical mirror. This thesis finally considers recovering object surfaces based on refraction of light and presents a novel depth from refraction method. A scene is captured several times by a fixed camera, with the first image (referred to as the direct image) captured directly by the camera and the others (referred to as the refracted images) by placing a transparent medium with two parallel planar faces between the scene and the camera. With a known pose and refractive index of the medium, a depth map of the scene is then recovered from the displacements of scene points in the images. Unlike traditional depth from refraction methods which require extra steps to estimate the pose and the refractive index of the medium, this thesis presents a novel method to estimate them from the direct and refracted images of the scene. It is shown that the pose of the medium can be recovered from one direct image and one refracted image. It is also shown that the refractive index of the medium can be recovered with a third image captured with the medium placed in a different pose. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

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We introduce the naive notion of a relative open book decomposition for contact 3-manifolds with torus boundary. We then use this to construct nice, minimal genus open book decompositions compatible with all of the universally tight contact structures (as well as a few others) on torus-bundles over S¹, following Honda's classification. In an accurate sense, we find Stein fillings of 'half' of the torus bundles. In addition, these give the first examples of open books compatible with the universally tight contact structures on circle bundles over higher genus surfaces, as well, following a pattern introduced by a branched covering of B⁴. Some interesting examples of open books without positive monodromy are emphasized.

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Traditionally, volumetric modalities such as CT and MRI have provided static snapshots of anatomy enabling insight into the progression of disease and to the severity of injury. Recently, 3D-registration algorithms, originating in the neurosurgical field, have been used to merge these images resulting in richer visualizations. However, in situations where trauma patients are unable to be moved or are at risk of infection, there have been comparatively few advances. This thesis presents a 3D-registration framework that supports longitudinal study of morphologic changes in surface images of the upper body based on an optical technique - structured light imaging. The framework incorporates soft-tissue deformation modeling to allow coordinate frame determination and specific point tracking required for applications of Computer-Integrated Surgery. The framework is implemented in three stages using a coarse-fine approach that separately addresses the different sources of registration error commonly found in temporal registration applications. The coarse stage defines seven thoracic fiducials that form a rigid body. A special anthropomorphic stand is designed and used to enforce a rigid body assumption. Experimental results show the fiducials to have precision of approximately 2 mm. The medium stage incorporates the novel use of ultraviolet light as a surface registration technique. UV is used to avoid error caused when the projected light stripes interfere with the marker material - a common problem with external landmarks and optical assessment systems. A semi-automatic algorithm for identifying the centre of the fiducials is given and shown to be highly accurate - to within 1 pixel precision compared to the visually assessed centre. The movement of these fiducials is also modelled at the extremes of the respiratory cycle with individual fiducials moving from 5-17 mm. A least-squares algorithm is implemented to bring surfaces together based on their fiducial locations and rigid-body motion. This algorithm results in RMS error of approximately 1.17 +/- 0.45 mm. The fine stage involves finding fixed point correspondences in changed regions between a base surface and a comparison surface acquired at a different time given the rigid body registration from the previous stages. Five algorithmic variants are assessed using two simulations of thoracic swelling. The results do not show statistical significance between variants but do indicate visually some promising results. An application of this framework could be the near real-time guidance of the FAROArm, a precision measuring instrument commonly used in Computer-Integrated Surgery, to these points. This would facilitate the collection of functional information of clinical interest while maintaining positional congruence with data acquired at a different time point.

Thesis (M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ. 81-84)

Thesis (Ph. D.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains vii, 99 p. : ill. (some col.), maps (some col.). Includes abstract. Includes bibliographical references.

Thesis (Ph.D.)--University of Texas at Dallas, 2007. / Includes vita. Includes bibliographical references (leaves 102-110)

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: N-dimensional; data; visualization; dimensional stacking; recursive. Includes bibliographical references (leaves 48-51).