Although stereo vision is a widely used mature technology for 3D surface reconstruction, there are still situations where stereo vision is difficult to apply. For example: surfaces with spatially slowly varying intensity; semi-transparent surfaces; and mirror-like surfaces. For these surfaces, making the necessary surface correspondences across multiple images is difficult if not impossible in a general setting. In these cases, there is often high contrast between object surface and background which enables 2D object boundaries to be more reliably detected. These 2D boundaries (silhouettes), often referred to as apparent contours, observed in 2D image, have complicated relations with the 3D object surface we want to reconstruct. These relations have been studied for the past three decades and several approaches have been developed. However all these approaches have various significant limitations. Proposed and studies in this thesis is a powerful and innovative mathematical framework for recovering 3D shape from silhouettes observed in a sequence of 2D images. The approach involves estimating the geometry of a surface dual to the 3D object to be reconstructed. The dual surface represents the family of 3D planes, in the scene being observed, that are tangent to the object to be reconstructed. This approach is very attractive because each tangent plane in the original space is directly measurable from an image and becomes a point in the dual space. The resulting object reconstruction algorithm is computationally fast, accurate, and robust.
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