Group-wise Point-set registration using a novel CDF-based Havrda-Charvát Divergence

Area of Science:

• Medical image analysis
• Computational geometry
• Information theory

Background:

• Group-wise registration aligns multiple datasets.
• Unknown correspondence poses a significant challenge.
• Existing methods can be computationally intensive and less accurate.

Purpose of the Study:

• To develop a novel and robust technique for group-wise registration of point sets with unknown correspondence.
• To introduce a new divergence measure for quantifying dissimilarities between cumulative distribution functions (CDFs).
• To enable unbiased point-set atlas construction without pre-established correspondences.

Main Methods:

• Definition of Havrda-Charvát (HC) entropy for CDFs, termed HC Cumulative Residual Entropy (HC-CRE).
• Proposal of CDF-HC divergence, a generalized and computationally efficient alternative to CDF-JS divergence.
• Derivation of a closed-form analytic gradient for efficient quasi-Newton optimization.

Main Results:

• The CDF-HC divergence is simpler to implement and more computationally efficient than previous methods.
• The derived analytic gradient facilitates efficient optimization of non-rigid registration parameters.
• Experimental results demonstrate superior efficiency, accuracy, and robustness compared to existing algorithms.

Conclusions:

• The proposed CDF-HC registration algorithm is highly effective for group-wise point set alignment.
• This technique facilitates unbiased atlas construction, overcoming the limitation of unknown correspondences.
• The method offers significant improvements in performance metrics over prior art in point set registration.