Image recti cation ensures valid interpolated views

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Unformatted text preview: images are appropriately recti ed and satisfy monotonicity. Image recti cation ensures valid interpolated views ^ ^ and a smooth transition between I1 and I2 . If, instead, the goal is to obtain a smooth transformation between the original images I1 and I2 , it is necessary to also interpolate the recti cation transformations, R, 1 , R, 2 , Hs , T1, and T2 . Accordingly, let I^1 ^ and I2 be two images recti ed by Eqs. 4 and 5. The angle, scale and translation of image Ii with re^ spect to Ii are given by i = 2 , i 1 + i , 1 2 , si = 2 , i + i , 1s, and Ti = 2 , iT1 + i , 1T2 . Using Eqs. 4 and 5 as boundary conditions, Ii , 1  i  2, produces a sequence of views that interpolates I1 and I2 given by ^ Ii = R H1=s Ii , Ti 7 i 6 A Scanline View Interpolation Algorithm In Section 4 we argued that synthesis of a range of views under monotonicity is possible. In this section we attest that view synthesis is practical and describe an algorithm for generating in-between views from two basis images and minimal user-provided correspondence information. It is assumed that at least 4 corresponding reference features are provided in images I1 and I2 . Based on these features, the images can be recti ed using the procedure described in Section 5.2 to produce im^ ^ ages I1 and I2 . Once the images have been recti ed, correspondences are found between uniform intervals in conjugate scanlines in the two images. With ideal data, the correspondence is completely determined by the monotonicity constraint. In practice, errors and noise in the imaging process complicate matters, causing monotonicity to be locally violated. Consequently, our approach is to nd the optimal monotonic warp ^^ ^^ ^ W of I1 that minimizes jW I1  , I2 j. We employ a stereo correspondence algorithm adapted from 13 to nd W that uses both inter-scanline and intra-scanline constraints. We chose to use dynamic programming techniques because they make strong use of monotonicity and are relatively simple to implement. It should be noted, however, that our approach is not dependent on a particular stereo matching algorithm; other researchers 1, 9, 10 have had success with di erent stereo algorithms for view synthesis. The complete algorithm is as follows: 1. Obtain either 4 or more feature correspondences or relative camera positions from the user ^ ^ 2. Rectify I1 and I2 to produce I1 and I2 . 3. Match uniform intervals of corresponding scan^ ^ lines in I1 and I2 4. For each scanline, linearly interpolate positions and intensities of corresponding intervals ^ 5. Derectify Ii to produce Ii using Eq. 7. A disadvantage of this ve-step approach is that it requires multiple image resampling operations, incurred by repeated rotations and scales. Since each i 5.4 Orthographic View Interpolation The above discussion demonstrates that interpolation of recti ed images produces valid views using a general a ne view model. In practice, a ne projection may be too lenient in that arbitrary image skews are permitted. If the two basis images were...
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