Regularized fusion : gray and color edge detection and surface reconstruction

The need to extract useful information from multisensor data exists for both biological and artificial systems. Multisensor data fusion is a crucial component for the success of a variety of applications, including intelligent weapon systems, autonomous robots, and advanced medical systems. The area of data fusion provides tools for solving problems which are charac-terized by distributed and diverse information sources. In this dissertation, we focus on the problem of extracting given features, such as image discontinuities, from images obtained using different sensing modalities. Since edge detection is an ill-posed problem in the sense of Hadamard, Tikhonov's regularization paradigm has been proposed as a basic tool to solve this inversion problem and to re-store well-posedness. The proposed framework includes: (i) a systematic view of one-dimensional as well as two-dimensional regularization, (ii) an evaluation (weighting) of the knowledge sources by considering individual noise characteris-tics, (iii) extension of the standard Tikhonov regularization method by allowing space-variant regularization parameters, and (iv) further extension of the regular-ization paradigm by adding, in a natural way, multiple data sources and allowing data fusion. The theoretical approach has been complemented by developing a series of algorithms and then solving various early vision problems, including regularized edge detection, surface reconstruction, and color edge detection.