This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

We describe a new direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of Horn- and-Weldon to three views. Adding the third view enables us to solve for motion, and compute a dense depth map of the scene, directly from image spatio -temporal derivatives in a linear manner without first having to find point correspondences or compute optical flow. We describe the advantages and limitations of this method which are then verified through simulation and experiments with real images.