Differentiable Manifold Reconstruction for Point Cloud Denoising (2007.13551v2)

Abstract: 3D point clouds are often perturbed by noise due to the inherent limitation of acquisition equipments, which obstructs downstream tasks such as surface reconstruction, rendering and so on. Previous works mostly infer the displacement of noisy points from the underlying surface, which however are not designated to recover the surface explicitly and may lead to sub-optimal denoising results. To this end, we propose to learn the underlying manifold of a noisy point cloud from differentiably subsampled points with trivial noise perturbation and their embedded neighborhood feature, aiming to capture intrinsic structures in point clouds. Specifically, we present an autoencoder-like neural network. The encoder learns both local and non-local feature representations of each point, and then samples points with low noise via an adaptive differentiable pooling operation. Afterwards, the decoder infers the underlying manifold by transforming each sampled point along with the embedded feature of its neighborhood to a local surface centered around the point. By resampling on the reconstructed manifold, we obtain a denoised point cloud. Further, we design an unsupervised training loss, so that our network can be trained in either an unsupervised or supervised fashion. Experiments show that our method significantly outperforms state-of-the-art denoising methods under both synthetic noise and real world noise. The code and data are available at https://github.com/luost26/DMRDenoise

Differentiable Manifold Reconstruction for Point Cloud Denoising: A Technical Overview

The paper "Differentiable Manifold Reconstruction for Point Cloud Denoising," presented at MM '20, addresses the challenge of reducing noise in 3D point clouds—a common problem due to the imperfections in data capture technologies like depth sensors and LiDARs. The authors propose a novel method that explicitly reconstructs the underlying manifold from noisy point clouds, intending to improve denoising outcomes for downstream tasks such as surface reconstruction and rendering.

Methodology

The core of the proposed method involves an autoencoder-like neural network architecture, focusing on capturing intrinsic manifold structures within point clouds. The network consists of two main components:

1. Representation Encoder: This module performs feature extraction and downsampling through a novel differentiable pooling strategy. The feature extraction unit leverages dynamic graph convolution layers to learn both local and non-local geometric features. The differentiable pooling operation adaptively selects points that are closer to the true underlying surfaces, thus setting up the network for improved manifold reconstruction.
2. Manifold Reconstruction Decoder: Post sampling, the decoder reconstructs a local manifold—termed as patch manifold—around each sampled point. The reconstruction leverages an MLP-based parameterized manifold, which enables resampling to form a denoised point cloud. This process inherently aligns with the geometric nature of 3D point clouds, preserving surface integrity during denoising.

The authors also introduce a dual loss function to train the network in both supervised and unsupervised settings, enhancing the flexibility and applicability of the approach in various scenarios. The supervised loss incorporates both Chamfer distance and Earth Mover's Distance (EMD), optimizing for spatial accuracy and evenness on surface reconstruction.

Numerical Results

The experimental results demonstrate significant improvements over existing methods. The paper compares its method to both deep-learning-based and traditional non-deep-learning methods. The proposed approach exhibits superior performance, particularly at higher noise levels, and shows robustness against both synthetic and real-world noise types. These results are encapsulated through extensive evaluations across noise levels ranging from 1% to 3% of the bounding box diagonal, confirming the network's efficacy in high-noise environments.

Implications and Future Work

This method's success in reconstructing manifolds from point clouds has substantial implications for 3D vision applications. By focusing on manifolds instead of simply displacing noisy points, the approach promises enhanced quality in rendering and related computational geometry tasks. The adaptive pooling and manifold reconstruction techniques may inspire new architectures and training methodologies in AI tasks involving geometric data processing.

Future developments could involve extending the idea of differentiable manifold reconstruction to broader datasets and more challenging environments, such as dynamic scenes captured in real-time. Additionally, integrating the learned manifolds directly into applications like autonomous driving systems or immersive AR experiences could be compelling.

In summary, this paper advances the field of point cloud processing by introducing an architecture capable of learning and reconstructing the inherent structures of 3D data. Its methodological contributions offer a direction that balances theoretical elegance with practical utility, laying the groundwork for further explorations in manifold learning and deep geometric representations.