Several researchers 1 7 8 9 10 have used

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Unformatted text preview: researchers 1, 7, 8, 9, 10 have used interpolation to produce new images without establishing the physical validity of the resulting images. In addition to computing new views, these methods can be used to interpolate images of two di erent objects to achieve interesting e ects, although the plausibility of such transformations is di cult to assess. The applicability of each of these previous approaches is limited by the requirement that complete correspondence information must be available. A complete correspondence is generally impossible to obtain automatically, due to the aperture problem. A theoretical contribution of this paper is to show that for a general class of scenes and views, the problem of view synthesis is in fact well-posed and does not require a full correspondence. I = S 4 View Synthesis from Images The process of rendering views of a known three dimensional scene is well-understood in the graphics community. The inverse problem, of reconstructing the scene from a collection of images, has been wellstudied, but is known to be ill-posed in general due to the aperture problem. In this paper, we are concerned with using a set of views of a scene to synthesize new views of the same scene. Because this would seem to entail solving both problems, i.e., reconstruction and rendering, the natural conclusion would be that imagebased view synthesis is also inherently ill-posed. However, this turns out not to be the case. We show in this section that image-based view synthesis is in fact a well-posed problem under a monotonic visibility constraint and is not a ected by the aperture problem. 4.1 The Monotonicity Constraint A fundamental di culty in 3D reconstruction from images is the problem of establishing correspondences between points in di erent images. The correspondence problem is often mitigated in practice by the epipolar constraint, which states that the projection of a scene feature in one image must appear along a particular line in a second image. This constraint reduces the search for correspondences to a 1-D search along epipolar lines. Further constraints have been used to help reduce the search within epipolar lines by making assumptions about the structure of the scene. One example of such a constraint is monotonicity 12, 13 , which requires that the relative ordering of points along epipolar lines be preserved. Let I1 and I2 be two images of a scene taken from views V1 and V2 , respectively. For brevity, quantities associated with view Vi will henceforth be written with subscript i. Any point P in the scene de nes an epipolar plane E12 spanned by the two plane normals and passing through P. The epipolar lines l1 and l2 are the respective intersections of E12 with V1 and V2 . Monotonicity states that the projections of any two points on E12 appear in the same order along l1 and l2 . If this property holds for all corresponding epipolar lines in the two views then we say that monotonicity holds for I1 and I2 . Let P and Q...
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