Filtering of uncertain irregularly sampled multidimensional data

Two new methods are presented: normalized convolution and normalized differential convolution. These methods are examples of the power of the signal/certainty-philosophy, i.e. the separation of both data and operator into a signal part and a certainty part. Missing data is simply handled by setting the certainty to zero. Localization or `windowing´ of operators is done using an applicability function, the operator equivalent to certainty, not by changing the actual operator coefficients. Spatially or temporally limited operators are handled by setting the applicability function to zero outside the window. The present work shows how false operator responses due to missing or uncertain data can be significantly reduced or eliminated. Perhaps the most well-known of such effects are the various `edge effects´ which invariably occur at the edges of the input data set. Examples of the performance of gradient, divergence and curl operators are given and applications to spectrum analysis is discussed. Further important applications are found in robot vision. Results showing that efficient compensation for camera saccades and elimination of visual responses due to robot arm motions can be attained. The theory is based on linear operations and is general in that it allows for both, data and operators to be scalars, vectors or tensors of higher order