Method for expressing and restoring image data

A method for expressing and restoring an image,comprising the steps of:

• representing said image as a two-dimensional figure in which image pixels accompany corresponding feature values to form a three-dimensional curved surface in which the z-axis in an x-y-z coordinate system is a feature axis;
• slicing said curved surface to obtain contour lines that are perpendicular to said z-axis at a plurality of z values;
• transmitting data relating to said contour lines;
• receiving and approximating each of said contour lines to corresponding polygons that approximate said contour lines;
• and
• paving a region between two mutually adjacent polygons by plane patches.

A method for expressing motion in a video sequence, comprising the steps of:

• representing a series of frames, each of said frames including a time stamped image at a time instant, wherein said time stamped image is represented by a curved surface in a three-dimensional x-y-z coordinate system in which said time stamped image is figured on an x-y plane and a feature of said time stamped image is measured on a z-axis;
• slicing each said curved surface to obtain a cross-sectional area perpendicular to said z-axis at a level on said z-axis;
• computing a center of gravity of corresponding to each of said cross-sectional areas in at least two of said time stamped images;
• translating said cross-sectional area from locations of said centers of gravity based on said video sequence;
• moving one of said cross-sectional areas along said translation to reach coincidence of a center of gravity of said one cross-sectional area with a center of gravity of another corresponding cross-sectional area;
• rotating said one of said cross-sectional areas around said common center of gravity to obtain a maximum overlap on said another corresponding cross-sectional area;
• and
• determining rotation of said cross-sectional area from an angle of rotation.

A method for expressing image data, comprising the steps of:

• assigning a distribution of feature values to each pixel in a two-dimensional image space;
• representing said pixel feature values by contour lines formed on a curved surface in a three-dimensional space on a Z-axis;
• and
• reproducing said curved surface as a polyhedron by feature interpolation of regions between said contour lines and of regions in which peaks or saddles exist without coinciding contour lines.

A method for expressing image data providing the steps of:

• providing a curved surface z=f(x, y) having feature values of said image in a Z-axis direction;
• representing said curved surface z=f(x, y) by contour lines;
• forming a polyhedron z=g(x, y) by either reproducing said curved surface as a polyhedron by feature interpolation of regions between said contour lines and of regions in which peaks or saddles exist without coinciding contour lines, or by covering said regions between contour lines with any of triangular and quadrangular patches to interpolate feature values;
• computing errors in a Z-axis component of said polyhedron z=g(x, y) to said curved surface z=f(x, y);
• obtaining curved surfaces z=h.sub.1,1 (x, y) and z=h.sub.1,2 (x, y), respectively corresponding to positive and negative values of said errors;
• representing said error curved surfaces z=h.sub.1,1 (x, y) and z=h.sub.1,2 (x, y) by equal difference lines;
• creating polyhedrons z=i.sub.1,1 (x, y) and z=i.sub.1,2 (x, y);
• computing errors in Z-axis components of the polyhedron Z=i.sub.k-1,1 (x, y) to the error curved surface Z=i.sub.k-2,1 (x, y), and errors in Z-axis components of the polyhedron z=i.sub.k-1,2 (x, y) to the error curved surface z=h.sub.k-2,2 (x, y);
• obtaining error curved surfaces Z=h.sub.k-1,1 (x, y) and Z=h.sub.k-1,2 (x, y), respectively corresponding to positive and negative values of said errors;
• representing said error curved surfaces z=h.sub.k-1,1 (x, y) and Z=h.sub.k-1,2 (x, y) by equal difference lines;
• creating polyhedrons Z=i.sub.k-1,1 (x, y) and Z=i.sub.k-1,2 (x, y) based on said equal difference lines;
• computing errors in Z-axis components of the polyhedron Z=i.sub.N-2,1 (x, y) to an error curved surface Z=h.sub.N-2,1 (x, y), and errors in z-axis components of the polyhedron Z=i.sub.N-2,2 (x, y) to the error curved surface Z=h.sub.N-2,2 (x, y);
• obtaining error curved surfaces z=h.sub.N-1,1 (x,y) and z=h.sub.N-1,2 (x,y) respectively corresponding to positive and negative values of said errors;
• and
• representing said error curved surfaces Z=h.sub.N-1,1 (x, y) and Z=h.sub.N-1,2 (x, y) by equal difference lines.