Now consider an in between view v3 with image i3 and

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Unformatted text preview: ith image I3 and epipolar line l3 corresponding to l1 and l2 . S1 , S2 , and S3 project to a set of uniform intervals of l3 , delimited by the projections of the visible endpoints of S1 , S2 , and S3 . Monotonicity is needed to ensure that the endpoints of each uniform interval in I3 correspond to the visible endpoints of S1 , S2 , and S3 . Notice that I3 does not depend on the speci c shape of surfaces in the scene, only on the positions of the visible endpoints of their cross sections. Any number of distinct scenes could have produced I1 and I2 , but each one would also project to I3 . Because correspondence or shape information within uniform regions is not necessary to predict in-between views, the aperture problem is avoided. To see why the monotonicity constraint is so crucial to view synthesis, observe that it is required not only to make the correspondence problem well-posed, but also to predict the appearance of uniform surfaces whose shapes are unknown. Furthermore, the in-between views are the only views that can be predicted with certainty due to the requirement that the visible endpoints of each surface remain xed. In practice, however, reasonable results may be obtained even when monotonicity is locally violated, as we demonstrate in Section 7. 4.2 The Aperture Problem Several tasks in 3D computer vision are complicated by the aperture problem, which arises due to uniformly colored surfaces in the scene. In the absence of strong lighting e ects, a uniform surface in the scene appears nearly uniform in projection. Although it is possible to determine which uniform regions correspond in different images, it is impossible to determine correspondences within these regions. As a result, additional smoothness assumptions are needed to solve problems such as optical ow and stereo vision 14 . In contrast, we show in this section that view synthesis does not su er from the aperture problem and is therefore inherently well-posed. Consider the projections of a set of uniform surfaces into images I1 and I2 each surface is uniformly colored, but any two surfaces may have di erent colors. Fig. 2 depicts the cross sections S1 , S2 , and S3 of three such surfaces projecting to epipolar lines l1 and l2 . Each connected cross section projects to a uniform interval of l1 and l2 . The monotonicity constraint induces a correspondence between the endpoints of the intervals in l1 and l2 , determined by their relative ordering. The points on S1 , S2 , and S3 projecting to 5 View Synthesis by Image Interpolation The previous section established that a speci c range of views of a scene can be predicted from two basis views. In this section we demonstrate that knowledge of camera positions is unnecessary and that new 3 views can be synthesized by geometrically interpolating the two basis images. First we describe morphing techniques and discuss their application for view synthesis. Then the connections between image transformations and changes in viewpoint are discussed. It is shown that after a simple recti c...
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