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Point2Mesh: A Self-Prior for Deformable Meshes (2005.11084v1)

Published 22 May 2020 in cs.GR, cs.CV, and cs.LG

Abstract: In this paper, we introduce Point2Mesh, a technique for reconstructing a surface mesh from an input point cloud. Instead of explicitly specifying a prior that encodes the expected shape properties, the prior is defined automatically using the input point cloud, which we refer to as a self-prior. The self-prior encapsulates reoccurring geometric repetitions from a single shape within the weights of a deep neural network. We optimize the network weights to deform an initial mesh to shrink-wrap a single input point cloud. This explicitly considers the entire reconstructed shape, since shared local kernels are calculated to fit the overall object. The convolutional kernels are optimized globally across the entire shape, which inherently encourages local-scale geometric self-similarity across the shape surface. We show that shrink-wrapping a point cloud with a self-prior converges to a desirable solution; compared to a prescribed smoothness prior, which often becomes trapped in undesirable local minima. While the performance of traditional reconstruction approaches degrades in non-ideal conditions that are often present in real world scanning, i.e., unoriented normals, noise and missing (low density) parts, Point2Mesh is robust to non-ideal conditions. We demonstrate the performance of Point2Mesh on a large variety of shapes with varying complexity.

Citations (103)

Summary

  • The paper introduces a novel approach that derives self-priors directly from point clouds to reconstruct deformable meshes.
  • It iteratively optimizes an initial mesh via a CNN that refines vertex positions to capture both coarse structure and fine details.
  • The method demonstrates robustness against noise, sparse data, and unoriented normals, advancing the accuracy of 3D geometric reconstructions.

An Overview of "Point2Mesh: A Self-Prior for Deformable Meshes"

The paper under consideration presents Point2Mesh, a novel surface reconstruction technique that leverages self-priors for reconstructing surface meshes from point clouds. The self-prior is an intrinsic property derived from the input data itself, circumventing the need for externally sourced priors typically necessary in geometric reconstructions. At the crux of Point2Mesh is the use of a convolutional neural network (CNN) to encode self-priors through its weight sharing, exploiting local geometric self-similarities within the object shapes.

Approach and Methodology

The Point2Mesh framework optimally fits an initial mesh to an input point cloud by iteratively deforming it. Contrary to conventional techniques that rely on externally defined priors such as smoothness, Point2Mesh directly defines this prior from the point cloud without any pre-training. The methodology incorporates convolutional kernels applied across the mesh which inherently emphasize geometric coherence and repetition at local scales. This encourages the reconstruction of both fine and global shape details, avoiding local minima traps typical in smooth-prior models.

The training of the CNN occurs at inference time, with the model optimizing vertex displacements via a process resembling iterative shrink-wrapping. This process is inherently robust against typical real-world inaccuracies, such as noise, unoriented normals, and sparse data, often compromising traditional methods. Mesh refinement occurs in a coarse-to-fine manner, enabling the global structure to be captured initially, followed by iterative refinement to capture finer details.

Results and Implications

The paper emphasizes Point2Mesh's robustness under non-ideal conditions where traditional techniques degrade significantly. The experimental results demonstrate that Point2Mesh can handle varying levels of shape complexity and real-world scanning issues. Particularly noteworthy is the method's capacity for handling unoriented normals and noise, without requiring initial normal orientation—a frequent constraint in scanning and reconstruction tasks.

The implications of Point2Mesh are profound for both theoretical and practical aspects of AI-driven geometric learning. Theoretically, the work contributes to understanding how self-priors can be effectively derived and leveraged for reconstruction tasks. Practically, Point2Mesh offers a substantial advancement in scenarios demanding precise geometric reconstructions from noisy and incomplete point clouds, such as those encountered in computer graphics, 3D modeling, and automated scanning technologies.

Future Developments

Given the unique approach initiated by Point2Mesh, future work can explore several avenues to extend its framework. One potential development could focus on improving mesh deformation capabilities while maintaining computational efficiency. Another interesting direction could involve integrating Point2Mesh within a broader generative model framework to enhance mesh-based shape generation. Additionally, exploring the application of self-priors for other inverse problems in computational geometry represents a valuable contribution to the ongoing research in AI and deep learning.

In conclusion, the introduction of a self-prior concept in Point2Mesh represents a significant departure from conventional methodologies, providing new insights into the efficient and effective use of neural networks for reconstructing complex geometric shapes under challenging conditions.

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