Differentiable volume rendering enables gradient-based optimization of volumetric scenes, but unbiased estimators suffer from high gradient variance. We observe that the extinction gradients split into two components on structurally different integration domains: a scattering term evaluated at a single path vertex, and a transmittance term integrated along the ray segment. Because the domains are mismatched, existing estimators sample the two components at different locations, leaving the negative correlation between their opposite-signed contributions unexploited. We expose this overlooked correlation and exploit it through a principle we call sample matching : evaluate both components at shared sample locations. To enable this, we derive the first reformulation of the differential path integral that couples the two contributions within a single integrand, yielding an unbiased Monte Carlo estimator that ties them together by construction. For efficiency, the estimator reuses partially sampled light paths and amortizes in-scattering cost by evaluating gradients at multiple probe points per segment. On voxel-grid reconstruction, our estimator reduces gradient variance by up to 80% over differential ratio tracking (DRT), yielding faster convergence and higher reconstruction quality.

2D Gaussian Splatting has recently emerged as a significant method in 3D reconstruction, enabling novel view synthesis and geometry reconstruction simultaneously. While the well-known Gaussian kernel is broadly used, its lack of anisotropy and deformation ability leads to dim and vague edges at object silhouettes, limiting the reconstruction quality of current Gaussian splatting methods. To enhance the representation power, we draw inspiration from quantum physics and propose to use the Gaussian-Hermite kernel as the new primitive in Gaussian splatting. The new kernel takes a unified mathematical form and extends the Gaussian function, which serves as the zero-rank special case in the updated general formulation. Our experiments demonstrate that the proposed Gaussian-Hermite kernel achieves improved performance over traditional Gaussian Splatting kernels on both geometry reconstruction and novel-view synthesis tasks. Specifically, on the DTU dataset, our method yields more accurate geometry reconstruction, while on datasets such as MipNeRF360 and our customized Detail dataset, it achieves better results in novel-view synthesis. These results highlight the potential of the Gaussian-Hermite kernel for high-quality 3D reconstruction and rendering.

By supervising camera rays between a scene and multi-view image planes, NeRF reconstructs a neural scene representation for the task of novel view synthesis. On the other hand, shadow rays between the light source and the scene have yet to be considered. Therefore, we propose a novel shadow ray supervision scheme that optimizes both the samples along the ray and the ray location. By supervising shadow rays, we successfully reconstruct a neural SDF of the scene from single-view images under multiple lighting conditions. Given single-view binary shadows, we train a neural network to reconstruct a complete scene not limited by the camera's line of sight. By further modeling the correlation between the image colors and the shadow rays, our technique can also be effectively extended to RGB inputs. We compare our method with previous works on challenging tasks of shape reconstruction from single-view binary shadow or RGB images and observe significant improvements. The code and data are available at https://github.com/gerwang/ShadowNeuS.

Parametric face models, such as morphable and blendshape models, have shown great potential in face representation, reconstruction, and animation. However, all these models focus on large-scale facial geometry. Facial details such as wrinkles are not parameterized in these models, impeding accuracy and realism. In this article, we propose a method to learn a Semantically Disentangled Variational Autoencoder (SDVAE) to parameterize facial details and support independent detail manipulation as an extension of an off-the-shelf large-scale face model. Our method utilizes the non-linear capability of Deep Neural Networks for detail modeling, achieving better accuracy and greater representation power compared with linear models. In order to disentangle the semantic factors of identity, expression and age, we propose to eliminate the correlation between different factors in an adversarial manner. Therefore, wrinkle-level details of various identities, expressions, and ages can be generated and independently controlled by changing latent vectors of our SDVAE. We further leverage our model to reconstruct 3D faces via fitting to facial scans and images. Benefiting from our parametric model, we achieve accurate and robust reconstruction, and the reconstructed details can be easily animated and manipulated. We evaluate our method on practical applications, including scan fitting, image fitting, video tracking, model manipulation, and expression and age animation. Extensive experiments demonstrate that the proposed method can robustly model facial details and achieve better results than alternative methods.

Blendshape representations are widely used in facial animation. Consistent semantics must be maintained for all the blendshapes to build the blendshapes of one character. However, this is difficult for real characters because the face shape of the same semantics varies significantly across identities. Previous studies have handled this issue by asking users to perform a set of predefined expressions with specified semantics. We observe that facial emotions can be used to define semantics. Herein, we propose a real-time technique that directly updates blendshapes without predefined expressions. Its aim is to preserve semantics based on the emotion information extracted from an arbitrary facial motion sequence. In addition, we have designed corresponding algorithms to efficiently update blendshapes with large- and middle-scale face shapes and fine-scale facial details, such as wrinkles, in a real-time face tracking system. The experimental results indicate that using a commodity RGBD sensor, we can achieve real-time online blendshape updates with well-preserved semantics and user-specific facial features and details.