Performance of phase-based algorithms for disparity estimation

Stereoscopic depth analysis by means of disparity estimation has been a classical topic of computer vision, from the biological models of stereopsis [1] to the widely used techniques based on correlation or sum of squared differences [2]. Most of the recent work on this topic has been devoted to the phase-based techniques, developed because of their superior performance and better theoretical grounding [3, 4]. In this article we characterize the performance of phase-based disparity estimators, giving quantitative measures of their precision and their limits, and how changes in contrast, imbalance, and noise in the two stereo images modify the attainable accuracy. We find that the theoretical range of measurable disparities, one period of the modulation of the filter, is not attainable: the actual range is approx. two-thirds of this value. We show that the phase-based disparity estimators are robust to changes in contrast of 100% or more and well tolerate imbalances of luminosity of 400% between the images composing the stereo pair. Clearing the Gabor filter of its DC component has been often advocated as a means to improve the accuracy of the results. We give a quantitative measure of this improvement and show that using a DC-free Gabor filter leads to disparity estimators nearly insensitive to contrast and imbalance. Our tests show that the most critical source of error is noise: the error increases linearly with the increase in noise level. We conclude by studying the influence of the spectra and the luminosity of the input images on the error surface, for both artificial and natural images, showing that the spectral structure of the images has little influence on the results, changing only the form of the error surface near the limits of the detectable disparity range. In conclusion, this study allows estimation of the expected accuracy of custom-designed phase-based stereo analyzers for a combination of the most common error sources.