TaylorGrid: Towards Fast and High-Quality Implicit Field Learning via Direct Taylor-based Grid Optimization (2402.14415v1)

Abstract: Coordinate-based neural implicit representation or implicit fields have been widely studied for 3D geometry representation or novel view synthesis. Recently, a series of efforts have been devoted to accelerating the speed and improving the quality of the coordinate-based implicit field learning. Instead of learning heavy MLPs to predict the neural implicit values for the query coordinates, neural voxels or grids combined with shallow MLPs have been proposed to achieve high-quality implicit field learning with reduced optimization time. On the other hand, lightweight field representations such as linear grid have been proposed to further improve the learning speed. In this paper, we aim for both fast and high-quality implicit field learning, and propose TaylorGrid, a novel implicit field representation which can be efficiently computed via direct Taylor expansion optimization on 2D or 3D grids. As a general representation, TaylorGrid can be adapted to different implicit fields learning tasks such as SDF learning or NeRF. From extensive quantitative and qualitative comparisons, TaylorGrid achieves a balance between the linear grid and neural voxels, showing its superiority in fast and high-quality implicit field learning.

• The paper introduces TaylorGrid, leveraging low-order Taylor expansions for direct grid optimization to boost both learning speed and implicit field quality.
• It demonstrates efficient convergence and superior 3D reconstruction performance compared to traditional linear grid and neural voxel methods.
• Its compact design and versatile application suggest promising future directions for enhancing scalability and extending to multi-field predictions.

Expanding the Horizons of Implicit Field Learning with TaylorGrid

Introduction to TaylorGrid

The recent surge in interest and development within the domain of coordinate-based implicit fields has significantly advanced 3D geometry representation and novel view synthesis. Despite the progression, the pursuit of optimizing both the speed and quality of implicit field learning remains relentless. Amidst various approaches to accelerate and refine learning, a notable convergence between linear grid methods and neural voxels (SMLP) methods surfaces, each offering distinct advantages in terms of speed and representation quality respectively. Bridging this gap, a novel methodology dubbed TaylorGrid emerges, employing low-order Taylor expansion strategies for direct grid optimization. By integrating the benefits of linear grid speed and the superior representation capacity akin to neural voxels, TaylorGrid marks a significant stride forward in the efficient and high-quality learning of implicit fields.

Theoretical Foundations and Methodology

TaylorGrid operates on the principle of utilizing Taylor expansion formulas to directly optimize grids that encode field signals, such as volume density and signed distance functions (SDFs). The method stores coefficients of low-order Taylor expansions at each grid vertex, significantly enhancing the representation capability through the incorporation of additional continuous non-linearity. This facet not only promises improved outcomes in applications like geometry reconstruction and novel view synthesis but also ensures a more compact and memory-efficient solution devoid of neural networks.

The representation enjoys several distinct advantages:

• Efficiency and Compactness: Liberated from the necessity of neural networks, TaylorGrid is remarkably efficient, presenting a rapid convergence rate akin to linear grid methods while occupying minimal memory.
• Enhanced Representation Power: The method transcends the limited representation ability of linear grids by embedding more sophisticated non-linearity through low-order Taylor expansions.
• Versatile Applicability: The simplicity and generality of TaylorGrid enable straightforward integration into various implicit field learning tasks, promising widespread utility.

Empirical Validation and Comparative Analysis

Extensive experimentation underscores the efficacy of TaylorGrid across two major applications: 3D geometry reconstruction and neural radiance fields. When benchmarked against existing methodologies such as DeepSDF, linear grids, and SMLP methods, TaylorGrid demonstrates a commendable balance of efficient convergence and superior representational quality. Specifically, in tasks involving the reconstruction of complex 3D models and generating novel views of scenes, the method consistently achieves impressive results, substantiating its potential advantages over both linear grids and neural voxel approaches.

Future Directions and Implications

Despite its promising capabilities, TaylorGrid, like all grid-based approaches, is not without limitations—particularly, the scalability issue concerning grid resolution and memory consumption, and challenges related to modeling high-order expansions. Future explorations might delve into integrating sparse data structures or grid decomposition schemes to circumvent these constraints, further amplifying the method's efficiency and applicability. Moreover, extending TaylorGrid to cater to non-scalar field predictions, such as color or texture, presents another avenue for research, potentially driving the technology towards a unified solution for a broader spectrum of implicit field learning tasks.

Concluding Remarks

TaylorGrid represents a significant step forward in the domain of implicit field learning, effectively marrying the speed of linear grid methods with the representation quality of neural voxels. Its introduction not only opens up new possibilities for the efficient and high-quality learning of complex 3D geometries and novel view synthesis but also sets the stage for future innovations in the field. As we continue to unravel the full potential of TaylorGrid, its foundational contribution to advancing implicit field learning remains indubitably clear.