Accurate and Robust Non-rigid Point Set Registration using Student's-t Mixture Model with Prior Probability Modeling

Area of Science:

• Computer Vision
• Machine Learning
• Computational Geometry

Background:

• Non-rigid point set registration is crucial for aligning complex shapes.
• Existing methods struggle with significant missing correspondences and outliers.
• Robust and accurate registration algorithms are needed for real-world applications.

Purpose of the Study:

• To propose a novel and robust non-rigid point set registration method, DSMM.
• To address challenges posed by missing correspondences and outliers.
• To develop a computationally efficient and statistically accurate registration algorithm.

Main Methods:

• Modeling point set relationships as random variables using Dirichlet distribution.
• Employing a Student's-t mixture model with prior probabilities assigned to correspondences.
• Incorporating local spatial information via a linear smoothing filter for posterior probabilities.
• Utilizing a Bayesian framework with hidden random variables to generalize mixture models.

Main Results:

• DSMM demonstrates high statistical accuracy and robustness in non-rigid point set registration.
• The method outperforms competing state-of-the-art finite mixture models on artificial and real 2D/3D datasets.
• The proposed approach achieves computational efficiency compared to other Student's-t mixture model methods.

Conclusions:

• DSMM offers a significant advancement in non-rigid point set registration, particularly in challenging scenarios.
• The generalized mixture model family provides a unified framework for existing registration methods.
• The algorithm's robustness and accuracy make it suitable for diverse 2D and 3D applications.