Computing shape and depth from stereo vision and shading is one of the important perceptual tasks in early vision. This thesis work is aimed at understanding the computational issues involved in reconstructing a viewed surface in three dimension.;In using stereo vision to compute depth, stereo correspondence between points in the left and right images can be reliably achieved only at points of intensity changes. Owing to the need for computing depth at every point in the image, interpolation of this sparse depth data becomes necessary. Since several surfaces can fit a given sparse grid, an appropriate choice comes from imposing additional constraints. In our work, we propose that the interpolant should not only introduce any additional discontinuities (other than those dictated by the intensity changes), but also that they should preserve those discontinuities. A class of interpolants known as Shepard's surfaces, is shown here to satisfy this constraint. The Shepard's interpolants have been implemented here and the result from testing them on Random DOt Stereograms shows that stereo vision can function alone without any additional visual cues. The natural stereo pair shows that even when intensity changes are sparse the reconstruction preserves the shape although, the interpolant exhibits a tendency to consider spurious stereo matches also as a potential data point.;Besides depth from stereopsis, shape information also becomes important to reconstruct the surface. An important shape cue is available in the smooth shading that an object renders. From the perspective of obtaining shape description (instead of surface normals alone), we propose a method to compute relative depth, normals and principal curvatures of the surface. Shape information is intrinsic to the surface and is independent of viewer position. Since continuity in normals is ensured through these shape descriptors, the numerical error introduced in the process of reconstruction is shown to be independent of coordinate axes chosen. Our method involves minimization of a global objective function formulated by imposing the following constraints: (i) continuity and integrability of the normals, (ii) minimal deviation from the irradiance values, and (iii) unit normal. Minimizing the objective function with respect to the normals n, relative depth z and shape descriptor A, results in direct computation of all these quantities. In addition, the principal curvatures are shown to be computable from the shape descriptor used here.;Shape and depth information may also be available from other visual cues. We show that depth information at arbitrary set of points can be included as additional set constraints in the shape computing algorithm. Also, any known set of normals can also be exploited to improve the convergence of the shape from shading algorithm, besides smoothly incorporating the additional source of information.;This work, in essence, has resulted in developing a framework that delivers shape information in the form of local curvatures and depth at every point in the image plane.
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