There is disclosed a technology of measuring three-dimensional geometric information on a plane and position information on a point from an image such as the optical flow pattern and a stereo image. It is to determine an azimuth of a measuring plane and/or a superposing time in which the measuring plane is superposed on a predetermined observation point, using a compound ratio {p.sub.inf p.sub.0 p.sub.1 p.sub.c }, which is determined by four positions p.sub.inf, p.sub.0, p.sub.1, p.sub.c of a measuring point, where p.sub.0 and p.sub.1 denote measuring positions at mutually different two measuring times on an arbitrary measuring point appearing on an image obtained through viewing a predetermined measurement space from a predetermined observation point inside the measurement space, respectively, p.sub.inf denotes a position of the measuring point after an infinite time elapses, and p.sub.c denotes a position of the measuring point at a superposing time in which a measuring plane including the measuring point is superposed on the observation point in the moving continuous state.

A volume rendering processor establishes a cut-plane region of a volume data set, the cut-plane region being defined by a plane equation and minimum and maximum distance values representing the values of the plane equation at outer faces of the cut-plane region. The plane equation is evaluated for each sample of the volume data, the result is compared with the minimum and maximum distance values to determine whether the sample is in the cut-plane region, and the visibility of the sample is adjusted depending on the comparison result. The plane equation is evaluated by continually accumulating the coefficient values in an order indicated by the ordering of the sequence of samples. Evaluation logic includes an accumulator, a 2-input adder, registers for saving intermediate accumulated values in corresponding dimensions of the volume data, multiplexers for selecting the adder inputs from among the coefficient values, the output of the accumulator and the values in the registers, and visibility calculation logic that adjusts the samples' visibility depending on the relationship between the output of the accumulator and the minimum and maximum distance values. In an inclusive operating mode, the visibility of the sample is set to zero if it is outside the cut-plane region, and in an exclusive mode the sample's visibility is set to zero if it lies in the cut-plane region. Falloff regions at each face of the cut-plane region are used to gradually adjust sample visibility to provide a smooth appearance.

Image processing method and apparatus wherein candidate points are first selected in a log-polar image domain. The points may be selected by edge detection, thresholding, or any method suitable for identifying image points which are likely to lie on some feature of interest. For every candidate point there is drawn, also in the log-polar domain, a mirror image of a curve that represents the log-polar image of a straight line. There is accumulated a log-polar domain histogram of "hits" from the drawing process. Finally, a peak bin is selected. The position of the peak bin corresponds to the position of the recognized line.

When the positions of two points within a uniform three dimensional space are known, this invention finds all the planes in the space that pass through an axis determined by those two points. It identifies all the points on each plane by their location and preserves their spatial relationship to one another within the three dimensional space. Every plane in a set of planes derived from a particular pair of points is defined by a unique formula. This invention is especially useful when the points represent units with characteristics dependent on their position in the space. Color systems exemplify this relationship. Several color systems exist in which all reproducible colors are arranged in a three dimensional color solid so that colors progressively change in lightness vertically, in saturation horizontally and in hue as the solid is rotated. Individual colors in these systems are represented by points within the color solid and spacing between these colors has been determined by studies to be perceptually equidistant. The embodiment described in this disclosure utilizes one of these color systems to create and manipulate orderly groups of colors, i.e., color palettes, in which each color is specified by a notational system defining both its location in the color space and its appearance. The most useful form of this embodiment is computer software that generates numerous color palettes and allows the user to view and select color palettes and individual colors. Appendix A contains the source code for this embodiment.

A method and apparatus for rendering textured spheres and spherical environment maps. The method of the present invention provides for real time rotation of a textured sphere and panning of the view into a spherical environment map, along multiple axes without the need for special rendering hardware. A two-level indexing scheme for accessing pixel data in a texture map, is used to identify shading values for pixels in a display window. The two-level indexing scheme is comprised of a screen look-up table and a parametric look-up table. The screen look-up table has the dimensions of the display window, whereas the parametric look-up table has the dimensions of the parametric spherical environment map (wherein the pixel addresses are rotated 90 degrees from the origin). The method for the present invention is comprised primarily of the steps of: providing a parametric spherical environment map of the image to be viewed, generating a screen look-up table comprised of look-up addresses, generating a parametric look-up table comprised of index values into the parametric spherical environment map, and for each look-up address in the screen look-up table, mapping to an entry in the parametric look-up table, retrieving the value in the entry, and using the value to retrieve pixel values from the parametric spherical environment map. Rotation or movement of the view being seen is accomplished by adding offsets to the look-up address and/or the index values.