Point Cloud Processing: Classification, Registration and Reconstruction

Abstract

Point cloud processing methods have been an important task of 3D computer vision and graphics, with broad applications in robotic navigation, autonomous driving, 3D modeling, and medical imaging. This thesis introduces several new methods for point cloud classification, point-based surface reconstruction, and point cloud registration, contributing significantly to the robustness and accuracy of these tasks.

Firstly, we propose a method for point cloud classification that uses spectral graph features as network input, and deep graph convolution network which is also rotation invariant to improve the accuracy and stability of feature extraction under various transformations. This method provides robust classification performance, even with noisy or incomplete data, improving its applicability in diverse settings.

For surface reconstruction, this thesis introduces a novel method called DiffSDF. DiffSDF receives an input of a point cloud and determines a continuous Signed Distance Function (SDF) that implicitly encodes the fundamental shape of the data. This method addresses limitations of previous methods by supervising the gradient of the SDF which is generated by differentiating the network regarding the input points. This gradient-based supervision ensures that the learned SDF remains valid and resilient to noise, enabling a more accurate representation of surface details.

Additionally, this thesis presents a novel approach designed to build descriptors for the task of rigid point cloud registration. These descriptors are developed to be completely invariant and equivariant to rotational transformations, thereby enhancing their effectiveness and applicability within this domain. Our network extracts both a rotation-invariant descriptor , which enables efficient correspondence matching, and a rotation-equivariant descriptor, which allows for direct recovery of the relative transformation from a single correspondence pair for each keypoint patch. This approach is different from conventional techniques that require at least three correspondences, enabling a reduction in the number of RANSAC iterations. Hence, even when the proportion of accurately identified correspondences to the total estimated correspondences is relatively small, the registration result still has a high registration recall. Through this strategy, our method improves both efficiency and accuracy in point cloud registration, making it highly suitable for real-world applications that demand robust alignment of noisy, unordered 3D data.

Finally, this thesis presents a novel method for non-rigid point cloud registration, specifically designed to handle large displacements, significant deformations, and low overlap between point clouds. Our approach introduces a recurrent update network block that progressively refines local registration results under a local rigidity assumption, starting from an initial global alignment. This progressive refinement leverages the recurrent update strategy to iteratively improve registration accuracy, adapting effectively to complex non-rigid transformations.

These contributions have state-of-the-art performance in point cloud processing, providing adaptable and precise solutions across critical tasks, including classification, surface reconstruction, and both rigid and non-rigid registration. By addressing challenges such as noise robustness, rotation invariance, and large-scale deformations, this work offers robust methods that enhance the accuracy and reliability of real-world 3D applications in diverse fields, from autonomous systems to medical imaging and digital content creation. Show more