By adaptively controlling the density and generating more Gaussians in regions with high-frequency information, 3D Gaussian Splatting (3DGS) can better represent scene details. From the signal processing perspective, representing details usually needs more Gaussians with relatively smaller scales. However, 3DGS currently lacks an explicit constraint linking the density and scale of 3D Gaussians across the domain, leading to 3DGS using improper-scale Gaussians to express frequency information, resulting in the loss of accuracy. In this paper, we propose to establish a direct relation between density and scale through the reparameterization of the scaling parameters and ensure the consistency between them via explicit constraints (i.e., density responds well to changes in frequency). Furthermore, we develop a frequency-aware density control strategy, consisting of densification and deletion, to improve representation quality with fewer Gaussians. A dynamic threshold encourages densification in high-frequency regions, while a scale-based filter deletes Gaussians with improper scale. Experimental results on various datasets demonstrate that our method outperforms existing state-of-the-art methods quantitatively and qualitatively.

In recent years, deep learning-based approaches have shown great strength in multi-view stereo because of their outstanding ability to extract robust visual features. However, most learning-based methods need to build the cost volume and increase the receptive field enormously to get a satisfactory result when dealing with large-scale textureless regions, consequently leading to prohibitive memory consumption. To ensure both memory-friendly and textureless-resilient, we innovatively transplant the spirit of deformable convolution from deep learning into the traditional PatchMatch-based method. Specifically, for each pixel with matching ambiguity (termed unreliable pixel), we adaptively deform the patch centered on it to extend the receptive field until covering enough correlative reliable pixels (without matching ambiguity) that serve as anchors. When performing PatchMatch, constrained by the anchor pixels, the matching cost of an unreliable pixel is guaranteed to reach the global minimum at the correct depth and therefore increases the robustness of multi-view stereo significantly. To detect more anchor pixels to ensure better adaptive patch deformation, we propose to evaluate the matching ambiguity of a certain pixel by checking the convergence of the estimated depth as optimization proceeds. As a result, our method achieves state-of-the-art performance on ETH3D and Tanks and Temples while preserving low memory consumption.

There is an emerging effort to combine the two popular 3D frameworks using Multi-View Stereo (MVS) and Neural Implicit Surfaces (NIS) with a specific focus on the few-shot / sparse view setting. In this paper, we introduce a novel integration scheme that combines the multi-view stereo with neural signed distance function representations, which potentially overcomes the limitations of both methods. MVS uses per-view depth estimation and cross-view fusion to generate accurate surfaces, while NIS relies on a common coordinate volume. Based on this strategy, we propose to construct per-view cost frustum for finer geometry estimation, and then fuse cross-view frustums and estimate the implicit signed distance functions to tackle artifacts that are due to noise and holes in the produced surface reconstruction. We further apply a cascade frustum fusion strategy to effectively captures global-local information and structural consistency. Finally, we apply cascade sampling and a pseudo-geometric loss to foster stronger integration between the two architectures. Extensive experiments demonstrate that our method reconstructs robust surfaces and outperforms existing state-of-the-art methods.