Most researchers [11] choose the position that gives the maximum correlation coefficient as the disparity value. We choose a slice of the correlation coefficient cube as a 2D Correlation Matrix for each scan line of the input image and use this matrix to obtain more reliable disparities. The width of the matrix is the same as the length of the scan line, and the height of the matrix equals the correlation search range, 2w+1. A typical Correlation Matrix is shown in Fig. 1(b). This image/matrix is actually one slice of the correlation cube obtained in Section 2.3. We will use the correlation matrix to find the disparity for any one scan line. Rather than choosing the maximum correlation coefficient, we find a best path through the correlation matrix. The position of the path indicates the best disparity for this scan line.
The algorithm for finding the best path through the correlation matrix is performed by using a dynamic programming technique [12]. The best path gives the minimum cost when certain constraints are imposed.
Sub-pixel accuracy can be obtained by fitting a second degree curve to the correlation coefficients in the neighbourhood of the disparity and the extrema of the curve can be obtained analytically. This second degree curve can be a parabola.