Recovery of 3D Models from Images

Recovery of 3D coordinates from sets of images is useful in many areas. This allows for reconstruction of objects and recovery of motion characteristics from images. For this to be possible, the orientation and position of the cameras with respect to each other must be recovered rst. This is the classic photogrammetric problem of relative orientation. Once this is solved, corresponding intersections from pairs of points may be found by projecting the rays from each camera through the images. The work here involves taking a 3D model and projecting it onto diierent planes. The resulting images are used to determine the relative orientation of the cameras. From these, matched rays are projected and nearest intersections are computed. The resulting intersections are the recovered 3D coordinates from the original model. This plan reassures that the methods for reconstruction are working properly. Then matched points from pairs of images are used to derive the 3D coordinates. 1 Background In reconstructing a 3D model from a pair of 2D images there are a number of problems that must be dealt with. The rst of these is the correspondence problem. Here the issue is determining points in the images that correspond to the same point on the 3D object. Next is the Relative Orientation Problem. Here the goal is to nd the correct orientation of one of the cameras relative to the other camera such that the pairs of corresponding rays (projected from the center of projections of each camera through the image and out into 3D space) all intersect one another. The problem of determining the relative orientation of two images is not a new one. Much of the work in solving this problem has been done in photogrammetry researchh5]. Unfortunately, this work has had the beneet of having datasets that were limited in complexity. That is, the assumptions that could be made concerning the orientation of the cameras and of the subject points were rather wide ranging and greatly reduced the complexity of the problem. In current research, however, there is a need for more general solutions to the relative orientation problem so that little (if any) information is required about the initial orientation of the cameras. Once the relative orientation of the cameras has been established then the reconstruction of the 3D model may be performed. 2 Related Work Haralick and Shapiroo4] take a traditional approach to the solution of the …