This paper presents a novel time-based visual motion cue called the Hybrid Visual Threat Cue (HVTC) that provides some measure for a change in relative range as well as absolute clearances, between a 3D surface and a moving observer. It is shown that the HVTC is a linear combination of Time-To-Contact (TTC), visual looming and the Visual Threat Cue (VTC). The visual field associated with the HVTC can be used to demarcate the regions around a moving observer into safe and danger zones of varying degree, which may be suitable for autonomous navigation tasks. The HVTC is independent of the 3D environment and needs almost no a-priori information about it. It is rotation independent, and is measured in ~time/sup -1/\ units Several approaches to extract the HVTC, are suggested. Also a practical method to extract it from a sequence of images of a 3D textured surface obtained by a visually fixating, fixed-focus monocular camera in motion is presented. This approach of extracting the HVTC is independent of the type of 3D surface texture and needs no optical flow information, 3D reconstruction, segmentation, feature tracking.

This paper presents a new visual motion cue, we call the Visual Threat Cue (VTC) that provides some measure for a relative change in range as well as clearance between a 3D surface and a fixing observer in motion. The VTC corresponds to visual fields surrounding a moving observer. The fields are time-based imaginary 3-D surfaces that move with the observer. They are analogous to equi-potential fields of an electric dipole. A practical method to extract the VTC is presented. The approach is independent of the 3D surface texture and needs no optical flow information, 3D reconstruction, segmentation, feature tracking or pre-processing. This algorithm to extract the VTC was applied to several indoor as well as outdoor real images of textures, where we observed a similar behavior for most of the textures employed.

The concept of visual looming can be used as a powerful visual cue for autonomous obstacle avoidance. In this paper a method that measures looming quantitatively by fixating a camera at a point on the surface of an object is presented. It is based on studying the texture and its temporal change near the fixation point. The surface may be tilted relative to the optical axis. Looming can be calculated from the relative change in texture density and from the local orientation of the surface. The orientation is obtained from a set of one-dimensional directional densities of the texture primitives. This visual cue is used as a feedback signal of a closed loop system to implement obstacle avoidance using a six-degree-of-freedom simulator.>

The paper deals with a visual-motion fixation invariant. We show that during fixation there is a measurable nonlinear function of optical flow that produces the same value for all points of a stationary environment, regardless of the 3D shape of the environment. During fixated camera motion relative to a rigid object, e.g., a stationary environment, the projection of the fixated point remains (by definition) at the same location in the image, and all other points located on the 3D rigid object can only rotate relative to the 3D fixation point. This rotation rate of the points is invariant for all points that lie on the particular environment, and it is measurable from a sequence of images. This new invariant is obtained from a set of monocular images, and is expressed explicitly as a closed form solution. We show how to extract this invariant analytically from a sequence of images using optical flow information, and we present results obtained from real data experiments.>

Both camera fixation and vision-based road following are problems that involve tracking or fixating on 3-D points and features. This paper presents a unified theoretical approach to analyzing camera fixation and vision-based road following. The approach is based on the concept of equal flow circles (EFCs) and zero flow circles (ZFCs). Using EFCs it is possible to locate points in space relative to the fixation point, and predict the behavior. The camera's instantaneous direction of translation and the fixation point determine the plane on which the EFCs can be found. We show that points on an EFC inside the ZFC produce optical flow that is opposite in sign to that produced by points outside the ZFC. When a point in space crosses a ZFC it produces zero flow. For explanation purposes we analyzed a special case of motion. However, a similar approach can be taken for a more general motion of the camera. The analysis for the current motion can also be extended to find equal flow curves.>

A closed-form solution for obtaining the 3-D structure of a scene for a given six-degree-of-freedom motion of the camera is provided. The solution is massively parallel, i.e., the range that corresponds to each pixel is dependent on the spatial and temporal changes in intensities of that pixel, and on the motion parameters of the camera. The measurements of the intensities are done in a priori known directions. The solution is for the general case of camera motion. The deviation is based upon representing the image in the spherical coordinate system, although a similar approach could be taken for other image domains, e.g., the planar coordinate system. Comments are made on the amount of computations, error and singular points of the solutions. A practical way to significantly reduce and implement them is suggested.>

The quantitative aspects of camera fixation for a static scene are addressed. In general, when the camera undergoes translation and rotation, there is an infinite number of points that produce equal optical flow for any instantaneous point in time. Using a camera-centered spherical coordinate system, it is shown how to find these points in space. For the case where the rotation axis of the camera is perpendicular to the instantaneous translation vector, these points lie on cylinders. If the elevation component of the optical flow is set to zero then these points form a circle (called the equal flow circle or simply EFC) and a line, i.e. all points that lie on this circle or line are observed as having the same azimuthal optical flow. A special case of the EFCs is the zero flow circle (ZFC) where both components of the optical flow are equal to zero. A fixation point is the intersection of all the ZFCs. Points inside and outside the ZFC can be quantitatively mapped using the EFCs. It is shown how the concept of the EFC and ZFC can be used to explain the optical flow produced by points near the fixation point.>

A fixation point is a point in 3-D space that projects to zero optical flow in an image over some period of time while the camera is moving. Quantitative aspects of fixation for a static scene are treated. For the case where the rotation axis of the camera is perpendicular to the instantaneous translation vector, it is shown that there is an infinite number of points that produce zero instantaneous optical flow. These points lie on a circle (called the zero flow circle, or ZFC) and a line. The ZFC changes its location and radius as a function of time, and the intersection of all the ZFCs is a fixation point. Points inside the ZFC produce optical flow that is opposite in sign to those that are outside the ZFC. This fact explains in a more quantitative way phenomena due to fixation. In particular, points in the neighborhood of the fixation point may change the sign of their optical flow as the camera moves. In a set of experiments, it is shown how the concept of the ZFC can be used to explain the optical flow produced by 3-D points near the fixation point.>

The authors describe a method for reconstruction of three-dimensional visible and invisible opaque surfaces using moving shadows. An object whose shape is to be determined is placed on a reference surface. A beam of substantially parallel rays of light is projected at the object at a set of different angles relative to the reference surface. Using a camera which is placed above the reference surface, the shadows cast by the object for each angle are transferred to a computer. A three-dimensional binary level shadow diagram (3DBL shadowgram) is formed and analyzed. The shadowgram has some features which make the reconstruction very simple: a section of the 3DBL shadowgram, referred to as a 2DBL shadowgram, can be used to determine the heights of points of the object to be reconstructed. Further analysis of some curves of the shadowgram can be used for the partial reconstruction of invisible surfaces. A set of experimental results to test the effects of the threshold, camera resolution, and the number of pictures demonstrates the robustness and usefulness of the method.>

A method for segmenting three-dimensional overlapping surfaces is presented that is based on moving a light source in a horizontal plane relative to the surfaces to be segmented. Using a camera that is placed above the surfaces. The shadows cast by the surfaces at each light source angle are recorded and analyzed. The segmentation algorithm is simple and based on Boolean processing of the data. A set of experimental results demonstrates the robustness and usefulness of the method.>