We present a solution for optimal triangulation in three views. The solution is guaranteed to find the optimal solution because it computes all the stationary points of the (maximum likelihood) objective function. Internally,

A great deal of dynamic computer vision literature deals with the determination of motion and structure of rigid objects by observing points or lines on objects at two or more time instants. In this paper we determine circumstances under which a unique solution to structure and motion is almost always guaranteed when various combinations of point and line correspondences among several snapshots of an object are known. The case given the most consideration is that in which the object is moving with constant motion, that is, with constant rotation about an unknown center which itself is moving with constant translation. In this case we show that there is a unique solution for motion and structure when either two point and one line or one point and two line correspondences are known over three frames with known timing. There is also a unique solution when one point and one line correspondence are known over four frames. Several examples are given to illustrate our results.

In this paper we determine the multiplicity of solutions in several cases where line correspondences from orthographic projections over three views are known. We show that in the general case where the motion may vary between frames, seven line correspondences over three views are sufficient to guarantee that in general there is a unique solution for the rotation and directions of the lines, up to a reflection about a plane parallel to the camera plane. There is a three-parameter infinite family of solutions for the translations and depths of each line in this case. If the object is experiencing constant rotation, then four lines are sufficient to obtain solutions up to the same ambiguities. If the object is moving with constant rotation about a center of rotation which itself is moving in a straight line at constant velocity, then three lines are sufficient, and there is just a one-parameter infinite family of solutions for the translation and depths of the lines. Several examples are given to illustrate our results.

This paper deals with a problem in computer vision: how to recover the motion of a disk, thrown towards an observer, from a sequence of images acquired by a pinhole camera. Polynomial equations describing the motion are established, and techniques from algebraic geometry are used to show that in general a sequence of three images is sufficient for the recovery of motion of the disk when it is known to be moving along a straight line, and that five images suffice in the more general situation in which the disk travels in a gravitational field. Examples are worked out in detail to illustrate our results. 1. Introduction In this paper we consider the problem of recovering the physical motion of a disk when its outline, or just several points on its perimeter, are assumed to be visible to a pinhole camera imaging system. The perspective projection of the disk's boundary onto the image plane is an ellipse in general, with a line segment or a circle being special cases. Individual point cor...

In this paper, we present a robust method to estimate the three-dimensional egomotion of an observer moving in a static environment. This method combines the optical flow fields observed with multiple cameras to avoid the ambiguity of 3D motion recovery due to small field of view and small depth variation in the field of view. Two residual functions are proposed to estimate the ego-motion for different situations. In the non-degenerate case, both the direction and the scale of the three-dimensional rotation and translation can be obtained. In the degenerate case, rotation can still be obtained but translation can only be obtained up to a scale factor. Both the number of cameras and the camera placement affect the accuracy of the estimated ego-motion. We compare different camera configurations through simulation. Some results of real-world experiments are also given to demonstrate the benefits of our method. Key words: Ego-motion estimation; Multiple sensors; Optical flow 1 Introducti...