Unsigned distance functions (UDFs) have been a vital representation for open surfaces. With different differentiable renderers, current methods are able to train neural networks to infer a UDF by minimizing the rendering errors with the UDF to the multi-view ground truth. However, these differentiable renderers are mainly handcrafted, which makes them either biased on ray-surface intersections, or sensitive to unsigned distance outliers, or not scalable to large scenes. To resolve these issues, we present a novel differentiable renderer to infer UDFs more accurately. Instead of using handcrafted equations, our differentiable renderer is a neural network which is pre-trained in a data-driven manner. It learns how to render unsigned distances into depth images, leading to a prior knowledge, dubbed volume rendering priors. To infer a UDF for an unseen scene from multiple RGB images, we generalize the learned volume rendering priors to map inferred unsigned distances in alpha blending for RGB image rendering. To reduce the bias of sampling in UDF inference, we utilize an auxiliary point sampling prior as an indicator of ray-surface intersection, and propose novel schemes towards more accurate and uniform sampling near the zero-level sets. We also propose a new strategy that leverages our pretrained volume rendering prior to serve as a general surface refiner, which can be integrated with various Gaussian reconstruction methods to optimize the Gaussian distributions and refine geometric details. Our results show that the learned volume rendering prior is unbiased, robust, scalable, 3D aware, and more importantly, easy to learn. Further experiments show that the volume rendering prior is also a general strategy to enhance other neural implicit representations such as signed distance function and occupancy. We evaluate our method on both widely used benchmarks and real scenes, and report superior performance over the state-of-the-art methods.

Unsigned distance functions (UDFs) have emerged as powerful representation for modeling and reconstructing geometries with open surfaces. However, the development of 3D generative models for UDFs remains largely unexplored, limiting current methods from generating diverse open-surface 3D content. Moreover, mainstream 3D datasets predominantly consist of watertight meshes, revealing a critical challenge: the absence of standardized datasets and benchmarks specifically tailored for open-surface generation and reconstruction. In this paper, we begin by introducing UDiFF, a novel diffusion-based 3D generative model specifically designed for UDFs. UDiFF supports both conditional and unconditional generation of textured 3D shapes with open surfaces. At its core, UDiFF generates UDFs in the spatial-frequency domain using a learnable wavelet transform. Instead of relying on manually selected wavelet transforms, which are labor-intensive and prone to information loss, we introduce a data-driven approach that learns the optimal wavelet transformation from UDFs datasets. Beyond UDiFF, we present the UWings dataset, comprising 1,509 high-quality 3D open-surface models of winged creatures. Using UWings, we establish comprehensive benchmarks for evaluating both generative and reconstruction methods based on UDFs.

Estimating the normal of a point requires constructing a local patch to provide center-surrounding context, but determining the appropriate neighborhood size is difficult when dealing with different data or geometries. Existing methods commonly employ various parameter-heavy strategies to extract a full feature description from the input patch. However, they still have difficulties in accurately and efficiently predicting normals for various point clouds. In this work, we present a new idea of feature extraction for robust normal estimation of point clouds. We use the fusion of multi-scale features from different neighborhood sizes to address the issue of selecting reasonable patch sizes for various data or geometries. We seek to model a patch feature fitting (PFF) based on multi-scale features to approximate the optimal geometric description for normal estimation and implement the approximation process via multi-scale feature aggregation and cross-scale feature compensation. The feature aggregation module progressively aggregates the patch features of different scales to the center of the patch and shrinks the patch size by removing points far from the center. It not only enables the network to precisely capture the structure characteristic in a wide range, but also describes highly detailed geometries. The feature compensation module ensures the reusability of features from earlier layers of large scales and reveals associated information in different patch sizes. Our approximation strategy based on aggregating the features of multiple scales enables the model to achieve scale adaptation of varying local patches and deliver the optimal feature description. Extensive experiments demonstrate that our method achieves state-of-the-art performance on both synthetic and real-world datasets with fewer network parameters and running time.

In this study, we introduce the concept of creative agents, aiming to enhance the capabilities of large language models (LLMs) in tasks related to the generation of prototypes of creative works. Our approach utilizes both self-collaboration and self-correction mechanisms, facilitated by hierarchical agents, to address the inherent complexities of target tasks. Our key observations are two-fold: first, effective task solving demands in-depth domain knowledge and intricate reasoning, for which deploying specialized agents for individual sub-tasks can markedly enhance LLM performance. Second, task solving intrinsically adheres to a hierarchical execution structure, comprising both high-level strategic planning and detailed task execution. Towards this end, our Creative-Agent paradigm aligns closely with this hierarchical structure, promising enhanced efficacy and adaptability across a wide range of scenarios. Specifically, our framework includes two novel modules, i.e., hierarchical Objects and Key Results generation and multi-level evaluation, both contributing to more efficient and robust task-solving. In practice, hierarchical OKR generation decomposes objects into multiple sub-objects and assigns new agents based on key results and agent responsibilities. These agents subsequently elaborate on their designated tasks and may further decompose them as necessary. Such generation operates recursively and hierarchically, culminating in a comprehensive set of detailed solutions. The multi-level evaluation module of Creative-Agent refines the solution by leveraging feedback from all associated agents, optimizing each step of the process. This scheme ensures the solution is accurate, practical, and meets the requirements of intricate tasks, enhancing the overall reliability and quality of the outcome. Experimental results demonstrated the effectiveness of Creative-Agent in completing the task of creating prototype generation works.

Recently, it has shown that priors are vital for neural implicit functions to reconstruct high-quality surfaces from multi-view RGB images. However, current priors require large-scale pre-training, and merely provide geometric clues without considering the importance of color. In this paper, we present NeRFPrior, which adopts a neural radiance field as a prior to learn signed distance fields using volume rendering for surface reconstruction. Our NeRF prior can provide both geometric and color clues, and also get trained fast under the same scene without additional data. Based on the NeRF prior, we are enabled to learn a signed distance function (SDF) by explicitly imposing a multi-view consistency constraint on each ray intersection for surface inference. Specifically, at each ray intersection, we use the density in the prior as a coarse geometry estimation, while using the color near the surface as a clue to check its visibility from another view angle. For the textureless areas where the multi-view consistency constraint does not work well, we further introduce a depth consistency loss with confidence weights to infer the SDF. Our experimental results outperform the state-of-the-art methods under the widely used benchmarks. Project page: https://wen-yuan-zhang.github.io/NeRFPrior/.

Monocular depth priors have been widely adopted by neural rendering in multi-view based tasks such as 3D reconstruction and novel view synthesis. However, due to the inconsistent prediction on each view, how to more effectively leverage monocular cues in a multi-view context remains a challenge. Current methods treat the entire estimated depth map indiscriminately, and use it as ground truth supervision, while ignoring the inherent inaccuracy and cross-view inconsistency in monocular priors. To resolve these issues, we propose MonoInstance, a general approach that explores the uncertainty of monocular depths to provide enhanced geometric priors for neural rendering and reconstruction. Our key insight lies in aligning each segmented instance depths from multiple views within a common 3D space, thereby casting the uncertainty estimation of monocular depths into a density measure within noisy point clouds. For high-uncertainty areas where depth priors are unreliable, we further introduce a constraint term that encourages the projected instances to align with corresponding instance masks on nearby views. MonoInstance is a versatile strategy which can be seamlessly integrated into various multi-view neural rendering frameworks. Our experimental results demonstrate that MonoInstance significantly improves the performance in both reconstruction and novel view synthesis under various benchmarks. Project page: https://wen-yuan-zhang.github.io/MonoInstance/.

Surface reconstruction from sparse views aims to reconstruct a 3D shape or scene from few RGB images. The latest methods are either generalization-based or overfitting-based. However, the generalization-based methods do not generalize well on views that were unseen during training, while the reconstruction quality of overfitting-based methods is still limited by the limited geometry clues. To address this issue, we propose SparseRecon, a novel neural implicit reconstruction method for sparse views with volume rendering-based feature consistency and uncertainty-guided depth constraint. Firstly, we introduce a feature consistency loss across views to constrain the neural implicit field. This design alleviates the ambiguity caused by insufficient consistency information of views and ensures completeness and smoothness in the reconstruction results. Secondly, we employ an uncertainty-guided depth constraint to back up the feature consistency loss in areas with occlusion and insignificant features, which recovers geometry details for better reconstruction quality. Experimental results demonstrate that our method outperforms the state-of-the-art methods, which can produce high-quality geometry with sparse-view input, especially in the scenarios with small overlapping views. Project page: https://hanl2010.github.io/SparseRecon/.

Diffusion models have shown remarkable results for im-age generation, editing and inpainting. Recent works ex-plore diffusion models for 3D shape generation with neural implicit functions, i.e., signed distance function and occu-pancy function. However, they are limited to shapes with closed surfaces, which prevents them from generating di-verse 3D real-world contents containing open surfaces. In this work, we present UDiFF, a 3D diffusion model for unsigned distance fields (UDFs) which is capable to gener-ate textured 3D shapes with open surfaces from text conditions or unconditionally. Our key idea is to generate UDFs in spatial-frequency domain with an optimal wavelet trans-formation, which produces a compact representation space for UDF generation. Specifically, instead of selecting an appropriate wavelet transformation which requires expen-sive manual efforts and still leads to large information loss, we propose a data-driven approach to learn the optimal wavelet transformation for UDFs. We evaluate UDiFF to show our advantages by numerical and visual comparisons with the latest methods on widely used benchmarks. Page: https://weiqi-zhang.github.io/UDiFF.

We propose a novel method called SHS-Net for point cloud normal estimation by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our algorithm outperforms the state-of-the-art methods in both unoriented and oriented normal estimation.

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are available at https://github.com/LeoQLi/SHS-Net.

Deep Implicit Function (DIF) has gained much popularity as an efficient 3D shape representation. To capture geometry details, current mainstream methods divide 3D shapes into local regions and then learn each one with a local latent code via a decoder. Such local methods can capture more local details due to less diversity among local regions than global shapes. Although the diversity of local regions has been decreased compared to global approaches, the diversity in different local regions still poses a challenge in learning an implicit function when treating all regions equally using only a single decoder. What is worse, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. This leads that fine geometry details could not be preserved well. To solve this problem, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, to represent a shape with clusters of local regions and multiple decoders, where each decoder only focuses on one cluster of local regions which share a certain pattern. Specifically, we first extract local codes for all regions, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train multiple decoders for mining local patterns of different groups, which simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder. To further alleviate the data-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder using a kernel density estimator, which dynamically re-weights the regions during learning. Our LP-DIF can restore more geometry details, and thus improve the quality of 3D reconstruction. Experiments demonstrate that our method can achieve the state-of-the-art performance over previous methods. Code is available at https://github.com/gtyxyz/lpdif.

Normal estimation for 3D point clouds is a fundamental task in 3D geometry processing. The state-of-the-art methods rely on priors of fitting local surfaces learned from normal supervision. However, normal supervision in benchmarks comes from synthetic shapes and is usually not available from real scans, thereby limiting the learned priors of these methods. In addition, normal orientation consistency across shapes remains difficult to achieve without a separate post-processing procedure. To resolve these issues, we propose a novel method for estimating oriented normals directly from point clouds without using ground truth normals as supervision. We achieve this by introducing a new paradigm for learning neural gradient functions, which encourages the neural network to fit the input point clouds and yield unit-norm gradients at the points. Specifically, we introduce loss functions to facilitate query points to iteratively reach the moving targets and aggregate onto the approximated surface, thereby learning a global surface representation of the data. Meanwhile, we incorporate gradients into the surface approximation to measure the minimum signed deviation of queries, resulting in a consistent gradient field associated with the surface. These techniques lead to our deep unsupervised oriented normal estimator that is robust to noise, outliers and density variations. Our excellent results on widely used benchmarks demonstrate that our method can learn more accurate normals for both unoriented and oriented normal estimation tasks than the latest methods. The source code and pre-trained model are publicly available.

We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying geometry of the data. We utilize a simple neural network to parameterize the objective function to produce gradients at points using a global implicit representation. However, the derived gradients usually drift away from the ground-truth oriented normals due to the lack of local detail descriptions. Therefore, we introduce Gradient Vector Optimization (GVO) to learn an angular distance field based on local plane geometry to refine the coarse gradient vectors. Finally, we formulate our method with a two-phase pipeline of coarse estimation followed by refinement. Moreover, we integrate two weighting functions, i.e., anisotropic kernel and inlier score, into the optimization to improve the robust and detail-preserving performance. Our method efficiently conducts global gradient approximation while achieving better accuracy and generalization ability of local feature description. This leads to a state-of-the-art normal estimator that is robust to noise, outliers and point density variations. Extensive evaluations show that our method outperforms previous works in both unoriented and oriented normal estimation on widely used benchmarks. The source code and pre-trained models are available at https://github.com/LeoQLi/NGLO .

Learning radiance fields has shown remarkable results for novel view synthesis. The learning procedure usually costs lots of time, which motivates the latest methods to speed up the learning procedure by learning without neural networks or using more efficient data structures. However, these specially designed approaches do not work for most of radiance fields based methods. To resolve this issue, we introduce a general strategy to speed up the learning procedure for almost all radiance fields based methods. Our key idea is to reduce the redundancy by shooting much fewer rays in the multi-view volume rendering procedure which is the base for almost all radiance fields based methods. We find that shooting rays at pixels with dramatic color change not only significantly reduces the training burden but also barely affects the accuracy of the learned radiance fields. In addition, we also adaptively subdivide each view into a quadtree according to the average rendering error in each node in the tree, which makes us dynamically shoot more rays in more complex regions with larger rendering error. We evaluate our method with different radiance fields based methods under the widely used benchmarks. Experimental results show that our method achieves comparable accuracy to the state-of-the-art with much faster training.

This paper proposes an algorithm for estimation of point projection parameters, based on pruning on the explicit convex hull of the squared distance function. The explicit expression of the squared distance function is deduced. According to the special requirement of point projection, the convex hull of the squared distance function is incrementally constructed. In each step, regions that obviously contain no projection points are eliminated from the base curve or surface, by intersecting the current nearest distance line with the convex hull. When the user-defined tolerances are satisfied, iteration algorithms are used to get the precise projection points. Experimental results show that compared with existing algorithms using clipping circle/sphere or line/plane, this algorithm possesses higher elimination rate and computation speed.

Anisotropic simplicial meshes are triangulations with elements elongated along prescribed directions. Anisotropic meshes have been shown well suited for interpolation of functions or solving PDEs. They can also significantly enhance the accuracy of a surface representation. Given a surface S endowed with a metric tensor field, we propose a new approach to generate an anisotropic mesh that approximates S with elements shaped according to the metric field. The algorithm relies on the well-established concepts of restricted Delaunay triangulation and Delaunay refinement and comes with theoretical guarantees. The star of each vertex in the output mesh is Delaunay for the metric attached to this vertex. Each facet has a good aspect ratio with respect to the metric specified at any of its vertices. The algorithm is easy to implement. It can mesh various types of surfaces like implicit surfaces, polyhedra, or isosurfaces in 3D images. It can handle complicated geometries and topologies, and very anisotropic metric fields.

We propose a specialized form of the curved-knot B-spline surface of Hayes [1982] that we call regular curved-knot spline surface . Unlike the original formulation where the knots of the first parametric coordinate can evolve arbitrarily with respect to the second coordinate, our formulation designs the knot functions as special curves that guarantee a monotonic blending of the knots corresponding to opposite surface boundaries. Furthermore, we demonstrate that local derivatives on the boundary can be described as an ordinary B-spline surface. The latter property allows for constructing smooth transitions between B-spline boundaries with different knot vectors.

Abstract Polar NURBS surface is a kind of periodic NURBS surface, one boundary of which shrinks to a degenerate polar point. The specific topology of its control‐point mesh offers the ability to represent a cap‐like surface, which is common in geometric modeling. However, there is a critical and challenging problem that hinders its application: curvature continuity at the extraordinary singular pole. We first propose a sufficient and necessary condition of curvature continuity at the pole. Then, we present constructive methods for the two key problems respectively: how to construct a polar NURBS surface with curvature continuity and how to reform an ordinary polar NURBS surface to curvature continuous. The algorithms only depend on the symbolic representation and operations of NURBS, and they introduce no restrictions on the degree or the knot vectors. Examples and comparisons demonstrate the applications of the curvature‐continuous polar NURBS surface in hole‐filling and free‐shape modeling.

N-sided hole filling plays an important role in vertex blending. Piegl and Tiller presented an algorithm to interpolate the given boundary and cross-boundary derivatives in B-spline form. To deal with the incompatible cases that their algorithm cannot handle, we propose an extension method to manipulate the transition between sharp and rounded features. The algorithm first patches n crescent-shaped extended surfaces to the boundary with G2continuity to handle incompatibility problem in the corners. Then, we compute the inner curves and the corresponding cross-boundary derivatives fulfilling tangent and twist compatibilities. The generated B-spline Coons patches are G1-continuously connected exactly, and have ε-G1continuity with the extended surfaces. Our method improves the continuity-quality of the shape and reduces the count of the inserted knots. It can be applied to all G0-continuous boundary conditions without any restrictions imposed on the boundary or cross-boundary derivatives. It generates better shapes than some popular industrial modeling systems on these incompatible occasions. Some examples underline its feasibility.