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authors Laveau, S. and Faugeras, O.
year 1994
title 3D Scene Representation as a Collection of Images and Fundamental Matrices
source INRIA Report
summary The problem we solve in this paper is the following. Suppose we are given N views of a static scene obtained from different viewpoints, perhaps with different cameras. These viewpoints we call reference viewpoints since they are all we know of the scene. We would like to decide if it is possible to predict ano- ther view of the scene taken by a camera from a viewpoint which is arbitrary and a priori di erent from all the reference viewpoints. One method for doing this would be to use these viewpoints to construct a three-dimensional repre- sentation of the scene and reproject this representation on the retinal plane of the virtual camera. In order to achieve this goal, we would have to establish some sort of calibration of our system of cameras, fuse the three-dimensional representations obtained from, say, pairs of cameras thereby obtaining a set of 3-D points, the scene. We would then have to approximate this set of points by surfaces, a segmentation problem which is still mostly unsolved, and then intersect the optical rays from the virtual camera with these sur- faces. This is the most straightforward way of going from a set of images to a new image using the current computer vision paradigm of rst building a three-dimensional representation of the environment from which the rest is derived. We do not claim that there does not exist any simpler way of using the three-dimensional representation than the one we just sketched, but this is just simply not our point. Our point is that it is possible to avoid entirely the explicit three-dimensional reconstruction process: the scene is represented by its images and by some ba- sically linear relations that govern the way points can be put in correspondence between views when they are the images of the same scene-point. These images and their algebraic relations are all we need for predicting a new image. This approach is similar in spirit to the one that has been used in trinocular stereo. Hypotheses of correspondences between two of the images are used to predict features in the third. These predictions can then be checked to validate or inva- lidate the initial correspondence. This approach has proved to be quite e cient and accurate. Related to these ideas are those develo- ped in the photogrammetric community under the name of transfer methods which nd for one or more image points in a given image set, the corresponding points in some new image set.
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