Data fusion: color edge detection and surface reconstruction through regularization

Data fusion provides tools for solving problems which are characterized by distributed and diverse information sources. In this paper, the authors focus on the problem of extracting features such as image discontinuities from both synthetic and real images. Since edge detection and surface reconstruction are ill-posed problems in the sense of Hadamard, Tikhonov's regularization paradigm is proposed as the basic tool for solving this inversion problem and restoring well-posedness. The proposed framework includes: (1) a systematic view of oneand two-dimensional regularization; (2) extension of the standard Tikhonov regularization method by allowing space-variant regularization parameters; and (3) further extension of the regularization paradigm by adding multiple data sources to allow for data fusion. The theoretical approach is complemented by developing a series of algorithms, then solving the early vision problems of color edge detection and surface reconstruction. An evaluation of these methods reveals that this new analytical data fusion technique output is consistently better than each of the individual RGB edge maps, and noisy corrupted images are reconstructed into smooth noiseless surfaces.