3D structure from a single calibrated view using distance constraints

We propose a new method to recover scene points from a single calibrated view using a subset of distances among the points. This paper first introduces the problem and its relationship with the perspective 17 point problem. Then the number of distances required to uniquely recover scene points are explored. The result is then developed into a practical vision algorithm to calculate the initial points' coordinates using distance constraints. Finally SQP (Sequential Quadratic Programming) is used to optimize the initial estimations. It can minimize a cost function defined as the sum of squared reprojection errors while keeping the specified distance constraints strictly satisfied. Both simulation data and real scene images have been used to test the proposed method, and good results have been obtained.