Topology Preserving Simplification of Medial Axes in 3D Models

We propose an efficient method for topology‐preserving simplification of medial axes of 3D models. Existing methods either cannot preserve the topology during medial axes simplification or have the problem of being geometrically inaccurate or computationally expensive. To tackle these issues, we restrict our topology‐checking to the areas around the topological holes to avoid unnecessary checks in other areas. Our algorithm can keep high precision even when the medial axis is simplified to be in very few vertices. Furthermore, we parallelize the medial axes simplification procedure to enhance the performance significantly. Experimental results show that our method can preserve the topology with highly efficient performance, much superior to the existing methods in terms of topology preservation, accuracy and performance.     

Scalable and Efficient Functional Map Computations on Dense Meshes

We propose a new scalable version of the functional map pipeline that allows to efficiently compute correspondences between potentially very dense meshes. Unlike existing approaches that process dense meshes by relying on ad-hoc mesh simplification, we establish an integrated end-to-end pipeline with theoretical approximation analysis. In particular, our method overcomes the computational burden of both computing the basis, as well the functional and pointwise correspondence computation by approximating the functional spaces and the functional map itself. Errors in the approximations are controlled by theoretical upper bounds assessing the range of applicability of our pipeline. With this construction in hand, we propose a scalable practical algorithm and demonstrate results on dense meshes, which approximate those obtained by standard functional map algorithms at the fraction of the computation time. Moreover, our approach outperforms the standard acceleration procedures by a large margin, leading to accurate results even in challenging cases.     

Practical Foldover‐Free Volumetric Mapping Construction

In this paper, we present a practically robust method for computing foldover‐free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non‐trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high‐quality foldover‐free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh‐based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.     

Procedural Modeling of a Building from a Single Image

Creating a virtual city is demanded for computer games, movies, and urban planning, but it takes a lot of time to create numerous 3D building models. Procedural modeling has become popular in recent years to overcome this issue, but creating a grammar to get a desired output is difficult and time consuming even for expert users. In this paper, we present an interactive tool that allows users to automatically generate such a grammar from a single image of a building. The user selects a photograph and highlights the silhouette of the target building as input to our method. Our pipeline automatically generates the building components, from large‐scale building mass to fine‐scale windows and doors geometry. Each stage of our pipeline combines convolutional neural networks (CNNs) and optimization to select and parameterize procedural grammars that reproduce the building elements of the picture. In the first stage, our method jointly estimates camera parameters and building mass shape. Once known, the building mass enables the rectification of the façades, which are given as input to the second stage that recovers the façade layout. This layout allows us to extract individual windows and doors that are subsequently fed to the last stage of the pipeline that selects procedural grammars for windows and doors. Finally, the grammars are combined to generate a complete procedural building as output. We devise a common methodology to make each stage of this pipeline tractable. This methodology consists in simplifying the input image to match the visual appearance of synthetic training data, and in using optimization to refine the parameters estimated by CNNs. We used our method to generate a variety of procedural models of buildings from existing photographs.     

Multi‐Pose Interactive Linkage Design

We introduce an interactive tool for novice users to design mechanical objects made of 2.5D linkages. Users simply draw the shape of the object and a few key poses of its multiple moving parts. Our approach automatically generates a one‐degree‐of freedom linkage that connects the fixed and moving parts, such that the moving parts traverse all input poses in order without any collision with the fixed and other moving parts. In addition, our approach avoids common linkage defects and favors compact linkages and smooth motion trajectories. Finally, our system automatically generates the 3D geometry of the object and its links, allowing the rapid creation of a physical mockup of the designed object.     

Feature Curve Co‐Completion in Noisy Data

Feature curves on 3D shapes provide important hints about significant parts of the geometry and reveal their underlying structure. However, when we process real world data, automatically detected feature curves are affected by measurement uncertainty, missing data, and sampling resolution, leading to noisy, fragmented, and incomplete feature curve networks. These artifacts make further processing unreliable. In this paper we analyze the global co‐occurrence information in noisy feature curve networks to fill in missing data and suppress weakly supported feature curves. For this we propose an unsupervised approach to find meaningful structure within the incomplete data by detecting multiple occurrences of feature curve configurations (co‐occurrence analysis). We cluster and merge these into feature curve templates, which we leverage to identify strongly supported feature curve segments as well as to complete missing data in the feature curve network. In the presence of significant noise, previous approaches had to resort to user input, while our method performs fully automatic feature curve co‐completion. Finding feature reoccurrences however, is challenging since naïve feature curve comparison fails in this setting due to fragmentation and partial overlaps of curve segments. To tackle this problem we propose a robust method for partial curve matching. This provides us with the means to apply symmetry detection methods to identify co‐occurring configurations. Finally, Bayesian model selection enables us to detect and group re‐occurrences that describe the data well and with low redundancy.     

Global Texture Mapping for Dynamic Objects

We propose a novel framework to generate a global texture atlas for a deforming geometry. Our approach distinguishes from prior arts in two aspects. First, instead of generating a texture map for each timestamp to color a dynamic scene, our framework reconstructs a global texture atlas that can be consistently mapped to a deforming object. Second, our approach is based on a single RGB‐D camera, without the need of a multiple‐camera setup surrounding a scene. In our framework, the input is a 3D template model with an RGB‐D image sequence, and geometric warping fields are found using a state‐of‐the‐art non‐rigid registration method [GXW*15] to align the template mesh to noisy and incomplete input depth images. With these warping fields, our multi‐scale approach for texture coordinate optimization generates a sharp and clear texture atlas that is consistent with multiple color observations over time. Our approach is accelerated by graphical hardware and provides a handy configuration to capture a dynamic geometry along with a clean texture atlas. We demonstrate our approach with practical scenarios, particularly human performance capture. We also show that our approach is resilient on misalignment issues caused by imperfect estimation of warping fields and inaccurate camera parameters.     

Hierarchical Functional Maps between Subdivision Surfaces

We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multi‐resolution spectral basis functions that are open used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high‐resolution sculpting displacement maps and textures between subdivision models.     

Improved Functional Mappings via Product Preservation

In this paper, we consider the problem of information transfer across shapes and propose an extension to the widely used functional map representation. Our main observation is that in addition to the vector space structure of the functional spaces, which has been heavily exploited in the functional map framework, the functional algebra (i.e., the ability to take pointwise products of functions) can significantly extend the power of this framework. Equipped with this observation, we show how to improve one of the key applications of functional maps, namely transferring real‐valued functions without conversion to point‐to‐point correspondences. We demonstrate through extensive experiments that by decomposing a given function into a linear combination consisting not only of basis functions but also of their pointwise products, both the representation power and the quality of the function transfer can be improved significantly. Our modification, while computationally simple, allows us to achieve higher transfer accuracy while keeping the size of the basis and the functional map fixed. We also analyze the computational complexity of optimally representing functions through linear combinations of products in a given basis and prove NP‐completeness in some general cases. Finally, we argue that the use of function products can have a wide‐reaching effect in extending the power of functional maps in a variety of applications, in particular by enabling the transfer of high‐frequency functions without changing the representation size or complexity.     

Computing Surface PolyCube‐Maps by Constrained Voxelization

We present a novel method to compute bijective PolyCube‐maps with low isometric distortion. Given a surface and its pre‐axis‐aligned shape that is not an exact PolyCube shape, the algorithm contains two steps: (i) construct a PolyCube shape to approximate the pre‐axis‐aligned shape; and (ii) generate a bijective, low isometric distortion mapping between the constructed PolyCube shape and the input surface. The PolyCube construction is formulated as a constrained optimization problem, where the objective is the number of corners in the constructed PolyCube, and the constraint is to bound the approximation error between the constructed PolyCube and the input pre‐axis‐aligned shape while ensuring topological validity. A novel erasing‐and‐filling solver is proposed to solve this challenging problem. Centeral to the algorithm for computing bijective PolyCube‐maps is a quad mesh optimization process that projects the constructed PolyCube onto the input surface with high‐quality quads. We demonstrate the efficacy of our algorithm on a data set containing 300 closed meshes. Compared to state‐of‐the‐art methods, our method achieves higher practical robustness and lower mapping distortion.     

Object Partitioning for Support‐Free 3D‐Printing

Fused deposition modeling based 3D‐printing is becoming increasingly popular due to it's low‐cost and simple operation and maintenance. While it produces rugged prints made from a wide range of materials, it suffers from an inherent printing limitation where it cannot produce overhanging surfaces of non‐trivial size. This limitation can be handled by constructing temporary support‐structures, however this solution involves additional material costs, longer print time, and often a fair amount of labor in removing it. In this paper we present a new method for partitioning general solid objects into a small number of parts that can be printed with no support. The partitioning is computed by applying a sequence of cutting‐planes that split the object recursively. Unlike existing algorithms, the planes are not chosen at random, rather they are derived from shape analysis routines that identify and resolve various commonly‐found geometric configurations. In addition, we guide this search by a revised set of conditions that both ensure the objects' printability as well as realistically model the printing capabilities of the printer at hand. Evaluation of the new method demonstrates its ability to efficiently obtain support‐free partitionings typically containing fewer parts compared to existing methods that rely on support‐structures.     

Limit Shapes – A Tool for Understanding Shape Differences and Variability in 3D Model Collections

We propose a novel construction for extracting a central or limit shape in a shape collection, connected via a functional map network. Our approach is based on enriching the latent space induced by a functional map network with an additional natural metric structure. We call this shape‐like dual object the limit shape and show that its construction avoids many of the biases introduced by selecting a fixed base shape or template. We also show that shape differences between real shapes and the limit shape can be computed and characterize the unique properties of each shape in a collection – leading to a compact and rich shape representation. We demonstrate the utility of this representation in a range of shape analysis tasks, including improving functional maps in difficult situations through the mediation of limit shapes, understanding and visualizing the variability within and across different shape classes, and several others. In this way, our analysis sheds light on the missing geometric structure in previously used latent functional spaces, demonstrates how these can be addressed and finally enables a compact and meaningful shape representation useful in a variety of practical applications.     

Learning Fuzzy Set Representations of Partial Shapes on Dual Embedding Spaces

Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of predefined semantic parts. We propose a novel framework based on neural networks that analyzes an uncurated collection of 3D models from the same category and learns two important types of semantic relations among full and partial shapes: complementarity and interchangeability. The former helps to identify which two partial shapes make a complete plausible object, and the latter indicates that interchanging two partial shapes from different objects preserves the object plausibility. Our key idea is to jointly encode both relations by embedding partial shapes as fuzzy sets in dual embedding spaces. We model these two relations as fuzzy set operations performed across the dual embedding spaces, and within each space, respectively. We demonstrate the utility of our method for various retrieval tasks that are commonly needed in geometric modeling interfaces.     

Distribution Update of Deformable Patches for Texture Synthesis on the Free Surface of Fluids

We propose an approach for temporally coherent patch‐based texture synthesis on the free surface of fluids. Our approach is applied as a post‐process, using the surface and velocity field from any fluid simulator. We apply the texture from the exemplar through multiple local mesh patches fitted to the surface and mapped to the exemplar. Our patches are constructed from the fluid free surface by taking a subsection of the free surface mesh. As such, they are initially very well adapted to the fluid's surface, and can later deform according to the free surface velocity field, allowing a greater ability to represent surface motion than rigid or 2D grid‐based patches. From one frame to the next, the patch centers and surrounding patch vertices are advected according to the velocity field. We seek to maintain a Poisson disk distribution of patches, and following advection, the Poisson disk criterion determines where to add new patches and which patches should e flagged for removal. The removal considers the local number of patches: in regions containing too many patches, we accelerate the temporal removal. This reduces the number of patches while still meeting the Poisson disk criterion. Reducing areas with too many patches speeds up the computation and avoids patch‐blending artifacts. The final step of our approach creates the overall texture in an atlas where each texel is computed from the patches using a contrast‐preserving blending function. Our tests show that the approach works well on free surfaces undergoing significant deformation and topological changes. Furthermore, we show that our approach provides good results for many fluid simulation scenarios, and with many texture exemplars. We also confirm that the optical flow from the resulting texture matches the fluid velocity field. Overall, our approach compares favorably against recent work in this area.     

Terrain Super‐resolution through Aerial Imagery and Fully Convolutional Networks

Despite recent advances in surveying techniques, publicly available Digital Elevation Models (DEMs) of terrains are low‐resolution except for selected places on Earth. In this paper we present a new method to turn low‐resolution DEMs into plausible and faithful high‐resolution terrains. Unlike other approaches for terrain synthesis/amplification (fractal noise, hydraulic and thermal erosion, multi‐resolution dictionaries), we benefit from high‐resolution aerial images to produce highly‐detailed DEMs mimicking the features of the real terrain. We explore different architectures for Fully Convolutional Neural Networks to learn upsampling patterns for DEMs from detailed training sets (high‐resolution DEMs and orthophotos), yielding up to one order of magnitude more resolution. Our comparative results show that our method outperforms competing data amplification approaches in terms of elevation accuracy and terrain plausibility.     

Functionality Representations and Applications for Shape Analysis

A central goal of computer graphics is to provide tools for designing and simulating real or imagined artifacts. An understanding of functionality is important in enabling such modeling tools. Given that the majority of man‐made artifacts are designed to serve a certain function, the functionality of objects is often reflected by their geometry, the way that they are organized in an environment, and their interaction with other objects or agents. Thus, in recent years, a variety of methods in shape analysis have been developed to extract functional information about objects and scenes from these different types of cues. In this report, we discuss recent developments that incorporate functionality aspects into the analysis of 3D shapes and scenes. We provide a summary of the state‐of‐the‐art in this area, including a discussion of key ideas and an organized review of the relevant literature. More specifically, the report is structured around a general definition of functionality from which we derive criteria for classifying the body of prior work. This definition also facilitates a comparative view of methods for functionality analysis. We focus on studying the inference of functionality from a geometric perspective, and pose functionality analysis as a process involving both the geometry and interactions of a functional entity. In addition, we discuss a variety of applications that benefit from an analysis of functionality, and conclude the report with a discussion of current challenges and potential future works.     

Reliable Rolling‐guided Point Normal Filtering for Surface Texture Removal

Semantic surface decomposition (SSD) facilitates various geometry processing and product re‐design tasks. Filter‐based techniques are meaningful and widely used to achieve the SSD, which however often leads to surface either under‐fitting or over‐fitting. In this paper, we propose a reliable rolling‐guided point normal filtering method to decompose textures from a captured point cloud surface. Our method is built on the geometry assumption that 3D surfaces are comprised of an underlying shape (US) and a variety of bump ups and downs (BUDs) on the US. We have three core contributions. First, by considering the BUDs as surface textures, we present a RANSAC‐based sub‐neighborhood detection scheme to distinguish the US and the textures. Second, to better preserve the US (especially the prominent structures), we introduce a patch shift scheme to estimate the guidance normal for feeding the rolling‐guided filter. Third, we formulate a new position updating scheme to alleviate the common uneven distribution of points. Both visual and numerical experiments demonstrate that our method is comparable to state‐of‐the‐art methods in terms of the robustness of texture removal and the effectiveness of the underlying shape preservation.     

Aura Mesh: Motion Retargeting to Preserve the Spatial Relationships between Skinned Characters

Applying motion‐capture data to multi‐person interaction between virtual characters is challenging because one needs to preserve the interaction semantics while also satisfying the general requirements of motion retargeting, such as preventing penetration and preserving naturalness. An efficient means of representing interaction semantics is by defining the spatial relationships between the body parts of characters. However, existing methods consider only the character skeleton and thus are not suitable for capturing skin‐level spatial relationships. This paper proposes a novel method for retargeting interaction motions with respect to character skins. Specifically, we introduce the aura mesh, which is a volumetric mesh that surrounds a character's skin. The spatial relationships between two characters are computed from the overlap of the skin mesh of one character and the aura mesh of the other, and then the interaction motion retargeting is achieved by preserving the spatial relationships as much as possible while satisfying other constraints. We show the effectiveness of our method through a number of experiments.