Efficient Symplectic-Energy-Momentum Integration of Hamiltonian Dynamical Systems

An apparatus and method identify at least one attribute of an article for use in accurately reproducing the article. The apparatus includes at least one detector having an array of cells. At least one cell, in the detector array, the sensor cell, is provided with an extra colored coating or is painted with an extra color. When the article is scanned by the detector, the at least one sensor cell will read a different color value from the other cells due to the extra coating applied to it. The color that the at least one sensor cell would have output without the extra coating is interpolated from the detection results of the neighboring cells. This color and the color actually detected by the at least one sensor cell are then input to a controller which determines the at least one attribute of the scanned article using a model, such as a neural network, an expert system, a fuzzy logic model, and the like. The controller performs appropriate processing based on the at least one determined attribute.