GiNGR: Generalized Iterative Non-Rigid Point Cloud and Surface Registration Using Gaussian Process Regression (2203.09986v1)

Abstract: In this paper, we unify popular non-rigid registration methods for point sets and surfaces under our general framework, GiNGR. GiNGR builds upon Gaussian Process Morphable Models (GPMM) and hence separates modeling the deformation prior from model adaptation for registration. In addition, it provides explainable hyperparameters, multi-resolution registration, trivial inclusion of expert annotation, and the ability to use and combine analytical and statistical deformation priors. But more importantly, the reformulation allows for a direct comparison of registration methods. Instead of using a general solver in the optimization step, we show how Gaussian process regression (GPR) iteratively can warp a reference onto a target, leading to smooth deformations following the prior for any dense, sparse, or partial estimated correspondences in a principled way. We show how the popular CPD and ICP algorithms can be directly explained with GiNGR. Furthermore, we show how existing algorithms in the GiNGR framework can perform probabilistic registration to obtain a distribution of different registrations instead of a single best registration. This can be used to analyze the uncertainty e.g. when registering partial observations. GiNGR is publicly available and fully modular to allow for domain-specific prior construction.

• The paper introduces GiNGR, unifying non-rigid registration by separating deformation modeling from adaptation.
• It leverages Gaussian Process Regression and explainable hyperparameters for efficient, multi-resolution point cloud and surface registration.
• The framework integrates expert annotations and probabilistic methods to assess uncertainty and enhance registration accuracy.

Overview of the GiNGR Framework

The paper "GiNGR: Generalized Iterative Non-Rigid Point Cloud and Surface Registration Using Gaussian Process Regression" by Dennis Madsen et al. presents a comprehensive framework known as GiNGR, which unifies various non-rigid registration methods under a single umbrella. The essence of GiNGR lies in its foundation on Gaussian Process Morphable Models (GPMM), separating the modeling of the deformation prior from model adaptation for registration tasks involving point sets and surfaces.

Technical Insights and Innovations

GiNGR utilizes Gaussian Process Regression (GPR) to address the challenges inherent in non-rigid point cloud registration. The framework introduces several key features and innovations:

1. Separation of Modeling and Adaptation: By leveraging GPMM, the framework distinctly separates the modeling of deformations from the adaptation process, enhancing flexibility and modularity.
2. Explained Hyperparameters and Multi-Resolution Registration: The framework includes explainable hyperparameters, facilitating better interpretability and ease of adjustment. Additionally, GiNGR supports multi-resolution registration processes, allowing for more efficient computation and better handling of large datasets.
3. Integration of Expert Annotations: The framework provides a straightforward way to incorporate expert annotations, enriching the registration process with domain-specific knowledge.
4. Analytical and Statistical Deformation Priors: GiNGR allows the use of both analytical and statistical deformation priors, offering a versatile tool for various applications by catering to different kinds of prior information.
5. Probabilistic vs Deterministic Registration: Unlike traditional deterministic approaches, GiNGR supports probabilistic registration methods capable of yielding a distribution of registrations, which is particularly useful for evaluating and understanding uncertainty in partial observations.

Core Methodology

At the core of GiNGR is its iterative registration process, where Gaussian Process Regression is employed to iteratively warp reference models toward target models using estimated correspondences. The framework provides a mechanism for probabilistic registration, allowing practitioners to explore the posterior distribution of deformations rather than merely seeking the optimal transformation.

This research elegantly recasts celebrated algorithms like Coherent Point Drift (CPD) and Iterative Closest Point (ICP) within the GiNGR framework, showcasing how these methodologies naturally arise as special cases of the proposed system. Through this synthesis, Madsen et al. facilitate a better understanding of how differing assumptions and regularizations in point set registration influence the behavior and outcomes of these algorithms.

Implications and Future Directions

The GiNGR framework proposes a significant advancement in the field of non-rigid point set and surface registration. By offering a unifying perspective to traditionally disparate methodologies, it paves the way for future research into hybrid and cross-method solutions that can leverage the strengths of multiple registration strategies.

Practically, the modularity and open-source nature of GiNGR mean it can be adapted to a wide range of domains requiring flexible, non-rigid registration solutions. As more varied and complex datasets become the norm in disciplines like medical imaging and robotic mapping, GiNGR's capability to use both learned and analytical priors will be invaluable.

Theoretically, GiNGR opens avenues for exploring how different types of deformation priors and probabilistic frameworks can improve registration accuracy and robustness under uncertainty. Future developments might investigate integrating deeper learning-based deformation priors with the GiNGR framework, potentially tackling the limitations of requiring extensive training datasets and capturing complex non-linear deformations.

In conclusion, GiNGR presents a methodologically sound and flexible framework for non-rigid registration, significantly contributing to the computational tools available for addressing complex surface and point cloud alignment challenges.