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Abstract. In a scene observed from a xed viewpoint, the set of shadow curves in an image changes as a point light source (nearby or at in nity) assumes di erent locations. We show that for any nite set of point light sources illuminating an object viewed under either orthographic or perspective projection, there isanequivalence class of object shapes having the same set of shadows. Members of this equivalence class di er by afourparameter family of projective transformations, and the shadows of a transformed object are identical when the same transformation is applied to the light source locations. Under orthographic projection, this family is the generalized bas-relief (GBR) transformation, and we show that the GBR transformation is the only family of transformations of an object's shape for which the complete set of imaged shadows is identical. Finally, we show that given multiple images under di ering and unknown light source directions, it is possible to reconstruct an object up to these transformations from the shadows alone. 1

We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual process is a central theme in visual psychology, psychophysics and computational vision. In many of the computational models employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence, the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters c...

Abstract. Since uncalibrated images permit only projective reconstruction, metric information requires either camera or scene calibration. We propose a stratified approach to projective reconstruction, in which gradual increase in domain information for scene calibration leads to gradual increase in 3D information. Our scheme includes the following steps: (1) Register the images with respect to a reference plane; this can be done using limited scene information, e.g., the knowledge that two pairs of lines on the plane are parallel. We show that this calibration is sufficient for ordinal reconstruction- sorting the points by their height over the reference plane. (2) If available, use the relative height of two additional out-of-plane points to compute the height of the remaining points up to constant scaling. Our scheme is based on the dual epipolar geometry in the reference frame, which we develop below. We show good results with five sequences of real images, using mostly scene calibration that can be inferred directly from the images themselves. 1

: A robot navigating in an unstructured environment needs to avoid obstacles in its way and determine free spaces through which it can safely pass. We present here a set of optical flow based behaviors which allow a robot moving on a ground plane to perform these tasks. The behaviors operate on a purposive representation of the environment called the "virtual corridor" which is computed as follows : The images captured by a forward-facing camera rigidly attached to the robot are first remapped using a space-variant transformation. Then, optical flow is computed from the remapped image stream. Finally, the virtual corridor is extracted from the optical flow by applying simple but robust statistics. The introduction of a space-variant image preprocessing stage is inspired by biological sensory processing, where the projection and remapping of a sensory input field onto higher-level cortical areas represents a central processing mechanism. Such transformations lead to a significant data r...

avigates using its perceptual sensors must have a number of capabilities that we can roughly separate into local and global ones. Local capabilities enable the system to interact effectively with its immediate surroundings, like understanding its own motion, recognizing obstacles and other moving objects, and obtaining a stable view of the world. Global capabilities enable the ? Unmanned Ground Vehicles. This research on navigation was funded partly by the Office of Naval Research under Grant N00014-96-1-0587, the National Science Foundation under Grant IRI-9057934, and ARPA Order #A422, through grant F49620-93-1-0576 (Integrated Active Vision for UGV RSTA), a project in which the author led a consortium including the Universities of Maryland, Rochester and Pennsylvania, as well as the National Institute of Standards and Technology, in the development of visual competences for an unmanned ground vehicle performing reconnaissance, surveillance,

Abstract. When an unknown object with Lambertian reflectance is viewed orthographically, there is an implicit ambiguity in determining its 3-d structure: we show that the object’s visible surface f (x, y) is indistinguishable from a “generalized bas-relief ” transformation of the object’s geometry, f ¯(x, y) = λf (x, y) + µx + νy, and a corresponding transformation on the object’s albedo. For each image of the object illuminated by an arbitrary number of distant light sources, there exists an identical image of the transformed object illuminated by similarly transformed light sources. This result holds both for the illuminated regions of the object as well as those in cast and attached shadows. Furthermore, neither small motion of the object, nor of the viewer will resolve the ambiguity in determining the flattening (or scaling) λ of the object’s surface. Implications of this ambiguity on structure recovery and shape representation are discussed. Keywords: variable illumination, shadows, shape ambiguity, object representation, object recognition