Generalized partial volume: an inferior density estimator to Parzen windows for normalized mutual information

Area of Science:

• Medical Imaging
• Computer Vision
• Image Processing

Background:

• Mutual Information (MI) and normalized mutual information (NMI) are widely used similarity measures for multimodal image registration.
• Current estimation methods include Parzen Window (PW) and Generalized Partial Volume (GPV), with their theoretical relationship previously unexplored.

Purpose of the Study:

• To establish the theoretical connection between PW and GPV for NMI in image registration.
• To compare the algorithmic and computational aspects of PW and GPV.
• To present efficient NMI algorithms for multimodal image registration.

Main Methods:

• Step-by-step derivation of Parzen Window (PW) and Generalized Partial Volume (GPV) for NMI estimation.
• Theoretical analysis of the relationship between PW and GPV.
• Development and implementation of NMI algorithms comparable in speed to Sum of Squared Differences (SSD).

Main Results:

• A direct theoretical link between PW and GPV for NMI in rigid and non-rigid image registration is established.
• GPV is shown to be algorithmically inferior to PW in terms of both model accuracy and computational complexity.
• Efficient NMI algorithms for both PW and GPV are presented, achieving speeds comparable to SSD.

Conclusions:

• The study clarifies the relationship between PW and GPV for NMI in image registration.
• PW is recommended over GPV due to superior algorithmic and computational properties.
• The developed NMI algorithms offer efficient solutions for multimodal image registration tasks.