Moment-Based 3D Gaussian Splatting: Resolving Volumetric Occlusion with Order-Independent Transmittance

The recent success of 3D Gaussian Splatting (3DGS) has reshaped novel view synthesis by enabling fast optimization and real-time rendering of high-quality radiance fields. However, it relies on simplified, order-dependent alpha blending and coarse approximations of the density integral within the rasterizer, thereby limiting its ability to render complex, overlapping semi-transparent objects. In this paper, we extend rasterization-based rendering of 3D Gaussian representations with a novel method for high-fidelity transmittance computation, entirely avoiding the need for ray tracing or per-pixel sample sorting. Building on prior work in moment-based order-independent transparency, our key idea is to characterize the density distribution along each camera ray with a compact and continuous representation based on statistical moments. To this end, we analytically derive and compute a set of per-pixel moments from all contributing 3D Gaussians. From these moments, a continuous transmittance function is reconstructed for each ray, which is then independently sampled within each Gaussian. As a result, our method bridges the gap between rasterization and physical accuracy by modeling light attenuation in complex translucent media, significantly improving overall reconstruction and rendering quality.

NeRFs are Mirror Detectors: Using Structural Similarity for Multi-View Mirror Scene Reconstruction with 3D Surface Primitives

While neural radiance fields (NeRF) led to a breakthrough in photorealistic novel view synthesis, handling mirroring surfaces still denotes a particular challenge as they introduce severe inconsistencies in the scene representation. Previous attempts either focus on reconstructing single reflective objects or rely on strong supervision guidance in terms of additional user-provided annotations of visible image regions of the mirrors, thereby limiting the practical usability. In contrast, in this paper, we present NeRF-MD, a method which shows that NeRFs can be considered as mirror detectors and which is capable of reconstructing neural radiance fields of scenes containing mirroring surfaces without the need for prior annotations. To this end, we first compute an initial estimate of the scene geometry by training a standard NeRF using a depth reprojection loss. Our key insight lies in the fact that parts of the scene corresponding to a mirroring surface will still exhibit a significant photometric inconsistency, whereas the remaining parts are already reconstructed in a plausible manner. This allows us to detect mirror surfaces by fitting geometric primitives to such inconsistent regions in this initial stage of the training. Using this information, we then jointly optimize the radiance field and mirror geometry in a second training stage to refine their quality. We demonstrate the capability of our method to allow the faithful detection of mirrors in the scene as well as the reconstruction of a single consistent scene representation, and demonstrate its potential in comparison to baseline and mirror-aware approaches.

TraM-NeRF: Tracing Mirror and Near-Perfect Specular Reflections through Neural Radiance Fields

Implicit representations like Neural Radiance Fields (NeRF) showed impressive results for photorealistic rendering of complex scenes with fine details. However, ideal or near-perfectly specular reflecting objects such as mirrors, which are often encountered in various indoor scenes, impose ambiguities and inconsistencies in the representation of the reconstructed scene leading to severe artifacts in the synthesized renderings. In this paper, we present a novel reflection tracing method tailored for the involved volume rendering within NeRF that takes these mirror-like objects into account while avoiding the cost of straightforward but expensive extensions through standard path tracing. By explicitly modeling the reflection behavior using physically plausible materials and estimating the reflected radiance with Monte-Carlo methods within the volume rendering formulation, we derive efficient strategies for importance sampling and the transmittance computation along rays from only few samples. We show that our novel method enables the training of consistent representations of such challenging scenes and achieves superior results in comparison to previous state-of-the-art approaches.