Marching-Primitives: Shape Abstraction from Signed Distance Function (2303.13190v2)

Abstract: Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at https://github.com/ChirikjianLab/Marching-Primitives.git.

• The paper presents a novel two-step algorithm that extracts and optimizes superquadric primitives directly from SDFs.
• It achieves computational efficiency and storage compactness while outperforming state-of-the-art methods on metrics like Chamfer-L1 and volumetric IoU.
• The approach demonstrates robustness to initialization errors and holds promise for applications in robotic perception and scene understanding.

Marching-Primitives: Shape Abstraction from Signed Distance Function

The paper introduces a novel technique, termed "Marching-Primitives," aimed at addressing the challenge of representing complex 3D shapes using basic geometric primitives directly extracted from Signed Distance Functions (SDFs). This approach is built on the premise that primitive-based representations offer improvements in computational efficiency and model compactness, especially beneficial for tasks such as collision checking and robotic manipulation.

Methodology

Unlike traditional methods, which tend to derive polygonal meshes from SDFs, Marching-Primitives extracts geometric primitives such as superquadrics. It employs a two-step iterative process:

1. Connectivity Marching: This step involves analyzing the connectivity of voxels at multiple signed distance levels. Specifically, it identifies connected volumes of interest (VOIs) where primitives are most likely to be encoded.
2. Probabilistic Primitive Marching: Within the identified VOIs, the algorithm marches through neighboring voxels, infers probabilistic correspondences to the potential primitive, and simultaneously optimizes the parameters to fit the local geometry.

This process allows the algorithm to adaptively identify, initialize, and refine the parameters of the potential primitives iteratively. By progressively capturing the underlying geometry of each segment, Marching-Primitives leads to more accurate shape abstractions compared to existing methods.

Performance Evaluation

The paper presents quantitative assessments on datasets like ShapeNet and DFAUST, which include diverse categories ranging from everyday objects to human body models. The algorithm outperforms state-of-the-art alternatives in terms of both Chamfer-L1 distances and volumetric intersection over union (IoU) metrics. Remarkably, even when using less expressive primitives like ellipsoids, the approach demonstrates significant capability in capturing detailed object structures.

Key Findings

1. Improved Accuracy and Generalizability: Marching-Primitives showcases superior performance in encoding 3D shapes across various object categories and scales.
2. Storage Efficiency: The primitive-based SDF produced is a compact representation requiring significantly less storage space than detailed mesh or volumetric data.
3. Robustness to Initialization: The algorithm incorporates an auto-degeneration mechanism and a probabilistic inference framework which ensure robustness against poor initializations.
4. Scene Understanding: Beyond single-object abstraction, the technique extends to complex scene representations, indicating its potential in real-world applications like robotic perception and computer graphics.

Implications and Future Prospects

The approach highlights the utility of SDF representations beyond conventional mesh generation, suggesting a shift towards more compact and informative geometric abstractions. As the algorithm inherently supports generalization beyond specific object categories, future developments may extend towards integrating semantic understanding. Additionally, there may be scope for parallelizing the marching process to enhance computational efficiency further. The speculation involves improving interactions between primitive-based and semantic-level data representations, increasingly relevant for advanced AI and robotic applications.

In conclusion, Marching-Primitives presents a significant advancement in geometric modeling, enabling more efficient and accurate representations directly usable in computational tasks that demand high efficiency and detailed geometrical understanding. This foundational research paves the way for further advancements in 3D shape abstraction and applications across various disciplines.