DiGS : Divergence guided shape implicit neural representation for unoriented point clouds (2106.10811v3)

Abstract: Shape implicit neural representations (INRs) have recently shown to be effective in shape analysis and reconstruction tasks. Existing INRs require point coordinates to learn the implicit level sets of the shape. When a normal vector is available for each point, a higher fidelity representation can be learned, however normal vectors are often not provided as raw data. Furthermore, the method's initialization has been shown to play a crucial role for surface reconstruction. In this paper, we propose a divergence guided shape representation learning approach that does not require normal vectors as input. We show that incorporating a soft constraint on the divergence of the distance function favours smooth solutions that reliably orients gradients to match the unknown normal at each point, in some cases even better than approaches that use ground truth normal vectors directly. Additionally, we introduce a novel geometric initialization method for sinusoidal INRs that further improves convergence to the desired solution. We evaluate the effectiveness of our approach on the task of surface reconstruction and shape space learning and show SOTA performance compared to other unoriented methods. Code and model parameters available at our project page https://chumbyte.github.io/DiGS-Site/.

• The paper introduces a divergence constraint that regularizes learning, enabling high-quality shape reconstructions from raw point clouds.
• It employs geometric initialization with periodic activations to set the zero level set near a sphere and gradually refines detailed features.
• Experimental results indicate that DiGS outperforms normal-dependent methods on benchmarks, ensuring robust and smooth 3D reconstructions.

An Overview of DiGS: Divergence Guided Shape Implicit Neural Representation for Unoriented Point Clouds

The research paper presents an innovative approach termed Divergence Guided Shape (DiGS) Implicit Neural Representation, specifically designed for reconstructing shapes from unoriented 3D point clouds. Implicit Neural Representations (INRs) have gained significant attention for their capacity to generate high-fidelity shape reconstructions, yet they typically rely on positional data augmented by normal vectors. In contrast, DiGS circumvents the need for normal vectors, which are often absent in raw point cloud data, while primarily focusing on guiding the learning process through a divergence constraint.

Methodological Advancements

The DiGS methodology is characterized by several notable features:

1. Divergence Constraint: A key novelty of this approach is the introduction of a divergence constraint acting as a regularization mechanism. This constraint is based on the premise that the divergence of the gradient vector field related to the signed distance function should remain low across most regions, guiding the shape representation to favor smooth transitions in the absence of explicit normal data.
2. Geometric Initialization: The paper introduces a geometric initialization technique tailored for networks utilizing periodic activation functions, like SIREN. This initialization seeks to set the initial zero level set close to a sphere to reduce initial bias and enhance the learning progression towards the desired geometric form.
3. Training Strategy: The training protocol progressively reduces the influence of the divergence constraint throughout the process, allowing for refinement in fine details while maintaining overall smoothness and correct geometric orientation.

Experimental Evaluation

DiGS is extensively validated on multiple benchmarks and typical datasets such as the Surface Reconstruction Benchmark (SRB) and ShapeNet, as well as human body scans from the DFaust dataset, demonstrating its effectiveness in shape space learning and surface reconstruction.

• Surface Reconstruction: Compared to state-of-the-art methods like SIREN and IGR that rely on normal vectors, DiGS provides superior performance when normals are unavailable. It achieves comparable results to normal-based methods by facilitating a divergence constraint and an informed initialization strategy, significantly minimizing issues like ghost geometries.
• Shape Space Learning: In evaluating human shape models from the DFaust dataset, DiGS maintains robust convergence properties without normal vectors, generating intuitive and plausible reconstructions. The technique shows reduced susceptibility to artifacts and prioritizes smoothness, albeit sometimes at the expense of very fine detail.

Implications and Future Directions

The paper underscores the practical implications of utilizing purely positional unstructured 3D data, which is advantageous in many real-world applications, such as robotic vision and augmented reality, where raw scan data typically does not include reliable normals. DiGS’s divergence-centric method paves the way for more robust, data-efficient shape reconstruction algorithms and offers a foundation for future work targeting the inclusion of more complex shape details.

Given the promising results demonstrated by DiGS, future research directions could explore adaptive divergence constraints across varying levels of abstraction and integrating multi-scale approaches to balance high-detail representation without sacrificing broad structural coherence. There is potential for extending these methodologies to handle even more challenging datasets characterized by higher noise levels and sparser point sampling.

In conclusion, DiGS introduces a new perspective of guiding implicit neural representations for 3D reconstruction, achieving commendable efficacy on par with approaches that require additional input data while promoting computational efficiency and direct applicability to raw scan environments.