Detecting Critical Configurations for Euclidean 3D Reconstruction by Analyzing the Scaled Measurement Matrix 3D reconstruction is ambiguous under socalled critical motions or critical surfaces. This paper proposes an algorithm to detect a few critical configurations where Euclidean reconstruction degenerates. Assuming that the focal lengths are the only unknown intrinsic parameters, the following critical configurations are detected: (1) coplanar 3D points, (2) pure rotation; (3) rotation around two camera centers; (4) presence of excessive noise and outliers in the measurements. The configurations in Cases (1), (2) and (4) will affect the rank of the scaled measurement matrix (SMM). The number of camera centers in Case (3) will affect the number of independent rows of the SMM. By examining the rankness and the number of independent rows of the SMM, we are able to detect the abovementioned critical configurations. Experimental results on both synthetic and real data demonstrate the effectiveness of the proposed algorithm on detecting the critical situations for factorizationbased 3D reconstruction.

Structure and Motion from Points, Lines and Conics with Affine Cameras We present an integrated approach that solves the structure and motion problem for affine cameras. Given images of corresponding points, lines and conics in any number of views, a reconstruction of the scene structure and the camera motion is calculated, up to an affine transformation. Starting with three views, two novel concepts are introduced. The first one is a quasitensor consisting of 20 components and the second one is another quasitensor consisting of 12 components. These tensors describe the viewing geometry for three views taken by an affine camera. It is shown how correspondences of points, lines and conics can be used to constrain the tensor components. A set of affine camera matrices compatible with the quasitensors can easily be calculated from the tensor components. The resulting camera matrices serve as an initial guess in a factorisation method, using points, lines and conics concurrently, generalizing the wellknown factorisation method by TomasiKanade (1992). Finally, examples are given that illustrate the developed methods on both simulated and real data