Abstract: A system for detecting lines in images using line neighborhoods and a parallel coordinate transformation. The process introduces the concept of line neighborhoods to accommodate the uncertainty in line detection arising from image noise. Because line neighborhoods in Cartesian coordinates have ambiguous and unbounded regions and always overlap one another, a parallel coordinate transform is used to transform Cartesian coordinate image plane line segments to points in a bounded and nonambiguous region of the parallel coordinate transform plane. Line detection then becomes a simple problem of detecting point clusters in the parallel coordinate transform plane.

Abstract: A multi-variate data set is displayed in a plurality of multi-dimensional presentations on a computer having a graphical interface and a keyboard input. The data set includes a plurality of independent variables and, for each independent variable, a plurality of dependent variables. A computer displays the data set in parallel coordinate form on the graphical interface so that each dependent variable of the data set is presented as a series of values along an axis, plural axes arranged in parallel. The graphical interface provides a polygonal line which connects a value on each parallel axis and illustrates a relationship between an independent variable and the dependent variables appearing on each axis. The user input enables a user to superimpose on the graphical interface graphical delimiters either on or between two succeeding parallel axes. The graphical delimiters identify a data subset that includes at least one independent variable and adjacent dependent variables.

Abstract: A system for detecting and resolving conflicts between a plurality of aircraft or other objects on potentially conflicting trajectories in space. A two-dimensional graph generated on a processor-controlled display depicts the trajectory of one of the aircraft and creates particles that have identical velocity as the particular aircraft of interest. Each particle is at a different initial position from all other particles (in the sense of mathematical physics, a field is defined). That is, motion constraints are defined in terms of particles with specific characteristics and a algorithms for conflict avoidance are constructed by selecting a given particle which satisfies all of the constraints.

Abstract: A machine-implemented method for detecting and resolving conflict between a plurality of objects on trajectories in space. A two-dimensional representation is generated which depicts the trajectory of one of the objects and the times remaining until conflict of said one object with front and back limiting trajectories, respectively, of at least one other of the objects. An indication of potential conflict is displayed on said representation when the trajectory of said one object is between the front and back limiting trajectories of said other object. The front and back limiting trajectories for each such other object are calculated by enclosing a preselected protected airspace about said one object in an imaginary parallelogram having one set of sides parallel to the trajectory of said one object and the other set of sides parallel to relative velocity of such other object with respect to said one object.

Abstract: Critical differences in the position and motion of aircraft in congested N-dimensional airspace are highly discernible when processed and mapped onto a parallel N-coordinate plane. Trajectory intersection in both time and space may be constantly monitored. The airspace may be accurately controlled by descriptively and prescriptively configuring proposed trajectories and monitoring critical differences before assignment to aircraft. Attributes such as angular deviation, in addition to closing speed and distance, can be evaluated.