Linear multi view reconstruction with missing data

Abstract

General multi view reconstruction from affine or projective cameras has so far been solved most efficiently using methods of factorizing image data matrices into camera and scene parameters. This can be done directly for affine cameras [18] and after computing epipolar geometry for projective cameras [17]. A notorious problem has been the fact that these factorization methods require all points to be visible in all views. This paper presents alternative algorithms for general affine and projective views of multiple points where a) points and camera centers are computed as the nullspace of one linear system constructed from all the image data b) only three points have to be visible in all views. The latter requirement increases the flexibility and usefulness of 3D reconstruction from multiple views. In the case of projective views and unknown epipolar geometry, an additional algorithm is presented which initially assumes affine views and compensates iteratively for the perspective effects. In this paper affine cameras are represented in a projective framework which is novel and leads to a unified treatment of parallel and perspective projection in a single framework. The experiments cover a wide range of different camera motions and compare the presented algorithms to factorization methods, including approaches which handle missing data.