Generalized L2-Divergence and Its Application to Shape Alignment
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Group-Wise Point-Set Registration Using a Novel CDF-Based Havrda-Charvát Divergence
International Journal of Computer Vision
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Free form shape registration using the barrier method
Computer Vision and Image Understanding
Accurate overlap area detection using a histogram and multiple closest points
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part II
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In this paper, we propose a novel and robust algorithm for the groupwise non-rigid registration of multiple unlabeled point-sets with no bias toward any of the given pointsets. To quantify the divergence between multiple probability distributions each estimated from the given point sets, we develop a novel measure based on their cumulative distribution functions that we dub the CDF-JS divergence. The measure parallels the well known Jensen-Shannon divergence (defined for probability density functions) but is more regular than the JS divergence since its definition is based on CDFs as opposed to density functions. As a consequence, CDF-JS is more immune to noise and statistically more robust than the JS. We derive the analytic gradient of the CDF-JS divergence with respect to the non-rigid registration parameters for use in the numerical optimization of the groupwise registration leading a computationally efficient and accurate algorithm. The CDF-JS is symmetric and has no bias toward any of the given point-sets, since there is NO fixed reference data set. Instead, the groupwise registration takes place between the input data sets and an evolving target dubbed the pooled model. This target evolves to a fully registered pooled data set when the CDF-JS defined over this pooled data is minimized. Our algorithm is especially useful for creating atlases of various shapes (represented as point distribution models) as well as for simultaneously registering 3D range data sets without establishing any correspondence. We present experimental results on non-rigid registration of 2D/3D real point set data.