Abstract
In this chapter, we show that although the 3D orientations of edges and surfaces are theoretically sufficient for reconstructing the 3D object shape, this does not mean that the 3D object shape can actually be reconstructed. Specifying the edge and surface orientations is often “over-specification”, and inconsistency may result if image data contain errors. We propose a scheme of optimization to construct a consistent object shape from inconsistent data. Our optimization is achived by solving a set of linear equations; no searches and iterations are necessary. This technique is first applied to the problem of shape from motion and then to the 3D recovery based on the rectangularity hypothesis and the parallelism hypothesis.
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