Weikai Chen

I am now a Principal Researcher at Tencent America. Previously, I was a postdoc and then a researcher at Vision and Graphics Lab (VGL)@USC ICT working with Prof. Hao Li. I got my PhD from the Department of Computer Science, University of Hong Kong, under Prof. Wenping Wang.

My research lies in the interplay among computer graphics, computer vision and machine learning. In particular, I am interested in broad topics in image-based 3D reasoning and 3D deep learning, including 3D reconstruction of humans (face/hair/body), general objects and scenes, differentiable rendering and point cloud analysis.

My research work SoftRas has been adopted by Pytorch3D for implementing its core functionality -- differentiable rendering. Check this out!

News

• 07/2024: Two papers accepted to SIGGRAPH Asia 2024 (ACM TOG).

• 07/2024: One paper accepted to IEEE TVCG.

• 07/2024: One paper accepted to ECCV 2024.

• 02/2024: One paper accepted to CVPR 2024.

• 11/2023: One paper accepted to TIP.

• 11/2023: One paper accepted to TPAMI.

• 07/2023: Two papers accepted to ICCV 2023.

• 02/2023: Four papers (including one highlight) accepted to CVPR 2023.

• 12/2022: One paper accepted to CVM 2023.

• 09/2022: Two papers accepted to NeurIPS 2022.

• 08/2022: Gave an invited talk at Shandong University on 3PSDF.

• 03/2022: Three papers (including one first-authored) accepted to CVPR 2022.

• 01/2022: Received the "Outstanding Contributor" award (the best performance rating, top 5%) from Tencent.

• 09/2021: One paper accepted to NeurIPS 2021.

• 07/2021: One paper accepted to ICCV 2021.

• 06/2021: Gave an invited talk on 3D reconstruction at CVPR'21 off hours representing Tencent US Vision and Graphics team.

• 03/2021: Three papers accepted to CVPR 2021.

Selected Publications (Full List)

DreamUDF: Generating Unsigned Distance Fields from A Single Image
Yu-Tao Liu, Xuan Gao, Weikai Chen, Jie Yang, Xiaoxu Meng, Bo Yang, Lin Gao
SIGGRAPH Asia 2024 (ACM Transactions on Graphics)
"a 3D generative model that can generate shapes with arbitrary topologies, including open surfaces"

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  Recent advances in diffusion models and neural implicit surfaces have shown promising progress in generating 3D models. However, existing generative frameworks are limited to closed surfaces, failing to cope with a wide range of commonly seen shapes that have open boundaries. In this work, we present DreamUDF, a novel framework for generating high-quality 3D objects with arbitrary topologies from a single image. To address the challenge of generating proper topology given sparse and ambiguous observations, we propose to incorporate both the data priors from a multi-view diffusion model and the geometry priors brought by an unsiged distance field (UDF) reconstructor. In particular, we leverage a joint framework that consists of 1) a generative module that produces a neural radiance field that provides photo-realistic renderings from the arbitrary view; and 2) a reconstructive module that distills the learnable radiance field into surfaces with arbitrary topologies. We further introduce a field coupler that bridges the radiance field and UDF under an novel optimization scheme. This allows the two modules to mutually boost each other during training. Extensive experiments and evaluations demonstrate that DreamUDF achieves high-quality reconstruction and robust 3D generation on both closed and open surfaces with arbitrary topologies, compared to the previous works.

NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering
Yu-Tao Liu, Li Wang, Jie Yang, Weikai Chen, Xiaoxu Meng, Bo Yang, Lin Gao
CVPR 2023
"NeuS for unsigned distance field"

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  Multi-view shape reconstruction has achieved impressive progresses thanks to the latest advances in neural implicit rendering. However, existing methods based on signed distance function (SDF) are limited to closed surfaces, failing to reconstruct a wide range of real-world objects that contain open-surface structures. In this work, we introduce a new neural rendering framework, coded NeUDF, that can reconstruct surfaces with arbitrary topologies solely from multi-view supervision. To gain the flexibility of representing arbitrary surfaces, NeUDF leverages the unsigned distance function (UDF) as surface representation. While a naive extension of SDF-based neural renderer cannot scale to UDF, we propose two new formulations of weight function specially tailored for UDF-based volume rendering. Furthermore, to cope with open surface rendering, where the in/out test is no longer valid, we present a dedicated normal regularization strategy to resolve the surface orientation ambiguity. We extensively evaluate our method over a number of challenging datasets, including two typical open surface datasets MGN and Deep Fashion 3D. Experimental results demonstrate that NeUDF can significantly outperform the state-of-the-art methods in the task of multi-view surface reconstruction, especially for the complex shapes with open boundaries.

NeAT: Learning Neural Implicit Surfaces with Arbitrary Topologies from Multi-view Images
Xiaoxu Meng, Weikai Chen, Bo Yang
CVPR 2023
"NeuS for 3-Pole signed distance field (3PSDF)"

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  Recent progress in neural implicit functions has set new state-of-the-art in reconstructing high-fidelity 3D shapes from a collection of images. However, these approaches are limited to closed surfaces as they require the surface to be represented by a signed distance field. In this paper, we propose NeAT, a new neural rendering framework that can learn implicit surfaces with arbitrary topologies from multi-view images. In particular, NeAT represents the 3D surface as a level set of a signed distance function (SDF) with a validity branch for estimating the surface existence probability at the query positions. We also develop a novel neural volume rendering method, which uses SDF and validity to calculate the volume opacity and avoids rendering points with low validity. NeAT supports easy field-to-mesh conversion using the classic Marching Cubes algorithm. Extensive experiments on DTU, MGN, and Deep Fashion 3D datasets indicate that our approach is able to faithfully reconstruct both watertight and non-watertight surfaces. In particular, NeAT significantly outperforms the state-of-the-art methods in the task of open surface reconstruction both quantitatively and qualitatively.

HSDF: Hybrid Sign and Distance Field for Modeling Surfaces with Arbitrary Topologies
Li Wang, Jie Yang, Weikai Chen, Xiaoxu Meng, Bo Yang, Jintao Li, Lin Gao
NeurIPS 2022
"a learnable implicit representation for modeling both closed and open surfaces"

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  Neural implicit function based on signed distance field (SDF) has achieved impressive progress in reconstructing 3D models with high fidelity. However, such approaches can only represent closed shapes. Recent works based on unsigned distance function (UDF) are proposed to handle both watertight and open surfaces. Nonetheless, as UDF is signless, its direct output is limited to point cloud, which imposes an additional challenge on extracting high-quality meshes from discrete points. To address this issue, we present a new learnable implicit representation, coded HSDF, that connects the good ends of SDF and UDF. In particular, HSDF is able to represent arbitrary topologies containing both closed and open surfaces while being compatible with existing iso-surface extraction techniques for easy field-to-mesh conversion. In addition to predicting a UDF, we propose to learn an additional sign field via a simple classifier. Unlike traditional SDF, HSDF is able to locate the surface of interest before level surface extraction by generating surface points following NDF. We are then able to obtain open surfaces via an adaptive meshing approach that only instantiates regions containing surface into a polygon mesh. We also propose HSDF-Net, a dedicated learning framework that factorizes the learning of HSDF into two easier problems. Experiments on multiple datasets show that HSDF outperforms state-of-the-art techniques both qualitatively and quantitatively.

3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies
Weikai Chen, Cheng Lin, Weiyang Li, Bo Yang
CVPR 2022
"a new implicit representation that can represent non-watertight shapes"

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  Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to closed surfaces as they require the space to be divided into inside and outside. More recent works based on unsigned distance function have been proposed to handle complex geometry containing both the open and closed surfaces. Nonetheless, as their direct outputs are point clouds, robustly obtaining high-quality meshing results from discrete points remains an open question. We present a novel learnable implicit representation, called three-pole signed distance function (3PSDF), that can represent non-watertight 3D shapes with arbitrary topologies while supporting easy field-to-mesh conversion using the classic Marching Cubes algorithm. The key to our method is the introduction of a new sign, the NULL sign, in addition to the conventional in and out labels. The existence of the null sign could stop the formation of a closed isosurface derived from the bisector of the in/out regions. Further, we propose a dedicated learning framework to effectively learn 3PSDF without worrying about the vanishing gradient due to the null labels. Experimental results show that our approach outperforms the previous state-of-the-art methods in a wide range of benchmarks both quantitatively and qualitatively.

OctField: Hierarchical Implicit Functions for 3D Modeling
Jia-Heng Tang*, Weikai Chen*, Jie Yang, Bo Wang, Songrun Liu, Bo Yang, Lin Gao
NeurIPS 2021
"a new hierarchical implicit representation with its generative model for high-precision modeling with low cost"

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  Recent advances in localized implicit functions have enabled neural implicit representation to be scalable to large scenes. However, the regular subdivision of 3D space employed by these approaches fails to take into account the sparsity of the surface occupancy and the varying granularities of geometric details. As a result, its memory footprint grows cubically with the input volume, leading to a prohibitive computational cost even at a moderately dense decomposition. In this work, we present a learnable hierarchical implicit representation for 3D surfaces, coded OctField, that allows high-precision encoding of intricate surfaces with low memory and computational budget. The key to our approach is an adaptive decomposition of 3D scenes that only distributes local implicit functions around the surface of interest. We achieve this goal by introducing a hierarchical octree structure to adaptively subdivide the 3D space according to the surface occupancy and the richness of part geometry. As octree is discrete and non-differentiable, we further propose a novel hierarchical network that models the subdivision of octree cells as a probabilistic process and recursively encodes and decodes both octree structure and surface geometry in a differentiable manner. We demonstrate the value of OctField for a range of shape modeling and reconstruction tasks, showing superiority over alternative approaches.

Deep Optimized Priors for 3D Shape Modeling and Reconstruction
Mingyue Yang, Yuxin Wen, Weikai Chen, Yongwei Chen, Kui Jia
CVPR 2021
"a framework to improve the performance and generality of 3D shape prior"

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  Many learning-based approaches have difficulty scaling to unseen data, as the generality of its learned prior is limited to the scale and variations of the training samples. This holds particularly true with 3D learning tasks, given the sparsity of 3D datasets available. We introduce a new learning framework for 3D modeling and reconstruction that greatly improves the generalization ability of a deep generator. Our approach strives to connect the good ends of both learning-based and optimization-based methods. In particular, unlike the common practice that fixes the pre-trained priors at test time, we propose to further optimize the learned prior and latent code according to the input physical measurements after the training. We show that the proposed strategy effectively breaks the barriers constrained by the pre-trained priors and could lead to high-quality adaptation to unseen data. We realize our framework using the implicit surface representation and validate the efficacy of our approach in a variety of challenging tasks that take highly sparse or collapsed observations as input. Experimental results show that our approach compares favorably with the state-of-the-art methods in terms of both generality and accuracy.

Equivariant Point Network for 3D Point Cloud Analysis
Haiwei Chen, Shichen Liu, Weikai Chen, Hao Li
CVPR 2021
"a new approach for extracting SE(3) equivariant feature for point clouds"

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  Features that are equivariant to a larger group of symmetries have been shown to be more discriminative and powerful in recent studies. However, higher-order equivariant features often come with an exponentiallygrowing computational cost. Furthermore, it remains relatively less explored how rotation-equivariant features can be leveraged to tackle 3D shape alignment tasks. While many past approaches have been based on either nonequivariant or invariant descriptors to align 3D shapes, we argue that such tasks may benefit greatly from an equivariant framework. In this paper, we propose an effective and practical SE(3) (3D translation and rotation) equivariant network for point cloud analysis that addresses both problems. First, we present SE(3) separable point convolution, a novel framework that breaks down the 6D convolution into two separable convolutional operators alternatively performed in the 3D Euclidean and SO(3) spaces. This significantly reduces the computational cost without compromising the performance. Second, we introduce an attention layer to effectively harness the expressiveness of the equivariant features. While jointly trained with the network, the attention layer implicitly derives the intrinsic local frame in the feature space and generate attention vectors that can be integrated in different alignment tasks. We evaluate our approach through extensive studies and visual interpretations. The empirical results demonstrate that our proposed model outperforms strong baselines in a variety of benchmarks.

Deep Fashion3D: A Dataset and Benchmark for 3D Garment Reconstruction from Single Images
Heming Zhu, Yu Cao, Hang Jin, Weikai Chen, Dong Du, Zhangye Wang, Shuguang Cui, and Xiaoguang Han
ECCV 2020 (Oral Presentation)
"a large scale dataset and benchmark for real 3D garments"

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  High-fidelity clothing reconstruction is the key to achieving photorealism in a wide range of applications including human digitization, virtual try-on, etc. Recent advances in learning-based approaches have accomplished unprecedented accuracy in recovering unclothed human shape and pose from single images, thanks to the availability of powerful statistical models, e.g. SMPL [38], learned from a large number of body scans. In contrast, modeling and recovering clothed human and 3D garments remains notoriously difficult, mostly due to the lack of large-scale clothing models available for the research community. We propose to fill this gap by introducing Deep Fashion3D, the largest collection to date of 3D garment models, with the goal of establishing a novel benchmark and dataset for the evaluation of image-based garment reconstruction systems. Deep Fashion3D contains 2078 models reconstructed from real garments, which covers 10 different categories and 563 garment instances. It provides rich annotations including 3D feature lines, 3D body pose and the corresponded multi-view real images. In addition, each garment is randomly posed to enhance the variety of real clothing deformations. To demonstrate the advantage of Deep Fashion3D, we propose a novel baseline approach for single-view garment reconstruction, which leverages the merits of both mesh and implicit representations. A novel adaptable template is proposed to enable the learning of all types of clothing in a single network. Extensive experiments have been conducted on the proposed dataset to verify its significance and usefulness. We will make Deep Fashion3D publicly available upon publication

Learning to Infer Implicit Surfaces without 3D Supervision
Shichen Liu, Shunsuke Saito, Weikai Chen, Hao Li
NeurIPS 2019
"the first differentiable renderer for implicit field"

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  Recent advances in 3D deep learning have shown that it is possible to train highly effective deep models for 3D shape generation, directly from 2D images. This is particularly interesting since the availability of 3D models is still limited compared to the massive amount of accessible 2D images, which is invaluable for training. The representation of 3D surfaces itself is a key factor for the quality and resolution of the 3D output. While explicit representations, such as point clouds and voxels, can span a wide range of shape variations, their resolutions are often limited. Mesh-based representations are more efficient but are limited by their ability to handle varying topologies. Implicit surfaces, however, can robustly handle complex shapes, topologies, and also provide flexible resolution control. We address the fundamental problem of learning implicit surfaces for shape inference without the need of 3D supervision. Despite their advantages, it remains nontrivial to (1) formulate a differentiable connection between implicit surfaces and their 2D renderings, which is needed for image-based supervision; and (2) ensure precise geometric properties and control, such as local smoothness. In particular, sampling implicit surfaces densely is also known to be a computationally demanding and very slow operation. To this end, we propose a novel ray-based field probing technique for efficient image-to-field supervision, as well as a general geometric regularizer for implicit surfaces, which provides natural shape priors in unconstrained regions. We demonstrate the effectiveness of our framework on the task of single-view image-based 3D shape digitization and show how we outperform state-of-the-art techniques both quantitatively and qualitatively. 

Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning
Shichen Liu, Tianye Li, Weikai Chen, Hao Li
ICCV 2019 (Oral Presentation) - 3 Strong Accepts
"a truly differentiable renderer for rasterization-based rendering"

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  Rendering bridges the gap between 2D vision and 3D scenes by simulating the physical process of image formation. By inverting such renderer, one can think of a learning approach to infer 3D information from 2D images. However, standard graphics renderers involve a fundamental discretization step called rasterization, which prevents the rendering process to be differentiable, hence able to be learned. Unlike the state-of-the-art differentiable renderers, which only approximate the rendering gradient in the back propagation, we propose a truly differentiable rendering framework that is able to (1) directly render colorized mesh using differentiable functions and (2) back-propagate efficient supervision signals to mesh vertices and their attributes from various forms of image representations, including silhouette, shading and color images. The key to our framework is a novel formulation that views rendering as an aggregation function that fuses the probabilistic contributions of all mesh triangles with respect to the rendered pixels. Such formulation enables our framework to flow gradients to the occluded and far-range vertices, which cannot be achieved by the previous state-of-the-arts. We show that by using the proposed renderer, one can achieve significant improvement in 3D unsupervised single-view reconstruction both qualitatively and quantitatively. Experiments also demonstrate that our approach is able to handle the challenging tasks in image-based shape fitting, which remain nontrivial to existing differentiable renderers. 

Deep Mesh Reconstruction from Single RGB Images via Topology Modification Networks
Junyi Pan, Xiaoguang Han, Weikai Chen, Jiapeng Tang and Kui Jia
ICCV 2019
"a single-view mesh reconstruction approach that can handle objects with arbitrary topologies"

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  Reconstructing the 3D mesh of a general object from a single image is now possible thanks to the latest advances of deep learning technologies. However, due to the nontrivial difficulty of generating a feasible mesh structure, the state-of-the-art approaches~\cite{wang2018pixel2mesh,kanazawa2018learning} often simplify the problem by learning the displacements of a template mesh that deforms it to the target surface.Though reconstructing a 3D shape with complex topo logy can be achieved by deforming multiple mesh patches, it remains difficult to stitch the results to ensure a high meshing quality. In this paper, we present an end-to-end single-view mesh reconstruction framework that is able to generate high-quality meshes with complex topology from a single genus-0 template mesh. The key to our approach is a novel progressive shaping framework that alternates between shape deformation and topology modifying. While a deformation network predicts the per-vertex translations that reduce the gap between the reconstructed mesh and the ground truth, a novel topology modification network is employed to prune the error-prone faces and refine the boundary conditions, enabling the evolution of topology. By iterating over the two procedures, one can progressively modify the mesh topology while achieving higher reconstruction accuracy. Extensive experiments demonstrate that our approach significantly outperforms the current state-of-the-art methods both qualitatively and quantitatively, especially for the shapes with complex topology. 

SiCloPe: Silhouette-Based Clothed People
Ryota Natsume, Shunsuke Saito, Zeng Huang, Weikai Chen, Chongyang Ma, Hao Li, Shigeo Morishima
CVPR 2019 (Oral Presentation) - CVPR Best Paper Finalists
"single-view based clothed human reconstruction"

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  We introduce a new silhouette-based representation for modeling clothed human bodies using deep generative models. Our method can reconstruct a complete and textured 3D model of a person wearing clothes from a single input picture. Inspired by the visual hull algorithm, our implicit representation uses 2D silhouettes and 3D joints of a body pose to describe the immense shape complexity and variations of clothed people. Given a segmented 2D silhouette of a person and its inferred 3D joints from the input picture, we first synthesize consistent silhouettes from novel view points around the subject. The synthesized silhouettes, which are the most consistent with the input segmentation are fed into a deep visual hull algorithm for robust 3D shape prediction. We then infer the texture of the subject's back view using the frontal image and segmentation mask as input to a conditional generative adversarial network. Our experiments demonstrate that our silhouette-based model is an effective representation and the appearance of the back view can be predicted reliably using an image-to-image translation network. While classic methods based on parametric models often fail for single-view images of subjects with challenging clothing, our approach can still produce successful results, which are comparable to those obtained from multi-view input. 

Deep Volumetric Video From Very Sparse Multi-View Performance Capture
Zeng Huang, Tianye Li, Weikai Chen, Yajie Zhao, Jun Xing, Chloe LeGendre, Linjie Luo, Chongyang Ma, Hao Li
ECCV 2018
"volumetric body reconstruction from highly sparse views"

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  We present a deep learning based volumetric approach for performance capture using a passive and highly sparse multi-view capture system. State-of-the-art performance capture systems require either pre-scanned actors, large number of cameras or active sensors. In this work, we focus on the task of template-free, per-frame 3D surface reconstruction from as few as three RGB sensors, for which conventional visual hull or multi-view stereo methods fail to generate plausible results.We introduce a novel multi-view Convolutional Neural Network (CNN) that maps 2D images to a 3D volumetric field and we use this field to encode the probabilistic distribution of surface points of the captured subject. By querying the resulting field, we can instantiate the clothed human body at arbitrary resolutions. Our approach scales to different numbers of input images, which yield increased reconstruction quality when more views are used. Although only trained on synthetic data, our network can generalize to handle real footage from body performance capture. Our method is suitable for high-quality low-cost full body volumetric capture solutions, which are gaining popularity for VR and AR content creation. Experimental results demonstrate that our method is significantly more robust and accurate than existing techniques when only very sparse views are available. 

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High-Fidelity Facial Reflectance and Geometry Inference From an Unconstrained Image
Shugo Yamaguchi*, Shunsuke Saito*, Koki Nagano, Yajie Zhao, Weikai Chen, Shigeo Morishima, Hao Li
SIGGRAPH 2018
"inference of complete face reflectance maps from a single unconstrained image"

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  We present a deep learning-based technique to infer high-quality facial reflectance and geometry given a single unconstrained image of the subject, which may contain partial occlusions and arbitrary illumination conditions. The reconstructed high-resolution textures, which are generated in only a few seconds, include high-resolution skin surface reflectance maps, representing both the diffuse and specular albedo, and medium- and highfrequency displacement maps, thereby allowing us to render compelling digital avatars under novel lighting conditions. To extract this data, we train our deep neural networks with a high-quality skin reflectance and geometry database created with a state-of-the-art multi-view photometric stereo system using polarized gradient illumination. Given the raw facial texture map extracted from the input image, our neural networks synthesize complete reflectance and displacement maps, as well as complete missing regions caused by occlusions. The completed textures exhibit consistent quality throughout the face due to our network architecture, which propagates texture features from the visible region, resulting in high-fidelity details that are consistent with those seen in visible regions. We describe how this highly underconstrained problem is made tractable by dividing the full inference into smaller tasks, which are addressed by dedicated neural networks. We demonstrate the effectiveness of our network design with robust texture completion from images of faces that are largely occluded. With the inferred reflectance and geometry data, we demonstrate the rendering of high-fidelity 3D avatars from a variety of subjects captured under different lighting conditions. In addition, we perform evaluations demonstrating that our method can infer plausible facial reflectance and geometric details comparable to those obtained from high-end capture devices, and outperform alternative approaches that require only a single unconstrained input image.

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Fabricable Tile Decors
Weikai Chen, Yuexin Ma, Sylvain Lefebvre, Shiqing Xin, Jonàs Martínez and Wenping Wang
SIGGRAPH Asia 2017
"a *magic* way to fabricate curved surfaces flatly"

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  Recent advances in 3D printing have made it easier to manufacture customized objects by ordinary users in an affordable manner, and therefore spurred high demand for more accessible methods for designing and fabricating 3D objects of various shapes and functionalities. In this paper we present a novel approach to model and fabricate surface-like objects composed of connected tiles, which can be used as objects in daily life, such as ornaments, covers, shades or handbags. Our method is designed to maximize the efciency and ease of fabrication. Given a base surface and a set of tile elements as user input, our method generates a tight packing of connected tiles on the surface. We apply an efcient and tailored optimization scheme to pack the tiles on the base surface with fabrication constraints. Then, to facilitate the fabrication process, we use a novel method based on minimal spanning tree to decompose the set of connected tiles into several connected patches. Each patch is articulated and can be developed into a plane. This allows printing with an inexpensive FDM printing process without requiring any supporting structures, which are often troublesome to remove. Finally, the separately printed patches are reassembled to form the fnal physical object, a shell surface composed of connected user-specifed tiles that take the shape of the input base surface. We demonstrate the utility of our method by modeling and fabricating a variety of objects, from simple decorative spheres to moderately complex surfaces, such as a handbag and a teddy bear. Several user controls are available, to distribute different type of tiles over the surface and locally change their scales and orientations

Synthesis of Filigrees for Digital Fabrication
Weikai Chen, Xiaolong Zhang, Shiqing Xin, Yang Xia , Sylvain Lefebvre and Wenping Wang
SIGGRAPH 2016
"how to make example-based 3D jewelry"

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  Filigrees are thin patterns found in jewelry, ornaments and lace fabrics. They are often formed of repeated base elements manually composed into larger, delicate patterns. Digital fabrication simplifies the process of turning a virtual model of a filigree into a physical object. However, designing a virtual model of a filigree remains a time consuming and challenging task. The difficulty lies in tightly packing together the base elements while covering a target surface. In addition, the filigree has to be well connected and sufficiently robust to be fabricated. We propose a novel approach automating this task. Our technique covers a target surface with a set of input base elements, forming a filigree strong enough to be fabricated. We exploit two properties of filigrees to make this possible. First, as filigrees form delicate traceries they are well captured by their skeleton. This affords for a simpler definition of operators such as matching and deformation. Second, instead of seeking for a perfect packing of the base elements we relax the problem by allowing appearance preserving partial overlaps. We optimize a filigree by a stochastic search, further improved by a novel boosting algorithm that records and reuses good configurations discovered during the process. We illustrate our technique on a number of challenging examples reproducing filigrees on large objects, which we manufacture by 3D printing. Our technique affords for several user controls, such as the scale and orientation of the elements.

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