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Unformatted text preview: produced by orthographic projection, what can be said about the interpolated images, i.e., are they also orthographic projections of the scene? ^ ^ To address this question, suppose that I1 and I2 are recti ed orthographic images of a scene with respective ^ ^ ^ views V1 and V2 , and Vi is an interpolated view. To see that the axes of the interpolated view are orthogonal, ^ ^ note that X1 and X2 both lie in the epipolar plane de^ 1 and Z2 . It follows by interpolation that Xi ^ ^ ned by Z also lies in the same epipolar plane. Because the view ^ coordinate systems are assumed orthonormal, Y1 and ^ 2 both coincide with the epipolar plane unit normal. Y ^ Therefore, Yi also coincides with the unit normal and ^ ^ the orthogonality of Xi and Yi follows. To determine the projective scale factors of an in^ terpolated view, we must consider the norms of Xi and ^ i . Although the unity of Yi is preserved, the norm ^ Y ^ of Xi depends on the interior angle between gaze di^^ rections: = arccosZ1  Z2 . Speci cally, it can be ^ shown by a geometric argument that the norm of Xi is given by q ^ kXi k = 2 , i2 + 22 , ii , 1cos + i , 12 6 resampling operation decreases image quality, it is advantageous to minimize the number of image transformations. One solution would be to perform steps 1 5 to obtain composite warping functions that directly map I1 to Ii and I2 to Ii respectively. Then the warp and cross-dissolve may be performed once at the end. 2 3 7 Experiments We present the results of the algorithm applied to two views of a Band-Aid box and to two views of a stapler and cube scene. For each pair of images, 5-10 point correspondences were manually chosen. Fig. 4 illustrates the control ow of the algorithm for the Band-Aid images. The original images, I1 and I2 , were rst recti ed using the procedure described in Section 5.2. A correspondence between uniform re^ ^ gions of I1 and I2 was found using a stereo matching ^ ^ algorithm. Then an image I1:5 halfway between I1 and ^ I2 was produced by linear interpolation of correspond^ ing regions. Finally, I1:5 was derecti ed to produce the intermediate image I1:5 . Notice that ne details such as the word BAND-AID" are preserved in I1:5 despite the fact that the image has undergone a warp, a crossdissolve, and multiple rotation, scale, and resampling operations. Fig. 5 shows two views of a stapler and cube scene. These images pose a challenge because some regions that are visible in one image are occluded in the other. For example, a metallic surface of the stapler is visible in I1 but completely occluded in I2 . This region appears fuzzy in I1:5 due to the cross-dissolve between the two images. We have found that local violations of the monotonicity assumption cause only local errors in corresponding regions of the interpolated images and do not corrupt the entire view interpolation procedure. This property is re ected in I1:5 where the occlusion of a surface of the stapler a ected only a limited area in the interpolated image. 4 5 6 7 8 9 10 11 8 Conclusion 12 In this p...
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This note was uploaded on 06/13/2011 for the course CAP 6938 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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