The structure and motion problem of multiple onedimensional projections of a two-dimensional environment is studied. One-dimensional cameras have proven useful in several different applications, most prominently for autonomous guided vehicles, but also in ordinary vision for analysing planar motion and the projection of lines. Previous results on one-dimensional vision are limited to classifying and solving minimal cases, bundle adjustment for finding local minima to the structure and motion problem and linear algorithms based on algebraic cost functions.In this paper, we present a method for finding the global minimum to the structure and motion problem using the max norm of reprojection errors. We show how the optimal solution can be computed efficiently using simple linear programming techniques. The algorithms have been tested on a variety of different scenarios, both real and synthetic, with good performance. In addition, we show how to solve the multiview triangulation problem, the camera pose problem and how to dualize the algorithm in the Carlsson duality sense, all within the same framework.978-1-4244-1631-8/07/$25.00 ©2007 IEEE

Abstract. Automatic construction of Shape Models from examples has recently been the focus of intense research. These methods have proved to be useful for shape segmentation, tracking, recognition and shape understanding. In this paper we discuss automatic landmark selection and correspondence determination from a discrete set of landmarks, typically obtained by feature extraction. The set of landmarks may include both outliers and missing data. Our framework has a solid theoretical basis using principles of Minimal Description Length (MDL). In order to exploit these ideas, new non-heuristic methods for (i) principal component analysis and (ii) Procrustes mean are derived -as a consequence of the modelling principle. The resulting MDL criterion is optimised over both discrete and continuous decision variables. The algorithms have been implemented and tested on the problem of automatic shape extraction from feature points in image sequences.