41-Issue 2
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Item Shape Transformers: Topology-Independent 3D Shape Models Using Transformers(The Eurographics Association and John Wiley & Sons Ltd., 2022) Chandran, Prashanth; Zoss, Gaspard; Gross, Markus; Gotardo, Paulo; Bradley, Derek; Chaine, Raphaëlle; Kim, Min H.Parametric 3D shape models are heavily utilized in computer graphics and vision applications to provide priors on the observed variability of an object's geometry (e.g., for faces). Original models were linear and operated on the entire shape at once. They were later enhanced to provide localized control on different shape parts separately. In deep shape models, nonlinearity was introduced via a sequence of fully-connected layers and activation functions, and locality was introduced in recent models that use mesh convolution networks. As common limitations, these models often dictate, in one way or another, the allowed extent of spatial correlations and also require that a fixed mesh topology be specified ahead of time. To overcome these limitations, we present Shape Transformers, a new nonlinear parametric 3D shape model based on transformer architectures. A key benefit of this new model comes from using the transformer's self-attention mechanism to automatically learn nonlinear spatial correlations for a class of 3D shapes. This is in contrast to global models that correlate everything and local models that dictate the correlation extent. Our transformer 3D shape autoencoder is a better alternative to mesh convolution models, which require specially-crafted convolution, and down/up-sampling operators that can be difficult to design. Our model is also topologically independent: it can be trained once and then evaluated on any mesh topology, unlike most previous methods. We demonstrate the application of our model to different datasets, including 3D faces, 3D hand shapes and full human bodies. Our experiments demonstrate the strong potential of our Shape Transformer model in several applications in computer graphics and vision.Item Dynamic Combination of Crowd Steering Policies Based on Context(The Eurographics Association and John Wiley & Sons Ltd., 2022) Cabrero-Daniel, Beatriz; Marques, Ricardo; Hoyet, Ludovic; Pettré, Julien; Blat, Josep; Chaine, Raphaëlle; Kim, Min H.Simulating crowds requires controlling a very large number of trajectories of characters and is usually performed using crowd steering algorithms. The question of choosing the right algorithm with the right parameter values is of crucial importance given the large impact on the quality of results. In this paper, we study the performance of a number of steering policies (i.e., simulation algorithm and its parameters) in a variety of contexts, resorting to an existing quality function able to automatically evaluate simulation results. This analysis allows us to map contexts to the performance of steering policies. Based on this mapping, we demonstrate that distributing the best performing policies among characters improves the resulting simulations. Furthermore, we also propose a solution to dynamically adjust the policies, for each agent independently and while the simulation is running, based on the local context each agent is currently in. We demonstrate significant improvements of simulation results compared to previous work that would optimize parameters once for the whole simulation, or pick an optimized, but unique and static, policy for a given global simulation context.Item ZoomShop: Depth-Aware Editing of Photographic Composition(The Eurographics Association and John Wiley & Sons Ltd., 2022) Liu, Sean J.; Agrawala, Maneesh; DiVerdi, Stephen; Hertzmann, Aaron; Chaine, Raphaëlle; Kim, Min H.We present ZoomShop, a photographic composition editing tool for adjusting relative size, position, and foreshortening of scene elements. Given an image and corresponding depth map as input, ZoomShop combines a novel non-linear camera model and a depth-aware image warp to reproject and deform the image. Users can isolate objects by selecting depth ranges and adjust their scale and foreshortening, which controls the paths of the camera rays through the scene. Users can also select 2D image regions and translate them, which determines the objective function in the image warp optimization. We demonstrate that ZoomShop can be used to achieve useful compositional goals, such as making a distant object more prominent while preserving foreground scenery, or making objects both larger and closer together so they still fit in the frame.Item Recursive Analytic Spherical Harmonics Gradient for Spherical Lights(The Eurographics Association and John Wiley & Sons Ltd., 2022) Mézières, Pierre; Mellado, Nicolas; Barthe, Loïc; Paulin, Mathias; Chaine, Raphaëlle; Kim, Min H.When rendering images using Spherical Harmonics (SH), the projection of a spherical function on the SH basis remains a computational challenge both for high-frequency functions and for emission functions from complex light sources. Recent works investigate efficient SH projection of the light field coming from polygonal and spherical lights. To further reduce the rendering time, instead of computing the SH coefficients at each vertex of a mesh or at each fragment on an image, it has been shown, for polygonal area light, that computing both the SH coefficients and their spatial gradients on a grid covering the scene allows the efficient and accurate interpolation of these coefficients at each shaded point. In this paper, we develop analytical recursive formulae to compute the spatial gradients of SH coefficients for spherical light. This requires the efficient computation of the spatial gradients of the SH basis function that we also derive. Compared to existing method for polygonal light, our method is faster, requires less memory and scales better with respect to the SH band limit. We also show how to approximate polygonal lights using spherical lights to benefit from our derivations. To demonstrate the effectiveness of our proposal, we integrate our algorithm in a shading system able to render fully dynamic scenes with several hundreds of spherical lights in real time.Item Procedural Roof Generation From a Single Satellite Image(The Eurographics Association and John Wiley & Sons Ltd., 2022) Zhang, Xiaowei; Aliaga, Daniel; Chaine, Raphaëlle; Kim, Min H.Urban procedural modeling has benefited from recent advances in deep learning and computer graphics. However, few, if any, approaches have automatically produced procedural building roof models from a single overhead satellite image. Large-scale roof modeling is important for a variety of applications in urban content creation and in urban planning (e.g., solar panel planning, heating/cooling/rainfall modeling). While the allure of modeling only from satellite images is clear, unfortunately structures obtained from the satellite images are often in low-resolution, noisy and heavily occluded, thus getting a clean and complete view of urban structures is difficult. In this paper, we present a framework that exploits the inherent structure present in man-made buildings and roofs by explicitly identifying the compact space of potential building shapes and roof structures. Then, we utilize this relatively compact space with a two-component solution combining procedural modeling and deep learning. Specifically, we use a building decomposition component to separate the building into roof parts and predict regularized building footprints in a procedural format, and use a roof ridge detection component to refine the individual roof parts by estimating the procedural roof ridge parameters. Our qualitative and quantitative assessments over multiple satellite datasets show that our method outperforms various state-of-the-art methods.Item Fast and Exact Root Parity for Continuous Collision Detection(The Eurographics Association and John Wiley & Sons Ltd., 2022) Wang, Bolun; Ferguson, Zachary; Jiang, Xin; Attene, Marco; Panozzo, Daniele; Schneider, Teseo; Chaine, Raphaëlle; Kim, Min H.We introduce the first exact root parity counter for continuous collision detection (CCD). That is, our algorithm computes the parity (even or odd) of the number of roots of the cubic polynomial arising from a CCD query. We note that the parity is unable to differentiate between zero (no collisions) and the rare case of two roots (collisions). Our method does not have numerical parameters to tune, has a performance comparable to efficient approximate algorithms, and is exact. We test our approach on a large collection of synthetic tests and real simulations, and we demonstrate that it can be easily integrated into existing simulators.Item A-ULMPM: An Adaptively Updated Lagrangian Material Point Method for Efficient Physics Simulation without Numerical Fracture(The Eurographics Association and John Wiley & Sons Ltd., 2022) Su, Haozhe; Xue, Tao; Han, Chengguizi; Aanjaneya, Mridul; Chaine, Raphaëlle; Kim, Min H.We present an adaptively updated Lagrangian Material Point Method (A-ULMPM) to alleviate non-physical artifacts, such as the cell-crossing instability and numerical fracture, that plague state-of-the-art Eulerian formulations of MPM, while still allowing for large deformations that arise in fluid simulations. A-ULMPM spans MPM discretizations from total Lagrangian formulations to Eulerian formulations. We design an easy-to-implement physics-based criterion that allows A-ULMPM to update the reference configuration adaptively for measuring physical states, including stress, strain, interpolation kernels and their derivatives. For better efficiency and conservation of angular momentum, we further integrate the APIC [JSS*15] and MLS-MPM [HFG*18] formulations in A-ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first-order derivatives. Our theoretical derivations use a nodal discretized Lagrangian, instead of the weak form discretization in MLS-MPM [HFG*18], and naturally lead to a ''modified'' MLS-MPM in A-ULMPM, which can recover MLS-MPM using a completely Eulerian formulation. A-ULMPM does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives during large topology changes. We present end-to-end 3D simulations of stretching and twisting hyperelastic solids, viscous flows, splashing liquids, and multi-material interactions with large deformations to demonstrate the efficacy of our new method.Item Interaction Fields: Intuitive Sketch-based Steering Behaviors for Crowd Simulation(The Eurographics Association and John Wiley & Sons Ltd., 2022) Colas, Adèle; van Toll, Wouter; Zibrek, Katja; Hoyet, Ludovic; Olivier, Anne-Hélène; Pettré, Julien; Chaine, Raphaëlle; Kim, Min H.The real-time simulation of human crowds has many applications. In a typical crowd simulation, each person ('agent') in the crowd moves towards a goal while adhering to local constraints. Many algorithms exist for specific local 'steering' tasks such as collision avoidance or group behavior. However, these do not easily extend to completely new types of behavior, such as circling around another agent or hiding behind an obstacle. They also tend to focus purely on an agent's velocity without explicitly controlling its orientation. This paper presents a novel sketch-based method for modelling and simulating many steering behaviors for agents in a crowd. Central to this is the concept of an interaction field (IF): a vector field that describes the velocities or orientations that agents should use around a given 'source' agent or obstacle. An IF can also change dynamically according to parameters, such as the walking speed of the source agent. IFs can be easily combined with other aspects of crowd simulation, such as collision avoidance. Using an implementation of IFs in a real-time crowd simulation framework, we demonstrate the capabilities of IFs in various scenarios. This includes game-like scenarios where the crowd responds to a user-controlled avatar. We also present an interactive tool that computes an IF based on input sketches. This IF editor lets users intuitively and quickly design new types of behavior, without the need for programming extra behavioral rules. We thoroughly evaluate the efficacy of the IF editor through a user study, which demonstrates that our method enables non-expert users to easily enrich any agent-based crowd simulation with new agent interactions.Item Fiblets for Real-Time Rendering of Massive Brain Tractograms(The Eurographics Association and John Wiley & Sons Ltd., 2022) Schertzer, Jérémie; Mercier, Corentin; Rousseau, Sylvain; Boubekeur, Tamy; Chaine, Raphaëlle; Kim, Min H.We present a method to render massive brain tractograms in real time. Tractograms model the white matter architecture of the human brain using millions of 3D polylines (fibers), summing up to billions of segments. They are used by neurosurgeons before surgery as well as by researchers to better understand the brain. A typical raw dataset for a single brain represents dozens of gigabytes of data, preventing their interactive rendering.We address this challenge with a new GPU mesh shader pipeline based on a decomposition of the fiber set into compressed local representations that we call fiblets. Their spatial coherence is used at runtime to efficiently cull hidden geometry at the task shader stage while synthesizing the visible ones as polyline meshlets in a warp-scale parallel fashion at the mesh shader stage. As a result, our pipeline can feed a standard deferred shading engine to visualize the mesostructures of the brain with various classical rendering techniques, as well as simple interaction primitives. We demonstrate that our algorithm provides real-time framerates on very large tractograms that were out of reach for previous methods while offering a fiber-level granularity in both rendering and interaction.Item Computational Design of Kinesthetic Garments(The Eurographics Association and John Wiley & Sons Ltd., 2022) Vechev, Velko; Zarate, Juan; Thomaszewski, Bernhard; Hilliges, Otmar; Chaine, Raphaëlle; Kim, Min H.Kinesthetic garments provide physical feedback on body posture and motion through tailored distributions of reinforced material. Their ability to selectively stiffen a garment's response to specific motions makes them appealing for rehabilitation, sports, robotics, and many other application fields. However, finding designs that distribute a given amount of reinforcement material to maximally stiffen the response to specified motions is a challenging problem. In this work, we propose an optimization-driven approach for automated design of reinforcement patterns for kinesthetic garments. Our main contribution is to cast this design task as an on-body topology optimization problem. Our method allows designers to explore a continuous range of designs corresponding to various amounts of reinforcement coverage. Our model captures both tight contact and lift-off separation between cloth and body. We demonstrate our method on a variety of reinforcement design problems for different body sites and motions. Optimal designs lead to a two- to threefold improvement in performance in terms of energy density. A set of manufactured designs were consistently rated as providing more resistance than baselines in a comparative user study.Item Dressi: A Hardware-Agnostic Differentiable Renderer with Reactive Shader Packing and Soft Rasterization(The Eurographics Association and John Wiley & Sons Ltd., 2022) Takimoto, Yusuke; Sato, Hiroyuki; Takehara, Hikari; Uragaki, Keishiro; Tawara, Takehiro; Liang, Xiao; Oku, Kentaro; Kishimoto, Wataru; Zheng, Bo; Chaine, Raphaëlle; Kim, Min H.Differentiable rendering (DR) enables various computer graphics and computer vision applications through gradient-based optimization with derivatives of the rendering equation. Most rasterization-based approaches are built on general-purpose automatic differentiation (AD) libraries and DR-specific modules handcrafted using CUDA. Such a system design mixes DR algorithm implementation and algorithm building blocks, resulting in hardware dependency and limited performance. In this paper, we present a practical hardware-agnostic differentiable renderer called Dressi, which is based on a new full AD design. The DR algorithms of Dressi are fully written in our Vulkan-based AD for DR, Dressi-AD, which supports all primitive operations for DR. Dressi-AD and our inverse UV technique inside it bring hardware independence and acceleration by graphics hardware. Stage packing, our runtime optimization technique, can adapt hardware constraints and efficiently execute complex computational graphs of DR with reactive cache considering the render pass hierarchy of Vulkan. HardSoftRas, our novel rendering process, is designed for inverse rendering with a graphics pipeline. Under the limited functionalities of the graphics pipeline, HardSoftRas can propagate the gradients of pixels from the screen space to far-range triangle attributes. Our experiments and applications demonstrate that Dressi establishes hardware independence, high-quality and robust optimization with fast speed, and photorealistic rendering.Item Semantic Segmentation in Art Paintings(The Eurographics Association and John Wiley & Sons Ltd., 2022) Cohen, Nadav; Newman, Yael; Shamir, Ariel; Chaine, Raphaëlle; Kim, Min H.Semantic segmentation is a difficult task even when trained in a supervised manner on photographs. In this paper, we tackle the problem of semantic segmentation of artistic paintings, an even more challenging task because of a much larger diversity in colors, textures, and shapes and because there are no ground truth annotations available for segmentation. We propose an unsupervised method for semantic segmentation of paintings using domain adaptation. Our approach creates a training set of pseudo-paintings in specific artistic styles by using style-transfer on the PASCAL VOC 2012 dataset, and then applies domain confusion between PASCAL VOC 2012 and real paintings. These two steps build on a new dataset we gathered called DRAM (Diverse Realism in Art Movements) composed of figurative art paintings from four movements, which are highly diverse in pattern, color, and geometry. To segment new paintings, we present a composite multi-domain adaptation method that trains on each sub-domain separately and composes their solutions during inference time. Our method provides better segmentation results not only on the specific artistic movements of DRAM, but also on other, unseen ones. We compare our approach to alternative methods and show applications of semantic segmentation in art paintings.Item CAST: Character labeling in Animation using Self-supervision by Tracking(The Eurographics Association and John Wiley & Sons Ltd., 2022) Nir, Oron; Rapoport, Gal; Shamir, Ariel; Chaine, Raphaëlle; Kim, Min H.Cartoons and animation domain videos have very different characteristics compared to real-life images and videos. In addition, this domain carries a large variability in styles. Current computer vision and deep-learning solutions often fail on animated content because they were trained on natural images. In this paper we present a method to refine a semantic representation suitable for specific animated content. We first train a neural network on a large-scale set of animation videos and use the mapping to deep features as an embedding space. Next, we use self-supervision to refine the representation for any specific animation style by gathering many examples of animated characters in this style, using a multi-object tracking. These examples are used to define triplets for contrastive loss training. The refined semantic space allows better clustering of animated characters even when they have diverse manifestations. Using this space we can build dictionaries of characters in an animation videos, and define specialized classifiers for specific stylistic content (e.g., characters in a specific animation series) with very little user effort. These classifiers are the basis for automatically labeling characters in animation videos. We present results on a collection of characters in a variety of animation styles.Item Deep Reconstruction of 3D Smoke Densities from Artist Sketches(The Eurographics Association and John Wiley & Sons Ltd., 2022) Kim, Byungsoo; Huang, Xingchang; Wuelfroth, Laura; Tang, Jingwei; Cordonnier, Guillaume; Gross, Markus; Solenthaler, Barbara; Chaine, Raphaëlle; Kim, Min H.Creative processes of artists often start with hand-drawn sketches illustrating an object. Pre-visualizing these keyframes is especially challenging when applied to volumetric materials such as smoke. The authored 3D density volumes must capture realistic flow details and turbulent structures, which is highly non-trivial and remains a manual and time-consuming process. We therefore present a method to compute a 3D smoke density field directly from 2D artist sketches, bridging the gap between early-stage prototyping of smoke keyframes and pre-visualization. From the sketch inputs, we compute an initial volume estimate and optimize the density iteratively with an updater CNN. Our differentiable sketcher is embedded into the end-to-end training, which results in robust reconstructions. Our training data set and sketch augmentation strategy are designed such that it enables general applicability. We evaluate the method on synthetic inputs and sketches from artists depicting both realistic smoke volumes and highly non-physical smoke shapes. The high computational performance and robustness of our method at test time allows interactive authoring sessions of volumetric density fields for rapid prototyping of ideas by novice users.Item Learning from Shader Program Traces(The Eurographics Association and John Wiley & Sons Ltd., 2022) Yang, Yuting; Barnes, Connelly; Finkelstein, Adam; Chaine, Raphaëlle; Kim, Min H.Deep learning for image processing typically treats input imagery as pixels in some color space. This paper proposes instead to learn from program traces of procedural fragment shaders - programs that generate images. At each pixel, we collect the intermediate values computed at program execution, and these data form the input to the learned model. We investigate this learning task for a variety of applications: our model can learn to predict a low-noise output image from shader programs that exhibit sampling noise; this model can also learn from a simplified shader program that approximates the reference solution with less computation, as well as learn the output of postprocessing filters like defocus blur and edge-aware sharpening. Finally we show that the idea of learning from program traces can even be applied to non-imagery simulations of flocks of boids. Our experiments on a variety of shaders show quantitatively and qualitatively that models learned from program traces outperform baseline models learned from RGB color augmented with hand-picked shader-specific features like normals, depth, and diffuse and specular color. We also conduct a series of analyses that show certain features within the trace are more important, and even learning from a small subset of the trace outperforms the baselines.Item The 3D Motorcycle Complex for Structured Volume Decomposition(The Eurographics Association and John Wiley & Sons Ltd., 2022) Brückler, Hendrik; Gupta, Ojaswi; Mandad, Manish; Campen, Marcel; Chaine, Raphaëlle; Kim, Min H.The so-called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2-manifold surfaces. Applications are in the fields of surface parametrization, spline space construction, semi-structured quad mesh generation, or geometry data compression. We describe a generalization of this motorcycle graph concept to the three-dimensional volumetric setting. Through careful extensions aware of topological intricacies of this higher-dimensional setting, we are able to guarantee important block decomposition properties also in this case. We describe algorithms for the construction of this 3D motorcycle complex on the basis of either hexahedral meshes or seamless volumetric parametrizations. Its utility is illustrated on examples in hexahedral mesh generation and volumetric T-spline construction.Item Meshlets and How to Shade Them: A Study on Texture-Space Shading(The Eurographics Association and John Wiley & Sons Ltd., 2022) Neff, Thomas; Mueller, Joerg H.; Steinberger, Markus; Schmalstieg, Dieter; Chaine, Raphaëlle; Kim, Min H.Commonly used image-space layouts of shading points, such as used in deferred shading, are strictly view-dependent, which restricts efficient caching and temporal amortization. In contrast, texture-space layouts can represent shading on all surface points and can be tailored to the needs of a particular application. However, the best grouping of shading points-which we call a shading unit-in texture space remains unclear. Choices of shading unit granularity (how many primitives or pixels per unit) and in shading unit parametrization (how to assign texture coordinates to shading points) lead to different outcomes in terms of final image quality, overshading cost, and memory consumption. Among the possible choices, shading units consisting of larger groups of scene primitives, so-called meshlets, remain unexplored as of yet. In this paper, we introduce a taxonomy for analyzing existing texture-space shading methods based on the group size and parametrization of shading units. Furthermore, we introduce a novel texture-space layout strategy that operates on large shading units: the meshlet shading atlas. We experimentally demonstrate that the meshlet shading atlas outperforms previous approaches in terms of image quality, run-time performance and temporal upsampling for a given number of fragment shader invocations. The meshlet shading atlas lends itself to work together with popular cluster-based rendering of meshes with high geometric detail.Item Learning Spectral Unions of Partial Deformable 3D Shapes(The Eurographics Association and John Wiley & Sons Ltd., 2022) Moschella, Luca; Melzi, Simone; Cosmo, Luca; Maggioli, Filippo; Litany, Or; Ovsjanikov, Maks; Guibas, Leonidas; Rodolà , Emanuele; Chaine, Raphaëlle; Kim, Min H.Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.Item Differentiable 3D CAD Programs for Bidirectional Editing(The Eurographics Association and John Wiley & Sons Ltd., 2022) Cascaval, Dan; Shalah, Mira; Quinn, Phillip; Bodik, Rastislav; Agrawala, Maneesh; Schulz, Adriana; Chaine, Raphaëlle; Kim, Min H.Modern CAD tools represent 3D designs not only as geometry, but also as a program composed of geometric operations, each of which depends on a set of parameters. Program representations enable meaningful and controlled shape variations via parameter changes. However, achieving desired modifications solely through parameter editing is challenging when CAD models have not been explicitly authored to expose select degrees of freedom in advance. We introduce a novel bidirectional editing system for 3D CAD programs. In addition to editing the CAD program, users can directly manipulate 3D geometry and our system infers parameter updates to keep both representations in sync. We formulate inverse edits as a set of constrained optimization objectives, returning plausible updates to program parameters that both match user intent and maintain program validity. Our approach implements an automatically differentiable domain-specific language for CAD programs, providing derivatives for this optimization to be performed quickly on any expressed program. Our system enables rapid, interactive exploration of a constrained 3D design space by allowing users to manipulate the program and geometry interchangeably during design iteration. While our approach is not designed to optimize across changes in geometric topology, we show it is expressive and performant enough for users to produce a diverse set of design variants, even when the CAD program contains a relatively large number of parameters.Item Vectorizing Line Drawings of Arbitrary Thickness via Boundary-based Topology Reconstruction(The Eurographics Association and John Wiley & Sons Ltd., 2022) Zhang, Zibo; Liu, Xueting; Li, Chengze; Wu, Huisi; Wen, Zhenkun; Chaine, Raphaëlle; Kim, Min H.Vectorization is a commonly used technique for converting raster images to vector format and has long been a research focus in computer graphics and vision. While a number of attempts have been made to extract the topology of line drawings and further convert them to vector representations, the existing methods commonly focused on resolving junctions composed of thin lines. They usually fail for line drawings composed of thick lines, especially at junctions. In this paper, we propose an automatic line drawing vectorization method that can reconstruct the topology of line drawings of arbitrary thickness. Our key observation is that no matter the lines are thin or thick, the boundaries of the lines always provide reliable hints for reconstructing the topology. For example, the boundaries of two continuous line segments at a junction are usually smoothly connected. By analyzing the continuity of boundaries, we can better analyze the topology at junctions. In particular, we first extract the skeleton of the input line drawing via thinning. Then we analyze the reliability of the skeleton points based on boundaries. Reliable skeleton points are preserved while unreliable skeleton points are reconstructed based on boundaries again. Finally, the skeleton after reconstruction is vectorized as the output. We apply our method on line drawings of various contents and styles. Satisfying results are obtained. Our method significantly outperforms existing methods for line drawings composed of thick lines.