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Probabilistic Analysis of Regularization
October 1993 (vol. 15 no. 10)
pp. 982-995

In order to use interpolated data wisely, it is important to have reliability and confidence measures associated with it. A method for computing the reliability at each point of any linear functional of a surface reconstructed using regularization is presented. The proposed method is to define a probability structure on the class of possible objects and compute the variance of the corresponding random variable. This variance is a natural measure for uncertainty, and experiments have shown it to correlate well with reality. The probability distribution used is based on the Boltzmann distribution. The theoretical part of the work utilizes tools from classical analysis, functional analysis, and measure theory on function spaces. The theory was tested and applied to real depth images. It was also applied to formalize a paradigm of optimal sampling, which was successfully tested on real depth images.

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Index Terms:
probabilistic analysis; reliability measures; regularization; interpolated data; confidence measures; probability structure; variance; Boltzmann distribution; functional analysis; measure theory; depth images; image processing; probability; reliability
D. Keren, M. Werman, "Probabilistic Analysis of Regularization," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 10, pp. 982-995, Oct. 1993, doi:10.1109/34.254057
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