Strip-decomposable quadrilateral (SDQ) meshes, i.e., quad meshes that can be decomposed into two transversal strip networks, are vital in numerous fabrication processes; examples include woven structures, surfaces from sheets, custom rebar, or cable-net structures. However, their design is often challenging and includes tedious manual work, and there is a lack of methodologies for editing such meshes while preserving their strip decomposability. We present an interactive methodology to generate and edit SDQ meshes aligned to user-defined directions, while also incorporating desirable properties to the strips for fabrication. Our technique is based on the computation of two coupled transversal tangent direction fields, integrated into two overlapping networks of strips on the surface. As a case study, we consider the fabrication scenario of robotic non-planar 3D printing of free-form surfaces and apply the presented methodology to design and fabricate non-planar print paths.

Smooth curves and surfaces can be characterized as minimizers of squared curvature bending energies subject to constraints. In the univariate case with an isometry (length) constraint this leads to classic non-linear splines. For surfaces, isometry is too rigid a constraint and instead one asks for minimizers of the Willmore (squared mean curvature) energy subject to a conformality constraint. We present an efficient algorithm for (conformally) constrained Willmore surfaces using triangle meshes of arbitrary topology with or without boundary. Our conformal class constraint is based on the discrete notion of conformal equivalence of triangle meshes. The resulting non-linear constrained optimization problem can be solved efficiently using the competitive gradient descent method together with appropriate Sobolev metrics. The surfaces can be represented either through point positions or differential coordinates. The latter enable the realization of abstract metric surfaces without an initial immersion. A versatile toolkit for extrinsic conformal geometry processing, suitable for the construction and manipulation of smooth surfaces, results through the inclusion of additional point, area, and volume constraints.

Real-life man-made objects often exhibit strong and easily-identifiable structure, as a direct result of their design or their intended functionality. Structure typically appears in the form of individual parts and their arrangement. Knowing about object structure can be an important cue for object recognition and scene understanding - a key goal for various AR and robotics applications. However, commodity RGB-D sensors used in these scenarios only produce raw, unorganized point clouds, without structural information about the captured scene. Moreover, the generated data is commonly partial and susceptible to artifacts and noise, which makes inferring the structure of scanned objects challenging. In this paper, we organize large shape collections into parameterized shape templates to capture the underlying structure of the objects. The templates allow us to transfer the structural information onto new objects and incomplete scans. We employ a deep neural network that matches the partial scan with one of the shape templates, then match and fit it to complete and detailed models from the collection. This allows us to faithfully label its parts and to guide the reconstruction of the scanned object. We showcase the effectiveness of our method by comparing it to other state-of-the-art approaches.

Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep AutoEncoder (AE) network with state-of-the-art reconstruction quality and generalization ability. The learned representations outperform existing methods on 3D recognition tasks and enable shape editing via simple algebraic manipulations, such as semantic part editing, shape analogies and shape interpolation, as well as shape completion. We perform a thorough study of different generative models including GANs operating on the raw point clouds, significantly improved GANs trained in the fixed latent space of our AEs, and Gaussian Mixture Models (GMMs). To quantitatively evaluate generative models we introduce measures of sample fidelity and diversity based on matchings between sets of point clouds. Interestingly, our evaluation of generalization, fidelity and diversity reveals that GMMs trained in the latent space of our AEs yield the best results overall.

Abstract We consider the problem of transporting shape descriptors across shapes in a collection in a modular fashion, in order to establish correspondences between them. A common goal when mapping between multiple shapes is consistency, namely that compositions of maps along a cycle of shapes should be approximately an identity map. Existing attempts to enforce consistency typically require recomputing correspondences whenever a new shape is added to the collection, which can quickly become intractable. Instead, we propose an approach that is fully modular, where the bulk of the computation is done on each shape independently. To achieve this, we use intermediate nonlinear embedding spaces, computed individually on every shape; the embedding functions use ideas from diffusion geometry and capture how different descriptors on the same shape inter‐relate. We then establish linear mappings between the different embedding spaces, via a shared latent space. The introduction of nonlinear embeddings allows for more nuanced correspondences, while the modularity of the construction allows for parallelizable calculation and efficient addition of new shapes. We compare the performance of our framework to standard functional correspondence techniques and showcase the use of this framework to simple interpolation and extrapolation tasks.

Abstract Spectral mesh analysis and processing methods, namely ones that utilize eigenvalues and eigenfunctions of linear operators on meshes, have been applied to numerous geometric processing applications. The operator used predominantly in these methods is the Laplace‐Beltrami operator, which has the often‐cited property that it is intrinsic, namely invariant to isometric deformation of the underlying geometry, including rigid transformations. Depending on the application, this can be either an advantage or a drawback. Recent work has proposed the alternative of using the Dirac operator on surfaces for spectral processing. The available versions of the Dirac operator either only focus on the extrinsic version, or introduce a range of mixed operators on a spectrum between fully extrinsic Dirac operator and intrinsic Laplace operator. In this work, we introduce a unified discretization scheme that describes both an extrinsic and intrinsic Dirac operator on meshes, based on their continuous counterparts on smooth manifolds. In this discretization, both operators are very closely related, and preserve their key properties from the smooth case. We showcase various applications of our operators, with improved numerics over prior work.

Many real-world tasks for autonomous agents benefit from understanding dynamic inter-object interactions. Detecting, analyzing and differentiating between the various ways that an object can be interacted with provides implicit information about its function. This can help train autonomous agents to handle objects and understand unknown scenes. We describe a general mathematical framework to analyze and classify interactions, defined as dynamic motions performed by an active object onto a passive one. We factorize interactions via motion features computed in the spatio-temporal domain, and encoded into a global, object-centric signature. Equipped with a similarity measure to compare such signatures, we showcase classification of interactions with a single object. We also propose a novel acquisition setup combining RGBD sensing with a virtual reality (VR) display, to capture interactions with purely virtual objects.

Abstract Direction fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector‐set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This report provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges.

This paper describes human classifiers that are 'viewpoint specific', meaning specific to subjects being observed by a particular camera in a particular scene. The advantages of the approach are (a) improved human detection in the presence of perspective foreshortening from an elevated camera, (b) ability to handle partial occlusion of subjects e.g. partial occlusion by furniture in an indoor scene, and (c) ability to detect subjects when partially truncated at the top, bottom or sides of the image. Elevated camera views will typically generate truncated views for subjects at the image edges but our viewpoint specific method handles such cases and thereby extends overall detection coverage. The approach is - (a) define a tiling on the ground plane of the 3D scene, (b) generate training images per tile using virtual humans, (c) train a classifier per tile (d) run the classifiers on the real scene. The approach would be prohibitive if each new deployment required real training images, but it is feasible because training is done with a virtual humans inserted into a scene model. The classifier is a linear SVM and HOGs. Experimental results provide a comparative analysis with existing algorithms to demonstrate the advantages described above.

Abstract In the digital world, assigning arbitrary colors to an object is a simple operation thanks to texture mapping. However, in the real world, the same basic function of applying colors onto an object is far from trivial. One can specify colors during the fabrication process using a color 3D printer, but this does not apply to already existing objects. Paint and decals can be used during post‐fabrication, but they are challenging to apply on complex shapes. In this paper, we develop a method to enable texture mapping of physical objects, that is, we allow one to map an arbitrary color image onto a three‐dimensional object. Our approach builds upon hydrographics, a technique to transfer pigments printed on a sheet of polymer onto curved surfaces. We first describe a setup that makes the traditional water transfer printing process more accurate and consistent across prints. We then simulate the transfer process using a specialized parameterization to estimate the mapping between the planar color map and the object surface. We demonstrate that our approach enables the application of detailed color maps onto complex shapes such as 3D models of faces and anatomical casts.

Editing materials in photos opens up numerous opportunities like turning an unappealing dirt ground into luscious grass and creating a comfortable wool sweater in place of a cheap t-shirt. However, such edits are challenging. Approaches such as 3D rendering and BTF rendering can represent virtually everything, but they are also data intensive and computationally expensive, which makes user interaction difficult. Leaner methods such as texture synthesis are more easily controllable by artists, but also more limited in the range of materials that they handle, for example, grass and wool are typically problematic because of their non-Lambertian reflectance and numerous self-occlusions. We propose a new approach for editing of complex materials in photographs. We extend the texture-by-numbers approach with ideas from texture interpolation. The inputs to our method are coarse user annotation maps that specify the desired output, such as the local scale of the material and the illumination direction. Our algorithm then synthesizes the output from a discrete set of annotated exemplars. A key component of our method is that it can cope with missing data, interpolating information from the available exemplars when needed. This enables production of satisfying results involving materials with complex appearance variations such as foliage, carpet, and fabric from only one or a couple of exemplar photographs.

We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locally-defined scalar functions, and this property is beneficial for creating surface parameterizations, since the gradients of the parameterization coordinate functions are then exactly aligned with the designed fields. We introduce a novel definition for discrete curl between unordered sets of vectors (PolyVectors), and devise a curl-eliminating continuous optimization that is independent of the matchings between them. Our algorithm naturally places the singularities required to satisfy the user-provided alignment constraints, and our fields are the gradients of an inversion-free parameterization by design.

A pervasive artifact that occurs when visualizing 3D content is the so-called "cardboarding" effect, where objects appear flat due to depth compression, with relatively little research conducted to perceptually quantify its effects. Our aim is to shed light on the subjective preferences and practical perceptual limits of stereo vision with respect to cardboarding. We present three experiments that explore the consequences of displaying simple scenes with reduced depths using both subjective ratings and adjustments and objective sensitivity metrics. Our results suggest that compressing depth to 80% or above is likely to be acceptable, whereas sensitivity to the cardboarding artifact below 30% is very high. These values could be used in practice as guidelines for commonplace depth mapping operations in 3D production pipelines.

Abstract We introduce N‐PolyVector fields, a generalization of N‐RoSy fields for which the vectors are neither necessarily orthogonal nor rotationally symmetric. We formally define a novel representation for N‐PolyVectors as the root sets of complex polynomials and analyze their topological and geometric properties. A smooth N‐PolyVector field can be efficiently generated by solving a sparse linear system without integer variables. We exploit the flexibility of N‐PolyVector fields to design conjugate vector fields, offering an intuitive tool to generate planar quadrilateral meshes.

We consider the problem of generalizing affine combinations in Euclidean spaces to triangle meshes: computing weighted averages of points on surfaces. We address both the forward problem , namely computing an average of given anchor points on the mesh with given weights, and the inverse problem , which is computing the weights given anchor points and a target point. Solving the forward problem on a mesh enables applications such as splines on surfaces, Laplacian smoothing and remeshing. Combining the forward and inverse problems allows us to define a correspondence mapping between two different meshes based on provided corresponding point pairs, enabling texture transfer, compatible remeshing, morphing and more. Our algorithm solves a single instance of a forward or an inverse problem in a few microseconds. We demonstrate that anchor points in the above applications can be added/removed and moved around on the meshes at interactive framerates, giving the user an immediate result as feedback.

This paper presents results achieved in the frames of a national research project (titled ldquoDIANOEMArdquo), where visual analysis and sign recognition techniques have been explored on Greek Sign Language (GSL) data. Besides GSL modelling, the aim was to develop a pilot application for teleoperating a mobile robot using natural hand signs. A small vocabulary of hand signs has been designed to enable desktopbased teleoperation at a high-level of supervisory telerobotic control. Real-time visual recognition of the hand images is performed by training a multi-layer perceptron (MLP) neural network. Various shape descriptors of the segmented hand posture images have been explored as inputs to the MLP network. These include Fourier shape descriptors on the contour of the segmented hand sign images, moments, compactness, eccentricity, and histogram of the curvature. We have examined which of these shape descriptors are best suited for real-time recognition of hand signs, in relation to the number and choice of hand postures, in order to achieve maximum recognition performance. The hand-sign recognizer has been integrated in a graphical user interface, and has been implemented with success on a pilot application for real-time desktop-based gestural teleoperation of a mobile robot vehicle.

Reliable segmentation and motion tracking algorithms are required to achieve gesture detection and tracking for human-machine interaction. In this paper we present an efficient method for detecting and tracking moving hands in sign language video frames. We make use of the geodesic active region framework in conjunction with new color and motion forces; color information is provided by a skin color model, while motion information is derived from the optical flow field. Extensive experimentation indicates that the proposed algorithm behaves sufficiently well for gesture detection and tracking.