Point Cloud Upsampling With Geometric Algebra Driven Inverse Heat Dissipation
Abstract: Point cloud upsampling is crucial for 3D reconstruction, with recent research significantly benefitting from the advances in deep learning technologies. The majority of existing methods, which focus on a sequence of processes including feature extraction, augmentation, and the reconstruction of coordinates, encounter significant challenges in interpreting the geometric attributes they uncover, particularly with respect to the intricacies of transitioning feature dimensionality. In this paper, we delve deeper into modeling Partial Differential Equations (PDEs) specifically tailored for the inverse heat dissipation process in dense point clouds. Our goal is to detect gradients within the dense point cloud data distribution and refine the accuracy of interpolated points’ positions along with their complex geometric nuances through a systematic iterative approximation method. Simultaneously, we adopt multivectors from geometric algebra as the primary tool for representing the geometric characteristics of point clouds, moving beyond the conventional vector space representations. The use of geometric products of multivectors enables us to capture the complex relationships between scalars, vectors, and their components more effectively. This methodology not only offers a robust framework for depicting the geometric features of point clouds but also enhances our modeling capabilities for inverse heat dissipation PDEs. Through both qualitative and quantitative assessments, we demonstrate that our results significantly outperform existing state-of-the-art techniques in terms of widely recognized point cloud evaluation metrics and 3D visual reconstruction fidelity.
Primary Subject Area: [Experience] Multimedia Applications
Secondary Subject Area: [Experience] Multimedia Applications
Relevance To Conference: Point clouds are a fundamental element in the domain of multimedia, serving as the backbone for a variety of applications ranging from virtual reality to spatial analytics. However, due to limitations in current acquisition technologies, point clouds often suffer from sparsity and noise, necessitating the need for effective upsampling techniques. Existing upsampling methods grapple with issues such as loss of geometric detail and computational inefficiency.
In response to these challenges, our work introduces a novel approach to point cloud upsampling that capitalizes on the strengths of geometric algebra and PDE-based inverse heat dissipation modeling. Our methodology not only enhances the precision of interpolated points but also faithfully preserves intricate geometric details.
Our contribution is set to propel the field of point cloud upsampling by offering a method that ensures highly accurate modeling of complex geometries, a crucial requirement for advanced multimodal systems.
Submission Number: 4327
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