Minimal Projective Reconstruction Including Missing Data

Anders Heyden 1 Fredrik Kahl 1 Long Quan 2
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : The minimal data necessary for projective reconstruction from point features is well-known when each object point is visible in all images. In this paper, we formulate and propose solutions to a new family of reconstruction problems for multiple images from minimal data, where there are missing points in some of the images. The ability to handle the minimal cases with missing data is of great theoretical and practical importance. It is unavoidable to use them to bootstrap robust estimation such as RANSAC and LMS algorithms and optimal estimation such as bundle adjustment. First, we develop a framework to parameterize the multiple view geometry, needed to handle the missing data cases. Then we present a solution to the minimal case of 8 points in 3 images, where one point is missing in one of the three images. We prove that there are in general as many as 11 solutions for this minimal case. Furthermore, all minimal cases with missing data for 3 and 4 images are catalogued. Finally, we demonstrate the method on both simulated and real images and show that the algorithms presented in this paper can be used for practical problems.
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IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2001, 23 (4), pp.418--423. 〈10.1109/34.917578〉
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Anders Heyden, Fredrik Kahl, Long Quan. Minimal Projective Reconstruction Including Missing Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2001, 23 (4), pp.418--423. 〈10.1109/34.917578〉. 〈inria-00590144〉

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