Triangulation of Points, Lines and Conics
The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions - they are either plagued by local minima or rely on a non-optimal cost-function.
A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data.
KeywordsFractional Programming Bundle Adjustment Convex Envelope Second Order Cone Program Point Case
- 2.Slama, C.C.: Manual of Photogrammetry. American Society of Photogrammetry, Falls Church (1980)Google Scholar
- 5.Stewénius, H., Schaffalitzky, F., Nistér, D.: How hard is three-view triangulation really? In: Int. Conf. Computer Vision, Beijing, China (2005)Google Scholar
- 6.Kahl, F., Henrion, D.: Globally optimal estimates for geometric reconstruction problems. In: Int. Conf. Computer Vision, Beijing, China (2005)Google Scholar
- 8.Harris, C., Stephens, M.: A combined corner and edge detector. In: Alvey Vision Conference, pp. 147–151 (1988)Google Scholar
- 9.Triggs, B.: Detecting Keypoints with Stable Position, Orientation, and Scale under Illumination Changes. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 100–113. Springer, Heidelberg (2004)Google Scholar