Title: Tetrahedron Splatting for 3D Generation
Venue: NeurIPS 2024
Accepted: yes
Keywords: text-to-3D

tetrahedron splatting

volumetric rendering
Abstract: 3D representation is essential to the significant advance of 3D generation with 2D diffusion priors. As a flexible representation, NeRF has been first adopted for 3D representation. With density-based volumetric rendering, it however suffers both intensive computational overhead and inaccurate mesh extraction. Using a signed distance field and Marching Tetrahedra, DMTet allows for precise mesh extraction and real-time rendering but is limited in handling large topological changes in meshes, leading to optimization challenges. Alternatively, 3D Gaussian Splatting (3DGS) is favored in both training and rendering efficiency while falling short in mesh extraction. In this work, we introduce a novel 3D representation, Tetrahedron Splatting (TeT-Splatting), that supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously. This is achieved by integrating surface-based volumetric rendering within a structured tetrahedral grid while preserving the desired ability of precise mesh extraction, and a tile-based differentiable tetrahedron rasterizer. Furthermore, we incorporate eikonal and normal consistency regularization terms for the signed distance field to improve generation quality and stability. Critically, our representation can be trained without mesh extraction, making the optimization process easier to converge. Our TeT-Splatting can be readily integrated in existing 3D generation pipelines, along with polygonal mesh for texture optimization. Extensive experiments show that our TeT-Splatting strikes a superior tradeoff among convergence speed, render efficiency, and mesh quality as compared to previous alternatives under varying 3D generation settings.

Tetrahedron Splatting for 3D Generation

Abstract

3D representation is essential to the significant advance of 3D generation with 2D diffusion priors. As a flexible representation, NeRF has been first adopted for 3D representation. With density-based volumetric rendering, it however suffers both intensive computational overhead and inaccurate mesh extraction. Using a signed distance field and Marching Tetrahedra, DMTet allows for precise mesh extraction and real-time rendering but is limited in handling large topological changes in meshes, leading to optimization challenges. Alternatively, 3D Gaussian Splatting (3DGS) is favored in both training and rendering efficiency while falling short in mesh extraction. In this work, we introduce a novel 3D representation, Tetrahedron Splatting ( TeT-Splatting ), that supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously . This is achieved by integrating surface-based volumetric rendering within a structured tetrahedral grid while preserving the desired ability of precise mesh extraction, and a tile-based differentiable tetrahedron rasterizer. Furthermore, we incorporate eikonal and normal consistency regularization terms for the signed distance field to improve

generation quality and stability. Critically, our representation can be trained without mesh extraction, making the optimization process easier to converge. Our TeTSplatting can be readily integrated in existing 3D generation pipelines, along with polygonal mesh for texture optimization. Extensive experiments show that our TeTSplatting strikes a superior tradeoff among convergence speed, render efficiency, and mesh quality as compared to previous alternatives under varying 3D generation settings.

1 Introduction

Automatic 3D content generation is revolutionizing fields such as virtual reality, augmented reality, video games, and industrial design. This technology can significantly enhance user experiences and streamline creative processes for reducing time demands and simplifying the complexities associated with creating high-quality 3D assets.

3D representations ( e.g. , Neural Radiance Field [28] (NeRF)) play an essential role in recent advancements in 3D generation, along with the Score Distillation Sampling (SDS) technique objective [32] for exploiting off-the-shelf 2D diffusion models [11, 37, 38, 1]. Although serving as a pioneer representation, NeRF is significantly limited due to its intensive computational demands, particularly when paired with high-resolution 2D diffusion models. Moreover, its density-based volumetric rendering struggles with accurate mesh extraction, which is crucial for practical applications.

By utilizing a signed distance field and Marching Tetrahedra for differentiable mesh extraction, DMTet [40] enables efficient high-resolution rendering and precise mesh extraction, overcoming the limitations of the NeRF approach. In cases, it becomes a favored choice [18, 33, 3]. However, DMTet is limited in its ability to handle large topological changes in meshes, as it can only backpropagate to the zero-level set of the signed distance field, constraining its geometry convergence during optimization. As a workaround, a two-stage 3D generation pipeline has been adopted that initially utilizes NeRF for rapid geometry convergence and then transitions to DMTet for detailed refinement [18]. However, transitioning from NeRF to DMTet often results in a degradation of quality, as the strengths of each representation are not fully leveraged throughout the entire optimization process.

Alternatively, recent methods have introduced 3D Gaussian Splatting [13] (3DGS) into the optimization process, significantly enhancing efficiency. For example, DreamGaussian [46] utilizes 3DGS but acknowledges that meshes directly generated from 3DGS can be blurry, and the mesh extraction process often results in unsatisfactory surfaces with visible holes [45]. Moreover, the text-to-3D process with 3DGS suffers from instability due to its unstructured nature and the densification process.

In this work, we introduce TeT-Splatting , a novel all-round 3D representation that integrates surfacebased volumetric rendering into the tetrahedral grid, while preserving precise mesh extraction through Marching Tetrahedra. It supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously , enabling high-fidelity 3D generation effectively (Figure 1). Drawing inspiration from 3DGS [13], we design a tile-based fast differentiable rasterizer for realtime rendering, efficiently handling the alpha-blending of projected 2D splats from 3D tetrahedra. These splats are blended based on opacity values derived from the signed distance field within each tetrahedron as in NeuS [49]. To further increase efficiency, we include a pre-filtering process to remove nearly transparent tetrahedra, reducing the number of tetrahedra necessary for splatting. Moreover, we introduce eikonal and normal consistency regularization terms to refine the signed distance field, which helps stabilize the optimization process and prevents the common issue of debris in the optimization with DMTet. In Table 1 we compare the features of different 3D representations.

Our contributions are fourfold: (i) Introducing a novel 3D representation, TeT-Splatting , that integrates synergistically volumetric rendering into a tetrahedral grid; (ii) Designing a fast differentiable rasterizer for tetrahedra; (iii) Forming a generic two-stage 3D generation pipeline that initially leverages TeT-Splatting for geometry optimization, and then transitions it to polygonal mesh for texturing; (iv) Extensive evaluations demonstrating the superior tradeoff of our method among easy convergence, real-time rendering, and precise mesh extraction over alternative representations (InstantNGP [29], DMTet [40], and 3DGS [13]) under a variety of settings with different diffusion priors.

2 Related work

3D representation Since the introduction of Neural Radiance Field (NeRF) [28], NeRF has become a foundational technique in the field of 3D reconstruction. It employs volumetric rendering to enable 3D optimization with only 2D supervision. Despite its significance, NeRF faces major issues, such as slow rendering speeds and high memory usage. To address these problems, several research[43, 39, 29, 2, 13] have developed novel variants of the radiance field, focusing on faster training and rendering and using less computing resources. Diverging from the path of NeRF, DMTet [40] has introduced an approach based on Marching Tetrahedra and surface rendering by differentiable rasterization [14], offering much faster rendering speed. Recently, 3D Gaussian Splatting [13] (3DGS) has unified NeRF-like alpha-blending with tile-based rasterization, achieving high performance in both quality and rendering speed. In this paper, our proposed TeT-Splatting takes inspiration from the structured tetrahedral grid in DMTet [40] and incorporates tile-based rasterization from 3DGS [13], utilizing tetrahedra for splatting. TeT-Splatting achieves high converge and rendering speed while preserving precise mesh extraction through Marching Tetrahedra.

3D generation The data-driven 2D diffusion models [11, 37, 38, 1] have demonstrated unprecedented success in image generation. However, the transition to direct 3D generation [31, 12, 10, 24, 8, 58, 6, 52, 19, 15, 45] faces formidable challenges, as this research line often fails to generate high-quality 3D assets limited by the lack of training data. To circumvent these issues, some works [20, 41, 23, 42, 21, 25, 50] train 2D diffusion models to make them have 3D awareness. However, discrete and sparse 2D images still cannot offer sufficient 3D information. In this context, DreamFusion [32] first introduced score distillation sampling (SDS) loss to leverage 2D diffusion priors for 3D generation. Subsequent studies [47, 57, 59, 54, 51, 17, 26, 44, 48] have aimed to improve the SDS loss, enhancing both the fidelity and stability of 3D generation. Moreover, several efforts [55, 5, 56, 4, 16, 42, 34, 22] have been made to improve the quality and multi-view consistency of 3D models by integrating a wider array of diffusion priors. Despite these advancements, some methods are hindered by the significant computational demands due to the usage of NeRF [28], which limits the effective use of high-resolution diffusion priors. Additionally, other mesh-based models [3, 16, 34] encounter issues with instability and slow convergence due to the nature of surface rendering. By contrast, our TeT-Splatting facilitates the use of high-resolution diffusion priors and ensures efficient updates, thanks to its volumetric rendering and tile-based differentiable rasterizer.

3 TeT-Splatting

3.1 Deformable tetrahedral grid

In this section, we will start with an introduction to the deformable tetrahedral grid, which is the geometric primitive for the proposed representation. The deformable tetrahedral grid is first employed in DefTet [7] and then extended in DMTet [40] to approximate the implicit surface by assigning each vertex an SDF value. Specifically, this structure considers a tetrahedral mesh composed of N vertices and K tetrahedra, denoted as ( V T , T ) , where V T = { v n | n ∈ 1 , . . . , N } signifies the positions of vertices, and T = { t k | k ∈ 1 , . . . , K } , with each t k representing the indices ( a k , b k , c k , d k ) of four vertices ( v a k , v b k , v c k , v d k ) that form a tetrahedron. Utilizing the SDF value associated with each vertex v n , denoted by f n , a signed distance field is established by interpolating the SDF values within each tetrahedron. DMTet [40] has developed a method for mesh extraction from the tetrahedral grid by assigning one or two triangles to each tetrahedron that intersects the zero-level set of the signed distance field, known as Marching Tetrahedra (MT). Employing a differentiable triangular rasterizer, it attains a remarkable rendering speed while maintaining minimal memory consumption.

TeT-Splatting

3D Generation

Geometry Optimization

TeT-Splatting

Normal / Depth / Opacity

SDS

Prompt

Tet grid

Texture Refinement

MT

Albedo / PBR

Rasterization

SDS

Tet grid

Prompt

Pre-filter

Depth

Normal

Opacity

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)GLYPH(cmap:d835)GLYPH(cmap:d835)GLYPH(cmap:d835)

GLYPH(cmap:d835)

GLYPH(cmap:d835)GLYPH(cmap:d835)GLYPH(cmap:d835)GLYPH(cmap:d835)

However, a particular limitation of the MT is that only the parameters associated with tetrahedra intersecting the zero-level set of the signed distance field can be updated during optimization. This restriction poses challenges in managing large topological changes and often causes the optimization to stuck in the undesired shape in the early stage. In contrast, NeRF is less affected by such instability thanks to its volumetric nature. Many prior works [18, 33] have employed NeRF in 3D generation. These works typically adopt a two-stage pipeline that starts with the volumetric representation to swiftly achieve a coarse model with low-resolution diffusion priors and then transitions to a polygonal mesh for further refinement with high-resolution diffusion priors. However, these approaches are often hindered by the slow optimization and inaccurate geometry brought by volume rendering. The inaccurate geometry would lead to obvious degradation after mesh extraction.

3.2 Differentiable tetrahedron splatting

In this work, we present a unified representation that combines the precise mesh extraction via the tetrahedral grid and the efficient optimization of volumetric rendering. Inspired by 3D Gaussian Splatting [13] (3DGS), we also integrate the tile-based rasterizer into our framework to facilitate real-time rendering. 3DGS enhances rendering efficiency through rasterization and ensures efficient optimization via alpha-blending by projecting 3D Gaussians to 2D splats followed by fast alphablending. However, 3DGS relies on unstructured 3D Gaussians as rendering primitives, necessitating carefully designed densification processes and learning rates to manage the highly noisy SDS loss. In contrast, the tetrahedral grid is structured while its vertices can only deform in a local region and are connected with neighbors to form tetrahedra. We explore treating tetrahedron as rendering primitive of the splatting process to perform alpha-blending. Moreover, we can directly extract polygonal mesh through Marching Tetrahedra from the tetrahedral grid, while the mesh extracted [46] from 3DGS may result in an unsatisfactory surface with visible holes.

Next, we will elaborate on how we realize differentiable tetrahedron splatting through alpha-blending. Consider a pixel on the image plane, along with its corresponding ray in 3D space. To perform alpha-blending, we need first determine the intersected tetrahedra between the ray and the tetrahedral grid. For a single tetrahedron t with vertices ( v a , v b , v c , v d ) and SDF values ( f a , f b , f c , f d ) , we can project the vertices onto the image plane, resulting in four overlapped triangles that form a 2D tetrahedron splat. Intersection with the tetrahedron t is equal to the intersection with the four triangles. The position and SDF value of an intersection point can be calculated using barycentric coordinates (see Appendix A for details). Different from 3DGS [13], we consider the opacity of tetrahedra instead of Gaussians. Note that a ray can only have two intersection points with a tetrahedron, we denote their SDF values as f prev and f next in depth order. Then the opacity of the tetrahedron t can be derived

Optimization progress

0 iter

100 iter

200 iter

500 iter

1500 iter

2000 iter

2500 iter

3000 iter

TeT-Splatting

TeT-Splatting

(MT)

Latent code

Normal

1000 iter

in NeuS [49] manner:

where Φ s ( x ) = (1 + e -sx ) -1 , and the s value controls the steepness of the conversion. Following Voxurf [53], we update s manually for each iteration i : s = i/s ratio + s start. The final normal map N , depth map D and opacity map O are derived by alpha-blending N sequentially ordered tetrahedra from front to back:

where n denotes the per-tetrahedron normal and z i denotes the average depths of four vertices. Pre-filtering To conserve computational resources, the tetrahedra with low opacity will be filtered. Depending on different intersection points, the opacity of a tetrahedron can take different values. We can establish the upper bound of the opacity, denoted as α max , by replacing s prev and s next in Eq. 1 with the maximum and minimum SDF values of four vertices. Tetrahedra with α max less than a predefined threshold T f = 1 255 are filtered to ensure that only tetrahedra with significant enough contribution to the alpha-blending are included in the subsequent splatting process.

Per-tetrahedron normal As discussed in Section 3.1, the tetrahedral grid establishes a signed distance field by interpolating the SDF values within each tetrahedron. This interpolation is a linear combination of the SDF values of four vertices. Correspondingly, the barycentric coordinates of an arbitrary point with respect to the four vertices of the tetrahedron exhibit a linear correlation with its spatial position. This ensures that the gradient g of the SDF within the tetrahedron results in a constant vector (see Appendix A for details). The normal vector n of the tetrahedron is thus obtained by normalizing this gradient.

Relationship between DMTet and TeT-Splatting During optimization, DMTet employs Marching Tetrahedra to extract polygonal mesh from the tetrahedral grid and subsequently renders through triangular rasterization [14]. Consequently, only a limited number of tetrahedra are involved in each single rendering process. In contrast, TeT-Splatting employs volumetric rendering, which allows all visible tetrahedra within the view frustum that have sufficient weight in alpha-blending to contribute to the final renderings. Moreover, the rendering process in TeT-Splatting is fully differentiable, enabling a single optimization step to influence a significantly larger number of parameters compared to DMTet. Figure 3 presents a comparative analysis of convergence speeds between DMTet and TeT-Splatting within the same Text-to-3D pipeline. As observed, TeT-Splatting achieves rapid convergence, whereas DMTet exhibits slower topological changes and gets stuck in an undesirable shape. Furthermore, as the inverse standard deviation s in Eq. 1 increases, the curve of Φ s ( x ) becomes steeper, causing

α to approach 1 under conditions that s prev > 0 and s next < 0 and to approach 0 otherwise. This behavior (Figure 3) aligns with the rendering process of DMTet [40] through Marching Tetrahedra, where only the tetrahedra intersecting the zero-level set of the signed distance field are visible.

3.3 Fast differentiable rasterizer for tetrahedra

We implement a tile-based differentiable rasterizer for tetrahedra with custom CUDA kernel building upon the framework of 3DGS [13]. Similarly, we begin by dividing the screen into tiles and culling tetrahedra that do not overlap with the view frustum. We then replicate the tetrahedra based on the number of tiles they overlap and sort them by their tile ID and the average depth of each tetrahedron's vertices, using a fast GPU radix sort [27]. Note that the per-tile sorting in 3DGS is not equivalent to per-pixel ordering. Differently, we maintain a short resorting window [36] of size N w for each pixel to re-sort the primitives based on the results of per-tile sorting using the insertion sort. Due to the structured nature of the tetrahedral grid, we find that the sorting error is almost eliminated with a window size of 5 under a grid resolution of 256. The operations after re-sorting for alpha-blending are the same as in 3DGS, except for the computation of α , which we have already given in Eq. 1.

4 3D generation with TeT-Splatting

In this section, we introduce our 3D generation pipeline and discuss various settings, aiming at validating the effectiveness of TeT-Splatting in 3D generation. As shown in Figure 2, our pipeline is divided into two stages: first get a detailed geometry with TeT-Splatting and then transition to polygonal mesh through Marching Tetrahedra [40] for texture optimization. We begin by describing our overall 3D model (Section 4.1), and then detail the regularizations (Section 4.2) and diffusion priors (Section 4.3) used in our experiments.

4.1 3D modeling

Geometry stage We employ a hash grid [29] Φ g with parameter Θ g to encode the signed distance field and deformation which allows each vertex in a tetrahedral grid to deform in a certain range. Φ g is initialized to a spherical shape. Given a randomly sampled camera, our tetrahedron rasterizer produces renderings of the normal map, depth map, and opacity map.

Texture stage Given the well-optimized signed distance field from the geometry stage, we convert it into a polygonal mesh through Marching Tetrahedra. To texture the polygonal mesh, we employ the physically based rendering (PBR) pipeline proposed by Nvdiffrec [30]. Please refer to [30, 9, 34] for details. We use another hash grid Φ t with parameter Θ t to encode the spatially varying materials of the surface: albedo, roughness, metallic, and bump. Finally, given a specific environment lighting and a randomly sampled camera, we can obtain the renderings of the albedo map and PBR map.

4.2 Regularization

Eikonal loss To ensure a proper signed distance field, we employ an eikonal term that regularizes the SDF gradient g in each tetrahedron: L eik = ∑ k ( ∥ g k ∥ 2 -1) 2 .

Normal consistency loss Inspired by the normal consistency loss for triangle meshes, we adapt this approach to tetrahedra. While we have designed a per-tetrahedron normal, we project these tetrahedral normals onto vertices and enhance the consistency of the signed distance field by regularizing the cosine similarity between normals of adjacent vertices connected by edges: L nc = ∑ i (1 -cos ( n e i 1 , n e i 2 )) , where e i 1 and e i 2 represent the vertices forming edge e i .

4.3 Diffusion priors

To validate the capability of TeT-Splatting for 3D generation, we employ two types of diffusion priors: the vanilla RGB-based diffusion priors and the rich diffusion priors proposed in RichDreamer [34].

Vanilla RGB-based diffusion priors Vanilla RGB-based diffusion models represent diffusion models that can generate RGB images from a given prompt. For both geometry and texture stages, we utilize SDS loss to leverage 2D diffusion priors from Stable Diffusion [37]:

Magic3D

Fantasia3D

DreamGaussian

Ours

Input

'

a DSLR photo of

a stack of pancakes

'

'a DSLR photo of

an ice cream sundae'

1 hour

38 min

5 min

15 min

7 min

3 min

2 min

3 min

13 FPS

166 FPS

145 FPS

133 FPS

∇ Θ L SDS = E [ ω ( t )( ϵ ϕ ( I ; y, t ) -ϵ ) ∂z ∂ I ∂ I ∂ Θ ] , where ω ( t ) is a weighting function, z denotes the VAE latent code, and ϵ ϕ ( N ; y, t ) represents the noise estimated by the UNet ϵ ϕ .

Rich diffusion priors The sole use of vanilla diffusion priors often leads to issues such as multi-face Janus problem, domain gap between image diffusion model and normal map while using normal maps as input of diffusion models, and inaccuracies in material decomposition. To this end, we utilize the rich diffusion priors proposed in RichDreamer [34] to handle high-fidelity 3D generation. Specifically, for geometry optimization, we combine a vanilla Stable Diffusion with a Normal-Depth diffusion model, which generates multi-view normal and depth maps from a given text prompt, represented as: L SDS = L SD SDS-Normal + L ND SDS-ND . For texture optimization, we combine a vanilla SD with a Depth-conditioned Albedo diffusion model, capable of producing multi-view albedo maps from a given text prompt, represented as: L SDS = L SD SDS-RGB + L Albedo SDS-Albedo .

In summary, the final loss function for the geometry stage is defined as: L geo = L SDS + λ eik L eik + λ nc L nc. For the texture stage, the loss function simplifies to: L tex = L SDS.

5 Experiment

In this section, we assess the efficacy of TeT-Splatting across two distinct tasks: 3D generation employing vanilla RGB-based diffusion priors and text-to-3D with rich diffusion priors. In Section 5.1, a qualitative evaluation of 3D generation for both text-to-3D and image-to-3D modalities is conducted to demonstrate the superiority of TeT-Splatting relative to other representations. To substantiate TeTSplatting 's proficiency in handling high-fidelity generations, we conduct experiments with advanced rich diffusion priors in Section 5.2. Section 5.3 encompasses a series of ablation studies aimed at validating the representation and pipeline. The details of implementation and experimental setting can be found in the Appendix B.

5.1 Results with vanilla RGB-based diffusion priors

Magic3D

DreamGaussian

Ours

Before

After

Before

After

Before

After

Input

Focusing on illustrating the effectiveness of the proposed representation, we primarily compare to three competitors: Magic3D [18], Fantasia3D [3] and DreamGaussian [46]. All these competitors employ a two-stage optimization pipeline and leverage Stable Diffusion with SDS loss, but utilize three different representative 3D representations in their initial stages: Instant-NGP [29] (a fast version of NeRF), DMTet [40], and 3DGS [13], respectively. We adapt the diffusion priors of all methods to Stable Zero-1-to-3 [20] for a fair comparison in the image-to-3D task, adding an identical MSE alignment loss. The qualitative evaluations, as shown in Figure 4, illustrate our method's ability to generate more detailed and compact meshes in a relatively short time. In Figure 4, we also report the rendering speed (FPS) of the first stage, at a rendering resolution of 512x512. Although TeT-Splatting operates at a lower FPS compared to DMTet (Fantasia3D) and 3DGS (DreamGaussian), it still achieves real-time rendering. Importantly, this lower FPS does not adversely affect the overall generation process, as the primary bottleneck in generation speed lies with the diffusion model.

We also conduct a comparison of the mesh extraction with Magic3D and DreamGaussian, visualized in Figure 5. It reveals that the meshes extracted from Magic3D often do not faithfully replicate the geometries from the first stage due to the imprecise threshold for converting densities to SDF values, and the extracted mesh in DreamGaussian can result in unsatisfactory surfaces with visible holes. In contrast, our method maintains high quality with negligible degradation after mesh extraction.

5.2 Results with rich diffusion priors

'

a DSLR photo of a porcelain dragon

'

'

a DSLR photo of a cup full of pens and pencils

'

'

a DSLR photo of a turtle standing on its hind legs, wearing a top hat

'

ProlificDreamer

MVDream

RichDreamer

Ours

11 hours

1 hour

2 hours

1.5 hours

Bear

Eagle

Piano

Typewriter

TeT-Splatting

Bear

Eagle

Piano

Typewriter

1

Our approach is also compatible with state-of-the-art diffusion priors. In this part, we evaluate TeT-Splatting on the text-to-3D task, equipped with rich diffusion priors from RichDreamer [34]. A key distinction between our approach and RichDreamer is the use of TeT-Splatting as the 3D representation during the geometry stage. We evaluate our method against two SOTA competitors, ProlificDreamer [51] and RichDreamer [34]. As illustrated in Figure 6, our method is capable of handling high-fidelity 3D generation, achieving superior geometric quality with considerably reduced generation times compared to these competitors.

Additionally, we present visualizations of the normal maps from early training iterations in Figure 7. The results from RichDreamer are fragmented at the early iterations due to the use of DMTet, which may harm subsequent optimization and slow convergence. In contrast, TeT-Splatting demonstrates rapid and smooth convergence. We employ the same quantitative evaluation method as RichDreamer to assess the quality of geometry and texture.

In Table 2, we report the Geometry CLIP [35] score and Appearance CLIP score. Notably, RichDreamer's prompt list, comprising 113 objects used for scoring, is not publicly available. Consequently, we calculate our scores using an alternative set of prompts (see Appendix B for details). Our method outperforms RichDreamer in terms of CLIP scores and significantly reduces the time required for geometry optimization (40 min vs 70 min).

In Figure 8, we present the decomposed albedo maps of generated 3D assets. Guided by the Depth-conditioned Albedo diffusion model, we achieve natural albedo maps.

5.3 Ablation

Under the settings of rich diffusion priors [34], we conduct ablation studies to evaluate our method.

w/o Eikonal loss

w/ Eikonal loss

(a) Eikonal loss

w/o consistency

w/ consistency

(b) Normal consistency loss

Resolution 128

Resolution 256

(c) Grid resolution

Eikonal loss We assess the role of eikonal loss in 3D generation by comparing 3D assets generated with and without it, illustrated in Figure 9a. Models created without eikonal loss tend to develop into undesirable shapes. This issue arises because the SDF values rapidly reach extreme levels and get trapped in local minima when eikonal loss is not applied.

Normal consistency loss Additionally, we assess the importance of normal consistency loss. Figure 9b demonstrates that applying normal consistency loss results in more compact models. This loss can act as a smoothing prior that helps prevent the surface of the model from becoming fragmented.

Tetrahedral grid resolution We investigate the effects of tetrahedral grid resolution on model performance by conducting experiments at resolutions of 128 and 256. Higher resolution yields more detailed geometries, as shown in Figure 9c.

6 Limitations

TeT-Splatting struggles with modeling high-frequency features, such as texture, because it uses tetrahedra as rendering primitives, which limits the final output by the resolution of the tetrahedral grid. Therefore, we transition it to a polygonal mesh for enhanced texture optimization. The rendering speed of our implemented rasterizer, although operating in real-time, is slower than that of 3DGS. Additionally, using only a pre-filter operation might not fully leverage TeT-Splatting 's potential in rendering quality and speed. A similar densification process as in 3DGS could improve this, which we leave for future work.

7 Conclusion

In this study, we introduce Tetrahedron Splatting ( TeT-Splatting ), a novel all-round 3D representation that integrates volumetric rendering within a structured tetrahedral grid while preserving precise mesh extraction through Marching Tetrahedra. Equipped with newly designed tile-based fast differentiable tetrahedron rasterizer, TeT-Splatting achieves real-time rendering. As showcase, we integrate TeT-Splatting in common 3D generation pipeline with polygonal mesh for texture optimization. Extensive experiments under varying 3D generation settings demonstrate TeT-Splatting 's superiority in producing high-fidelity 3D content compared to other 3D representations.

Acknowledgments

This work was supported in part by National Natural Science Foundation of China (Grant No. 62106050 and 62376060) and Natural Science Foundation of Shanghai (Grant No. 22ZR1407500).

References

Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Jiaming Song, Qinsheng Zhang, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, et al. ediff-i: Text-to-image diffusion models with an ensemble of expert denoisers. arXiv preprint , 2022. 2, 3

Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. Tensorf: Tensorial radiance fields. In ECCV , 2022. 3

Rui Chen, Yongwei Chen, Ningxin Jiao, and Kui Jia. Fantasia3d: Disentangling geometry and appearance for high-quality text-to-3d content creation. In ICCV , 2023. 2, 3, 8, 15

Yang Chen, Yingwei Pan, Yehao Li, Ting Yao, and Tao Mei. Control3d: Towards controllable text-to-3d generation. In ACM MM , 2023. 3

Zilong Chen, Feng Wang, and Huaping Liu. Text-to-3d using gaussian splatting. In CVPR , 2024. 2, 3

Yen-Chi Cheng, Hsin-Ying Lee, Sergey Tuyakov, Alex Schwing, and Liangyan Gui. SDFusion: Multimodal 3d shape completion, reconstruction, and generation. In CVPR , 2023. 3

Jun Gao, Wenzheng Chen, Tommy Xiang, Alec Jacobson, Morgan McGuire, and Sanja Fidler. Learning deformable tetrahedral meshes for 3d reconstruction. In NeurIPS , 2020. 3

Jun Gao, Tianchang Shen, Zian Wang, Wenzheng Chen, Kangxue Yin, Daiqing Li, Or Litany, Zan Gojcic, and Sanja Fidler. Get3d: A generative model of high quality 3d textured shapes learned from images. In NeurIPS , 2022. 3

Yuan-Chen Guo, Ying-Tian Liu, Ruizhi Shao, Christian Laforte, Vikram Voleti, Guan Luo, Chia-Hao Chen, Zi-Xin Zou, Chen Wang, Yan-Pei Cao, and Song-Hai Zhang. threestudio: A unified framework for 3d content generation. https://github.com/threestudio-project/ threestudio , 2023. 6, 15

Anchit Gupta, Wenhan Xiong, Yixin Nie, Ian Jones, and Barlas O˘ guz. 3dgen: Triplane latent diffusion for textured mesh generation. arXiv preprint , 2023. 3

Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In NeurIPS , 2020. 2, 3

Heewoo Jun and Alex Nichol. Shap-e: Generating conditional 3d implicit functions. arXiv preprint , 2023. 3

Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM TOG , 2023. 2, 3, 4, 6, 8, 15

Samuli Laine, Janne Hellsten, Tero Karras, Yeongho Seol, Jaakko Lehtinen, and Timo Aila. Modular primitives for high-performance differentiable rendering. ACM TOG , 2020. 3, 5

Ming Li, Pan Zhou, Jiawei Liu, Jussi Keppo, Min Lin, Shuicheng Yan, and Xiangyu Xu. Instant3d: Instant text-to-3d generation. arXiv preprint , 2023. 3

Weiyu Li, Rui Chen, Xuelin Chen, and Ping Tan. Sweetdreamer: Aligning geometric priors in 2d diffusion for consistent text-to-3d. In ICLR , 2024. 3

Yixun Liang, Xin Yang, Jiantao Lin, Haodong Li, Xiaogang Xu, and Yingcong Chen. Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. In CVPR , 2024. 3

Chen-Hsuan Lin, Jun Gao, Luming Tang, Towaki Takikawa, Xiaohui Zeng, Xun Huang, Karsten Kreis, Sanja Fidler, Ming-Yu Liu, and Tsung-Yi Lin. Magic3d: High-resolution text-to-3d content creation. In CVPR , 2023. 2, 4, 8, 15

Minghua Liu, Chao Xu, Haian Jin, Linghao Chen, Mukund Varma T, Zexiang Xu, and Hao Su. One-2-3-45: Any single image to 3d mesh in 45 seconds without per-shape optimization. In NeurIPS , 2024. 3

Ruoshi Liu, Rundi Wu, Basile Van Hoorick, Pavel Tokmakov, Sergey Zakharov, and Carl Vondrick. Zero-1-to-3: Zero-shot one image to 3d object. In ICCV , 2023. 3, 8

Yuan Liu, Cheng Lin, Zijiao Zeng, Xiaoxiao Long, Lingjie Liu, Taku Komura, and Wenping Wang. Syncdreamer: Learning to generate multiview-consistent images from a single-view image. In CVPR , 2024. 3

Zexiang Liu, Yangguang Li, Youtian Lin, Xin Yu, Sida Peng, Yan-Pei Cao, Xiaojuan Qi, Xiaoshui Huang, Ding Liang, and Wanli Ouyang. Unidream: Unifying diffusion priors for relightable text-to-3d generation. arXiv preprint , 2023. 3

Xiaoxiao Long, Yuan-Chen Guo, Cheng Lin, Yuan Liu, Zhiyang Dou, Lingjie Liu, Yuexin Ma, Song-Hai Zhang, Marc Habermann, Christian Theobalt, et al. Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint , 2023. 3

Jonathan Lorraine, Kevin Xie, Xiaohui Zeng, Chen-Hsuan Lin, Towaki Takikawa, Nicholas Sharp, Tsung-Yi Lin, Ming-Yu Liu, Sanja Fidler, and James Lucas. Att3d: Amortized text-to-3d object synthesis. In ICCV , 2023. 3

Yuanxun Lu, Jingyang Zhang, Shiwei Li, Tian Fang, David McKinnon, Yanghai Tsin, Long Quan, Xun Cao, and Yao Yao. Direct2. 5: Diverse text-to-3d generation via multi-view 2.5 d diffusion. arXiv preprint , 2023. 3

Yiwei Ma, Yijun Fan, Jiayi Ji, Haowei Wang, Xiaoshuai Sun, Guannan Jiang, Annan Shu, and Rongrong Ji. X-dreamer: Creating high-quality 3d content by bridging the domain gap between text-to-2d and text-to-3d generation. arXiv preprint , 2023. 3

Duane G Merrill and Andrew S Grimshaw. Revisiting sorting for gpgpu stream architectures. In ICPAC , 2010. 6

Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. Nerf: Representing scenes as neural radiance fields for view synthesis. In ECCV , 2020. 2, 3

Thomas Müller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution hash encoding. ACM TOG , 2022. 3, 6, 8

Jacob Munkberg, Jon Hasselgren, Tianchang Shen, Jun Gao, Wenzheng Chen, Alex Evans, Thomas Müller, and Sanja Fidler. Extracting triangular 3d models, materials, and lighting from images. In CVPR , 2022. 6

Alex Nichol, Heewoo Jun, Prafulla Dhariwal, Pamela Mishkin, and Mark Chen. Point-e: A system for generating 3d point clouds from complex prompts. arXiv preprint , 2022. 3

Ben Poole, Ajay Jain, Jonathan T Barron, and Ben Mildenhall. Dreamfusion: Text-to-3d using 2d diffusion. In ICLR , 2023. 2, 3

Guocheng Qian, Jinjie Mai, Abdullah Hamdi, Jian Ren, Aliaksandr Siarohin, Bing Li, HsinYing Lee, Ivan Skorokhodov, Peter Wonka, Sergey Tulyakov, et al. Magic123: One image to high-quality 3d object generation using both 2d and 3d diffusion priors. In ICLR , 2023. 2, 4

Lingteng Qiu, Guanying Chen, Xiaodong Gu, Qi zuo, Mutian Xu, Yushuang Wu, Weihao Yuan, Zilong Dong, Liefeng Bo, and Xiaoguang Han. Richdreamer: A generalizable normal-depth diffusion model for detail richness in text-to-3d. arXiv preprint , 2023. 2, 3, 5, 6, 7, 9, 10, 16

Alec Radford, Jong Wook Kim, Chris Hallacy, A. Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. Learning transferable visual models from natural language supervision. In ICML , 2021. 9, 16

Lukas Radl, Michael Steiner, Mathias Parger, Alexander Weinrauch, Bernhard Kerbl, and Markus Steinberger. Stopthepop: Sorted gaussian splatting for view-consistent real-time rendering. arXiv preprint , 2024. 6

Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In CVPR , 2022. 2, 3, 6

Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. In NeurIPS , 2022. 2, 3

Sara Fridovich-Keil and Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In CVPR , 2022. 3

Tianchang Shen, Jun Gao, Kangxue Yin, Ming-Yu Liu, and Sanja Fidler. Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. In NeurIPS , 2021. 2, 3, 5, 6, 8, 9, 16

Ruoxi Shi, Hansheng Chen, Zhuoyang Zhang, Minghua Liu, Chao Xu, Xinyue Wei, Linghao Chen, Chong Zeng, and Hao Su. Zero123++: a single image to consistent multi-view diffusion base model. arXiv preprint , 2023. 3

Yichun Shi, Peng Wang, Jianglong Ye, Long Mai, Kejie Li, and Xiao Yang. Mvdream: Multiview diffusion for 3d generation. In ICLR , 2024. 3, 10

Cheng Sun, Min Sun, and Hwann-Tzong Chen. Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction. In CVPR , 2022. 3

Boshi Tang, Jianan Wang, Zhiyong Wu, and Lei Zhang. Stable score distillation for high-quality 3d generation. arXiv preprint , 2023. 3

Jiaxiang Tang, Zhaoxi Chen, Xiaokang Chen, Tengfei Wang, Gang Zeng, and Ziwei Liu. Lgm: Large multi-view gaussian model for high-resolution 3d content creation. arXiv preprint , 2024. 2, 3

Jiaxiang Tang, Jiawei Ren, Hang Zhou, Ziwei Liu, and Gang Zeng. Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. In ICLR , 2024. 2, 4, 8

Haochen Wang, Xiaodan Du, Jiahao Li, Raymond A Yeh, and Greg Shakhnarovich. Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In CVPR , 2023. 3

Peihao Wang, Zhiwen Fan, Dejia Xu, Dilin Wang, Sreyas Mohan, Forrest Iandola, Rakesh Ranjan, Yilei Li, Qiang Liu, Zhangyang Wang, et al. Steindreamer: Variance reduction for text-to-3d score distillation via stein identity. arXiv preprint , 2023. 3

Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. arXiv preprint , 2021. 2, 5

Peng Wang and Yichun Shi. Imagedream: Image-prompt multi-view diffusion for 3d generation. arXiv preprint , 2023. 3

Zhengyi Wang, Cheng Lu, Yikai Wang, Fan Bao, Chongxuan Li, Hang Su, and Jun Zhu. Prolificdreamer: High-fidelity and diverse text-to-3d generation with variational score distillation. In NeurIPS , 2024. 3, 9, 10

Chao-Yuan Wu, Justin Johnson, Jitendra Malik, Christoph Feichtenhofer, and Georgia Gkioxari. Multiview compressive coding for 3D reconstruction. In CVPR , 2023. 3

Tong Wu, Jiaqi Wang, Xingang Pan, Xudong Xu, Christian Theobalt, Ziwei Liu, and Dahua Lin. Voxurf: Voxel-based efficient and accurate neural surface reconstruction. In ICLR , 2023. 5

Zike Wu, Pan Zhou, Xuanyu Yi, Xiaoding Yuan, and Hanwang Zhang. Consistent3d: Towards consistent high-fidelity text-to-3d generation with deterministic sampling prior. In ICLR , 2024. 3

Jiale Xu, Xintao Wang, Weihao Cheng, Yan-Pei Cao, Ying Shan, Xiaohu Qie, and Shenghua Gao. Dream3d: Zero-shot text-to-3d synthesis using 3d shape prior and text-to-image diffusion models. In CVPR , 2023. 3

Taoran Yi, Jiemin Fang, Junjie Wang, Guanjun Wu, Lingxi Xie, Xiaopeng Zhang, Wenyu Liu, Qi Tian, and Xinggang Wang. Gaussiandreamer: Fast generation from text to 3d gaussians by bridging 2d and 3d diffusion models. In CVPR , 2024. 3

Xin Yu, Yuan-Chen Guo, Yangguang Li, Ding Liang, Song-Hai Zhang, and Xiaojuan Qi. Text-to-3d with classifier score distillation. arXiv preprint , 2023. 3

Xiaohui Zeng, Arash Vahdat, Francis Williams, Zan Gojcic, Or Litany, Sanja Fidler, and Karsten Kreis. Lion: Latent point diffusion models for 3d shape generation. In NeurIPS , 2022. 3

Junzhe Zhu, Peiye Zhuang, and Sanmi Koyejo. Hifa: High-fidelity text-to-3d generation with advanced diffusion guidance. In ICLR , 2023. 3

A More implementation details of TeT-Splatting

In this section, we provide additional implementation details about the tetrahedron splatting process.

A.1 Barycentric coordinates

Recall that projecting a single tetrahedron, encompassing four vertices v a , v b , v c , v d ∈ R 3 along with their SDF values f a , f b , f c , f d ∈ R , onto a 2D plane results in an array of 2D vectors v ′ a , v ′ b , v ′ c , v ′ d ∈ R 2 representing the coordinates of these vertices on the image plane.

Given a pixel p with coordinate v ′ p ∈ R 2 , its barycentric coordinates u ′ , v ′ ∈ R with repsect to a triangle ( v ′ a , v ′ b , v ′ c ) satisfy v ′ p = (1 -u ′ -v ′ ) v ′ a + u ′ v ′ b + v ′ v ′ c . We can apply the following equations to derive the barycentric coordinates u ′ , v ′ :

If u ′ , v ′ ∈ [0 , 1] , the pixel p is considered inside the triangle.

A.2 Perspective correction

The calculated barycentric coordinates u ′ , v ′ are based on 2D projections and require adjustment to reflect the original 3D spatial relationships accurately. This adjustment, known as perspective correction, is necessary because 3D depth information is not preserved in the 2D projection. We perform this correction using:

where z ∗ denotes the depth of each vertex. Subsequently, the SDF value and depth of the 3D position corresponding to this pixel are interpolated:

A.3 Gradient of the SDF value inside a tetrahedron

Consider an arbitrary 3D point v q with SDF value f q inside the tetrahedron ( v a , v b , v c , v d ) . We establish the SDF value f q using the 3D barycentric coordinates u, v, w : f q = (1 -u -v -w ) f a + uf b + vf c + wf d . The derivation of u, v, w is similar to 2D case in Section A.1, i.e. ,

Therefore, the formula of f q can be expressed by:

Moreover, the gradient of the SDF value at v q , denoted by g , is straightforwardly derived by differentiating with respect to v q . This gradient is constant across the tetrahedron:

This results in a constant vector within any tetrahedron, providing a consistent gradient that aids in precise mesh extractions and surface optimizations.

B More implementation details of 3D generation

In this section, we provide additional implementation details of 3D generation. Note that all experiments are conducted on one NVIDIA RTX A6000 GPU.

B.1 Geometry stage

Unlike 3DGS [13], we separate operations that are repeated across multiple images from different camera viewpoints within a single training iteration and shift them to the beginning of each iteration, including the inference of SDF values and deformations for each vertex from the hash grid, prefiltering tetrahedra based on their α max , and calculating the per-tetrahedron normal. These preprocessed results are then passed to the rasterizer for rendering a batch of images. Moreover, we implement a coarse-to-fine approach in the pre-filtering process: initially, we establish a tighter axis-aligned bounding box from the pre-filtered tetrahedral grid in the first round and then resize the tetrahedral grid based on this bounding box for a second round of pre-filtering, which enhances the precision of the geometry. For the schedule of the s value in Eq. 1, we set s ratio = 5 and s start = 20 , which allows the curve of Φ s ( x ) to be sufficiently steep at the final of optimization. Additionally, we set both λ eik and λ nc to 1000.

B.2 Evaluation with vanilla RGB-based diffusion priors

This part is implemented based on the threestudio codebase [9] using the settings of Fantasia3D [3]. The tetrahedral grid resolution is set to 128, and the batch size is set to 1.

Text-to-3D For the text-to-3D task, we use Stable Diffusion 2.1 base. The geometry is optimized for 3,000 iterations and the texture for another 1,000 iterations. Following Fantasia3D [3], during the initial training iterations, we concatenate the rendered normal and depth maps to serve directly as the latent code for the diffusion models, facilitating rapid convergence to a basic shape. As Magic3D [18] haven't released their code, we use the implementation from threestudio. To ensure a fair comparison with Fantasia3D [3], we also adopt the threestudio implementation.

Image-to-3D In the image-to-3D task, we use Stable Zero-1-to-3 and adapt our pipeline by incorporating Φ t in the initial stage to encode the materials at the center of each tetrahedron. Specifically, we start by inferring the materials at the center of each tetrahedron. Next, we compute the pertetrahedron PBR color c using the rendering equation for each tetrahedron. This per-tetrahedron PBR color c is subsequently passed to the rasterizer to perform the alpha-blending for the final output: C = ∑ i ∈ N T i α i c i . To further refine the output, we introduce an MSE loss that aligns the rendering color map C r and opacity map O r at reference view with the provided reference image ˜ C r and mask ˜ O r : L ref = λ rgb ||C r -˜ C r || 2 2 + λ mask ||O r -˜ O r || 2 2 . We set the loss weights λ rgb and λ mask to 10,000 and 1,000, respectively. Also, we decrease λ eik and s ratio to 100 and 2, respectively.

B.3 Evaluation with rich diffusion priors

This part is implemented based on the RichDreamer [34] codebase using the settings of DMTet [40]. The tetrahedral grid resolution is set to 256 and the batch size is set to 4 for two stages. We optimize the geometry for 3,000 steps, with the first 1,000 steps using latent code, followed by an additional 2,000 steps for texture optimization. While RichDreamer reports significantly increased stability at a rendering resolution of 1024, we achieve stable results at a lower resolution of 512. Therefore, we set our rendering resolution to 512.

CLIP score We adopt the evaluation process in RichDreamer [34] to calculate CLIP scores using the CLIP model [35] (vit-g-14). For geometry CLIP scores, we render generated meshes with uniform albedo and produce 16 different views for each object. The average CLIP scores are computed by discarding the highest and lowest scores from the provided text prompts. For texture CLIP scores, textured meshes are rendered. Since RichDreamer has not released the prompt list (113 objects) used for their metrics, we utilize an alternative list named ' prompts_dmtet.txt ' (183 objects) available on their official GitHub repository.

C More results

We present an extensive gallery of visual results in Figure 10-13.

D Discussions on the potential social impacts

The proposed TeT-Splatting method can make it easier for people to enter the animation and related industries. This can simplify production processes, reduce costs, and allow more people to create high-quality 3D assets. However, these improvements could also lead to job losses for professionals who work in traditional roles. To address this, it may be necessary to gradually adjust training programs and align the workforce with future demands.

Additionally, while our method improves the efficiency of 3D generation, it also carries the biases present in the foundational models we use. These models can have built-in biases related to race, gender, and culture, which might appear in the generated content, reinforcing stereotypes. The easier creation of realistic 3D models also raises concerns about copyright infringement and misuse, highlighting the need for strong ethical guidelines and regulatory frameworks.

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a beautiful dress made out of garbage bags, on a

mannequin. Studio lighting, high quality, high resolution

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a completely destroyed car

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a crocodile playing a drum set

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a ficus planted in a pots

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a zoomed out DSLR photo of a fresh cinnamon roll

covered in glaze

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a DSLR photo of a giant worm emerging from the sand

in the middle of the desert

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a hotdog in a tutu skirt

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a llama wearing a suit

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a DSLR photo of a mug of hot chocolate with whipped

cream and marshmallows

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a DSLR photo of a pair of tan cowboy boots, studio

lighting, product photography

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a palm tree, low poly 3d model

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a DSLR photo of a plate of fried chicken and waffles

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a DSLR photo of a delicious croissant

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a delicious hamburger

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with maple syrup on them

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a sliced loaf of fresh bread

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a squirrel dressed like Henry VIII king of England

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a squirrel dressed up like a Victorian woman

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a DSLR photo of a stack of pancakes covered in maple

syrup

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a DSLR photo of a straw basket with a cobra coming out of it

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a tiger karate master

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a zoomed out DSLR photo of a tiger wearing sunglasses

and a leather jacket, riding a motorcycle

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a DSLR photo of a toilet made out of gold

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a DSLR photo of a red cardinal bird singing

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a zoomed out DSLR photo of a red rotary telephone

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a DSLR photo of a plush t-rex dinosaur toy, studio

lighting, high resolution

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a DSLR photo of a model of the eiffel tower made out of

toothpicks

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an origami motorcycle

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a DSLR photo of an ornate silver gravy boat sitting on a

patterned tablecloth

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a DSLR photo of an unstable rock cairn in the middle of

a stream

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banana

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Coffee cup with many holes

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a zoomed out DSLR photo of miniature schnauzer

wooden sculpture, high quality studio photo

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a DSLR photo of a train engine made out of clay

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a DSLR photo of a very cool and trendy pair of sneakers,

studio lighting

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an amigurumi bulldozer

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a DSLR photo of an astronaut standing on the surface of

mars

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a DSLR photo of an old car overgrown by vines and

weeds

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method for 3D mesh generation from a text. The idea is to improve gradient propagation ability of DMTet framework by splatting multiple tetrahedra instead of rendering only one surface triangle per pixel. Qualitative results on 3D mesh generation show good quality results with competitive processing time.\n\nSTRENGTHS:\n-\tThe proposed idea is interesting. Splatting multiple tetrahedra around the surface allows to backpropagate gradients further in the model and avoid getting stuck in local minima.\n-\tFigure 3 is interesting and shows advantage of the proposed framework.\n-\tI am not so familiar with the datasets and tasks of 3D mesh generation from text but qualitative results look good and competitive with state-of-the-art\n\nWEAKNESSES:\n-\tSome explanations are missing to fully understand the experiments section.\n-\tResults are few and maybe cherry picked. Only qualitative cannot prove better performance of the proposed method. Again, more explanations about the generation process is required to understand advantages. For example, in figure 6 the 2D images are different, with different level of details in the 2D images. Then it is expected than the 3D models are also different and level of details also different. Then does it really make sense to compare these output 3D meshes? The difference may come from other parts in the framework than the proposed model.\n-\tThe authors motivate many of text for computational speed. But in the end advantage in computational power is not clear.\n\nQUESTIONS:\n-\tHow many tetrahedra are used in the experiments?\n\nThe proposed idea to splat tetrahedra and improve gradients propagation ability of original DMTet is interesting. Qualitative results show good performance. However, the explanations in the paper of the 3D generation process is lacking. Quantitative evaluation is few and only few qualitative results are maybe not enough to confirm advantage of proposed method.\n\nLIMITATIONS:\nThere is no specific section or discussion about the limitations of the proposed method", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

comments: SUMMARY:
The paper presents a novel method for generating 3D models from the given inputs. The authors, for that purpose, propose the use of tetrahedra instead of 3D Gaussians in the recent proposed Gaussian Splatting framework.

STRENGTHS:
The paper proposes the use of TeT Splatting, that are well formulated and demonstrated  throughout the paper. The method allows for precise and fast mesh extraction, that is a well-known limitation of 3d gaussian splatting. The motivation to use TeT Splatting against the well-known DMTet is also well tackled.

WEAKNESSES:
1. For the task of 3D Reconstruction, 3D Consistency is highly important. However, lack of videos of the generated result is a major drawback that highly affects my decision since just two views are not enough to judge the quality of the output and created mesh. This is also a standard in the baseline papers such as DreamFusion that the authors compare with. I am happy to revise my scores otherwise.

2. The paper uses hash grids as described in sec 4.1. Is it really necessary to use that, or how well the method will work without a hash grid or some other encoding such as positional encoding?

QUESTIONS:
Please see weakness section.

LIMITATIONS:
The authors provide limitations and potential societal impact in the supplementary pages of their work.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-12

comments: SUMMARY:
The paper presents a new differentiable 3D shape representation based on DMTet. It borrows the efficient rasterization-based rendering techniques from Gaussian Splatting to improve the global optimization of DMTet. The new TeT splatting is shown to perform well in the task of text-to-3D.

STRENGTHS:
- The paper presents an interesting new differentiable representation for 3D meshes. It is more efficient than DMTet in optimization.   

- The representation works well in text-to-3D generation.

WEAKNESSES:
- The comparison in the experiment section is mostly qualitative.  A quantative comparison with DMTet on a 3D mesh reconstruction task would be appriciated.

- The quality of underlying mesh connectivities is unclear to me.

QUESTIONS:
-  How to ensure the sharpness of texture obtained without extracting mesh during optimization?

- Can the proposed method be used in a feedforward generative model?

LIMITATIONS:
Yes, the limitation and societal impact discussions look good to me.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 4
DATE: 2024-07-15

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis submission is proposing a new representation for 3D content generation combining the three following benefits:\n- easy to optimize,\n- real-time rendering,\n- allowing the extraction of precise meshes.\nRecent advances in novel view synthesis, i.e. NeRF and then 3D Gaussian Splatting (3DGS) are eventually bringing two of these benefits but the lack of quality output meshes still limits a number of applications.\n\nThe proposed approach follows the deformable tetrahedral grid approach of DMTet while using it instead for volume rendering and making it suitable for splatting as in 3DGS. Meshes can be easily extracted which facilitates chaining a first geometric optimization stage based on splat rendering with a later mesh-based texturing stage for complete 3D generation of geometry and appearance.\n\nThe paper makes the following contributions:\n- using a deformable tetrahedral grid rendered via tetrahedra splatting as a new 3D representation,\n- adapting 3DGS to work with such new representation with the implementation of a fast differentiable rasterizer for tetrahedra-based splatting,\n- leveraging this representation and optimization in a two-stage 3D generation pipeline, first to optimize tetrahedra geometry before optimizing mesh texturing,\n- An array of qualitative evaluations against other generative baselines (with some quantitative evaluations), either on image-to-3D or text-to-3D tasks using vanilla RGB diffusion priors or with rich diffusion priors.\n\nSTRENGTHS:\n- This paper proposes to tackle a known shortcoming of 3D generative approaches when leveraging 3D representation from modern novel view synthesis techniques: poor meshed outputs. Identifying a suitable representation that is easy to optimize, enables real-time rendering while allowing mesh extraction is very relevant to the research community, especially to better bridge 3D and generative work.\n\n- The presented approach elegantly solves the issue of DMNet where only part of the representation (near the zero level set) can effectively be updated. This is addressed by turning the optimization into a full volumetric rendering of tetrahedra via an adaptation of 3DGS to different primitives.\n\n- The qualitative evaluations using vanilla RGB-based diffusion priors against the selected comparable techniques: Magic3D, Fantasia3D and DreamGaussian but based on NeRF, DMTet or 3DGS respectively do a rather convincing job to demonstrate the superiority and versatility of the proposed approach (Figure 4) that maintains high mesh quality with real-time rendering speed. Similarly the qualitative results with rich diffusion priors show pretty high surface quality with a reasonable training time,\n\nWEAKNESSES:\n- Apart from the CLIP scores of Table 2 (or the training time and rendering speed), the shown results are essentially qualitative. For a stronger comparison against other baselines, it would have been more helpful to try to integrate measures of the quality of the generated surface to demonstrate the benefits of the approach (instead of relying only on normal maps and renders). Also note that the presentation of these qualitative results could be improved by zooming on specific areas with artifacts (or lack or thereof) to better highlight them and guide the reader.\n\n- It seems there is no information on how the tetrahedral grid is initialized (besides its spatial resolution and Figure 3 hinting at a sphere).\n\n- Some suggestions for improvements:\n  - l. 107-109: the formulation make it sound like DMTet invented the established marching tetrahedra algorithm - rephrase\n  - Figure 2: Geometry Opimization -> Geometry Optimization\n  - Figures 4 and 6: it would be helpful to match the orientation for normals across objects (i.e. have consistent coloring for the whole figure)\n\nQUESTIONS:\n- To address the above weakness, do the authors have some measures of surface quality to provide some form of quantitative evaluation against baselines?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-15"}