Sub-pixel precision image matching for measuring surface displacements on mass movements using normalized cross-correlation

This study evaluates the performance of two fundamentally different approaches to achieve sub-pixel precision of normalised cross-correlation when measuring surface displacements on mass movements from repeat optical images. In the first approach, image intensities are interpolated to a desired sub-pixel resolution using a bi-cubic interpolation scheme prior to the actual displacement matching. In the second approach, the image pairs are correlated at the original image resolution and the peaks of the correlation coefficient surface are then located at the desired sub-pixel resolution using three techniques, namely bi-cubic interpolation, parabola fitting and Gaussian fitting. Both principal approaches are applied to three typical mass movement types: rockglacier creep, glacier flow and land sliding. In addition, the influence of pixel resolution on the accuracies of displacement measurement using image matching is evaluated using repeat images resampled to different spatial resolutions. Our results show that bi-cubic interpolation of image intensity performs best followed by bi-cubic interpolation of the correlation surface. Both Gaussian and parabolic peak locating turn out less accurate. By increasing the spatial resolution (i.e. reducing the ground pixel size) of the matched images by 2 to 16 times using intensity interpolation, 40% to 80% reduction in mean error in reference to the same resolution original image could be achieved. The study also quantifies how the mean error, the random error, the proportion of mismatches and the proportion of undetected movements increase with increasing pixel size (i.e. decreasing spatial resolution) for all of the three mass movement examples investigated.