Improving the robustness of least squares template matching with a line-search algorithm

The Adaptive Least Squares Matching (ALSM) problem of Gruen is conventionally described as a statistical estimation problem. This paper shows that the ALSM problem may also be interpreted as a weighted non-linear least squares problem. This enables optimization theory to be applied to the ALSM problem. The ALSM algorithm may be interpreted as an instance of the well-known Gauss-Newton algorithm. A problem-independent termination criteria is introduces based on angles in high-dimensional vector spaces. The line-search modification of the Gauss-Newton method is explained and applied to the ALSM problem. The implications of the line-search modification is an increased robustness, reduced oscillations, and increased pull-in range. A potential drawback is the increased number of convergences toward side minima in images with repeating patterns