Simplified interpolation for an optical navigation system that correlates images of one bit resolution

Abstract

Interpolation along an axis is performed on a Correlation Surface Array that was created from counting the instances of difference (XOR) between corresponding pixels of single bit resolution images having trial displacements. The interpolation is performed by finding the intersection of two straight line segments that are identified by the shape of the cross section of the Correlation Surface along the axis of interest. In the case of nine trial shifts there are three values in such a cross section, and they may seen as representing three points whose abscissas are the pixel shift amounts minus one, no shift, and plus one, and whose ordinates are the corresponding correlation values. In situations where navigation (and interpolation) is possible, these three points will have certain properties. The ususal case is that two of the points determine one line having a slope m, and the other point determines the other line (assumed to have slope −m). The three points may also lie along the same line, although this represents an exceptional case that may be handled differently. The three points might also describe other conditions that are associated with Correlation Surfaces that are not suitable for navigation, and these are ignored. In the usual case the point of intersection for the two lines is found and its abscissa is the interpolated value for motion along the axis of interest.