PROBABILISTIC ANALYSIS OF REGULARIZATION

In order to wisely use interpolated data, it is important to have reli ability and confidence measures associated with it. In this paper, we show how to compute the reliability at each point of any linear functi onal, for example, height or derivative, of a surface reconstructed us ing regularization. The proposed method is to define a probability str ucture on the class of possible objects (for example surfaces) and com pute the variance of the corresponding random variable (for example, t he height at a certain point). This variance is a natural measure for uncertainty, and experiments have shown it to correlate well with real ity. The probability distribution used is based on the Boltzmann distr ibution. The theoretical part of the work utilizes tools from classica l 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 success fully tested on real depth images.