Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.

We present a technique for building a three-dimensional description of a static scene from a dense sequence of images. These images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image. The technique utilizes knowledge of the camera motion to form and analyze slices of this solid. These slices directly encode not only the three-dimensional positions of objects, but also such spatiotemporal events as the occlusion of one object by another. For straight-line camera motions, these slices have a simple linear structure that makes them easier to analyze. The analysis computes the threedimensional positions of object features, marks occlusion boundaries on the objects, and builds a threedimensional map of "free space. " In our article, we first describe the application of this technique to a simple camera motion, and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects. 1

Leonard McMillan Jr. An Image-Based Approach to Three-Dimensional Computer Graphics (Under the direction of Gary Bishop) The conventional approach to three-dimensional computer graphics produces images from geometric scene descriptions by simulating the interaction of light with matter. My research explores an alternative approach that replaces the geometric scene description with perspective images and replaces the simulation process with data interpolation. I derive an image-warping equation that maps the visible points in a reference image to their correct positions in any desired view. This mapping from reference image to desired image is determined by the center-of-projection and pinhole-camera model of the two images and by a generalized disparity value associated with each point in the reference image. This generalized disparity value, which represents the structure of the scene, can be determined from point correspondences between multiple reference images. The image-warpi...

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We evaluated six algorithms for computing egomotion from image velocities. We established benchmarks for quantifying bias and sensitivity to noise, and for quantifying the convergence properties of those algorithms that require numerical search. Our simulation results reveal some interesting and surprising results. First, it is often written in the literature that the egomotion problem is difficult because translation (e.g., along the X-axis) and rotation (e.g., about the Y-axis) produce similar image velocities. We found, to the contrary, that the bias and sensitivity of our six algorithms are totally invariant with respect to the axis of rotation. Second, it is also believed by some that fixating helps to make the egomotion problem easier. We found, to the contrary, that fixating does not help when the noise is independent of the image velocities. Fixation does help if the noise is proportional to speed, but this is only for the trivial reason that the speeds are slower under fixatio...

This report describes research done within the Artificial Intelligence Laboratory and the Center for Biological Information Processing (Whitaker College) at the Massachusetts Institute of Technology. Support for the A.I. Laboratory 's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-85-K-0124. Support for this research is also provided by the Alfred P. Sloan Foundation, the Office of Naval Research, Cognitive and Neural Systems Division, the National Science Foundation and the McDonnell Foundation

A novel approach for the computation of optical flow based on an L type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of synthetic and real image sequences in order to illustrate the theory as well as the numerical approach.

This paper presents a method for efficiently rendering a sequence of regularly spaced perspectives of a scene. The algorithm presented, called Multiple Viewpoint Rendering (MVR), exploits perspective coherence by rendering epipolar plane images. The computer graphics camera geometry is constrained to produce epipolar plane images with linear features. Transformation and shading operations can be performed once per image sequence instead of once per view. Geometric position, color, and texture coordinates can be computed using linear interpolation. Both view independent and dependent shading algorithms are supported. Both one and two-dimensional grids of perspectives can be rendered. Details of a hardware-accelerated implementation of a multiple viewpoint polygon renderer are given. 1 Introduction Most of the time, photography captures information about the world as seen from a single viewpoint. A still camera's single lens records a scene as it appears at one instant, while a movie cam...

In robot navigation a model of the environment needs to be reconstructed for various applications, including path planning, obstacle avoidance and determining where the robot is located. Traditionally, the model was acquired using two images (two--frame Structure from Motion) but the acquired models were unreliable and inaccurate. Recently, research has shifted to using several frames (multi--frame Structure from Motion) instead of just two frames. However, almost none of the reported multi--frame algorithms has produced accurate and stable reconstructions for general robot motion. The main reason seems to be that the primary source of error in the reconstruction -- the error in the underlying motion -- has been mostly ignored. Intuitively, if a reconstruction of the scene is made up of points, this motion error affects each reconstructed point in a systematic way. For example, if the translation of the robot is erroneous in a certain direction, all the reconstructed points would be sh...

This paper presents a visibility solution for a specific type of scene description, called a