A locally adaptive window for signal matching

Abstract

This article presents a signal matching algorithm that can select an appropriate window size adaptively so as to obtain both precise and stable estimation of correspondences.

Matching two signals by calculating the sum of squared differences (SSD) over a certain window is a basic technique in computer vision. Given the signals and a window, there are two factors that determine the difficulty of obtaining precise matching. The first is the variation of the signal within the window, which must be large enough, relative to noise, that the SSD values exhibit a clear and sharp minimum at the correct disparity. The second factor is the variation of disparity within the window, which must be small enough that signals of corresponding positions are duly compared. These two factors present conflicting requirements to the size of the matching window, since a larger window tends to increase the signal variation, but at the same time tends to include points of different disparity. A window size must be adaptively selected depending on local variations of signal and disparity in order to compute a most-certain estimate of disparity at each point.

There has been little work on a systematic method for automatic window-size selection. The major difficulty is that, while the signal variation is measurable from the input, the disparity variation is not, since disparities are what we wish to calculate. We introduce here a statistical model of disparity variation within a window, and employ it to establish a link between the window size and the uncertainty of the computed disparity. This allows us to choose the window size that minimizes uncertainty in the disparity computed at each point. This article presents a theory for the model and the resultant algorithm, together with analytical and experimental results that demonstrate their effectiveness.