Abstract: Shape expressions in CAD or CG have often been carried out in polygon data. In polygon representations, the amount of data becomes very large if precision is pursued. Another shape representation utilizing the existing polygon data asset is proposed. Polygon data showing the shape of an object is first obtained. Topological information of the object is extracted from the polygon data. Based on the information, the polygon data is converted into topological data. The inversion is carried out upon necessity.

Abstract: After a digital content is loaded into an information terminal such as a PC, ID information unique to a viewer or a user of the PC is imprinted into the content. The ID information is imprinted into a predetermined location of the content or alternatively, it may be imprinted over the entire content in the form of a spatial frequency. The content with an ID added thereto is then enabled to be used in the terminal.

Abstract: A topography information data processing system acquires ground surface data which represents bumps and hollows on the ground, generates manifold data which represents the shape of the manifold that encloses the bumps and hollows on the ground based on the ground surface data, and acquires topological geometric data applying the Morse theory to the manifold data. A new type of geographic information data representation is provided by using topological geometric data generated based on the Morse theory known in differential geometry and differential topology. Geographic information data suitable to be stored in a recording medium or to be transmitted through a network is provided.

Abstract: A multiresolutional filter called a critical point filter is introduced. This filter extracts a maximum, a minimum, and two types of saddle points of pixel intensity for every 2.times.2 (horizontal.times.vertical) pixels so that an image of a lower level of resolution is newly generated for every type of a critical point. Using this multiresolutional filter, a source image and a destination image are hierarchized, and source hierarchical images and destination hierarchical images are matched using image characteristics recognized through a filtering operation.

Abstract: A multiresolutional filter called a critical point filter is introduced. This filter extracts a maximum, a minimum, and two types of saddle points of pixel intensity for every 2.times.2 (horizontal x vertical) pixels so that an image of a lower level of resolution is newly generated for every type of a critical point. Using this multiresolutional filter, a source image and a destination image are hierarchized, and source hierarchical images and destination hierarchical images are matched using image characteristics recognized through a filtering operation.

Abstract: An animation solid is created by an animation solid generator such that the shape of its cross section at t=t0 coincides with the shape of the contour of an object contained in a frame to be displayed at t=t0, wherein time t is set in the height z direction of the solid. For creation of this solid, topological considerations, including connected components and the tree structure of contours, are used. By chopping this solid, intermediate dividing can be performed. The basis of the topological geometry rests on Morse theory.