Abstract: Systems and methods for calculating a modification of a geometrical shape by applying an inverse modification function to an array representing the shape. An array representing the geometrical shape is defined on a multi-dimensional space. A modification function is used to modify the geometrical shape. A user or a programmed computer can select the modification function. The computer applies an inverse of the modification function to the array. The computer deduces a change in the geometrical shape from the modified array.

Abstract: A method and system for an approximation of a filter function for computing a characteristic value of an output pixel based on characteristic values of a plurality of input pixels is provided. A filter response curve adjustment value is obtained, preferably from a lookup table, based on a distance interval between coordinates of the output pixel and coordinates of a selected input pixel. A normalized filter response curve input value is computed based on the distance interval and the filter response curve adjustment value, preferably by adding the values together. The characteristic values at a plurality of input pixels are obtained. A linearly interpolated value for the characteristic value of the output pixel is then computed based on the characteristic values of the plurality of input pixels and the normalized filter response curve input value.

Abstract: In the document identification apparatus, a ruled line feature extraction section determines a black pixel ratio of a document to be identified, and adds the black pixel ratio for each block to extract a ruled line feature. A ruled line feature verification section verifies the ruled line feature with a ruled line feature already registered in a ruled line feature dictionary to thereby identify the document. If identification is not possible with this procedure, a details judgment section verifies the image data in a specific area with the image data (characters or the like) registered in a specific area dictionary.

Abstract: An interactive method of visualization and graphical analysis of functions considered in multi-dimensional domain is provided. The inventive method substitutes continuum objects represented by one or more functions by discrete approximation represented by a set of multi-dimensional points, to analyze the dataset graphically.

Abstract: A display control system includes: a display control apparatus including command data transmission means for transmitting command data; and a display apparatus for performing display based on command data transmitted from the command data transmission means, it wherein the display apparatus includes: command data receiving means for receiving the command data; command data interpretation means for applying a mathematical operation to the received command data so as to generate image data; and display means for displaying an image in accordance with the image data.