Statistical method for sub-pixel interpolation function estimation

Depth accuracy is one of the most important characteristics for sensors used in distance estimation. Stereo-vision systems employ sub-pixel interpolation to achieve such accuracy. Literature in this domain is usually dedicated to simple window based stereo solutions. There are currently several new stereo algorithms developed to counter pixel level errors, but they neglect sub-pixel results. We propose the use of function fitting to generate interpolation functions optimized for each algorithm type. Dedicated interpolation functions require the mathematical model of the algorithm. In the proposed methodology of generating the interpolation function the explicit model of the stereo algorithm is replaced by modeling the data distribution resulted from a pre-defined input. Several transformations are also proposed to reduce the dimensionality of the fitting data without loosing any information. The most accurate match for the fitting data-set was a sinusoidal function, a novel shape for sub-pixel interpolation. The function shows a significant improvement compared to legacy solutions, by reducing the error magnitude by several factor for both synthetic and real scenarios.