Abstract
This paper presents a novel and robust technique for group-wise registration of point sets with unknown correspondence. We begin by defining a Havrda-Charvát (HC) entropy valid for cumulative distribution functions (CDFs) which we dub the HC Cumulative Residual Entropy (HC-CRE). Based on this definition, we propose a new measure called the CDF-HC divergence which is used to quantify the dis-similarity between CDFs estimated from each point-set in the given population of point sets. This CDF-HC divergence generalizes the CDF Jensen-Shannon (CDF-JS) divergence introduced earlier in the literature, but is much simpler in implementation and computationally more efficient.
A closed-form formula for the analytic gradient of the cost function with respect to the non-rigid registration parameters has been derived, which is conducive for efficient quasi-Newton optimization. Our CDF-HC algorithm is especially useful for unbiased point-set atlas construction and can do so without the need to establish correspondences. Mathematical analysis and experimental results indicate that this CDF-HC registration algorithm outperforms the previous group-wise point-set registration algorithms in terms of efficiency, accuracy and robustness.
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This research was in part funded by the NIH grant RO1 NS046812 and NSF grant NSF 0307712.
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Chen, T., Vemuri, B.C., Rangarajan, A. et al. Group-Wise Point-Set Registration Using a Novel CDF-Based Havrda-Charvát Divergence. Int J Comput Vis 86, 111–124 (2010). https://doi.org/10.1007/s11263-009-0261-x
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DOI: https://doi.org/10.1007/s11263-009-0261-x