The construction of networks of maps among shapes in a collection enables a variety of applications in data-driven geometry processing. A key task in network construction is to make the maps consistent with each other. This consistency constraint, when properly defined, leads not only to a concise representation of such networks, but more importantly, it serves as a strong regularizer for correcting and improving noisy initial maps computed between pairs of shapes in isolation. Up-to-now, however, the consistency constraint has only been fully formulated for point-based maps or for shape collections that are fully similar. In this paper, we introduce a framework for computing consistent functional maps within heterogeneous shape collections. In such collections not all shapes share the same structure --- different types of shared structure may be present within different (but possibly overlapping) sub-collections. Unlike point-based maps, functional maps can encode similarities at multiple levels of detail (points or parts), and thus are particularly suitable for coping with such diversity within a shape collection. We show how to rigorously formulate the consistency constraint in the functional map setting. The formulation leads to a powerful tool for computing consistent functional maps, and also for discovering shared structures, such as meaningful shape parts. We also show how to adapt the procedure for handling very large-scale shape collections. Experimental results on benchmark datasets show that the proposed framework significantly improves upon state-of-the-art data-driven techniques. We demonstrate the usefulness of the framework in shape co-segmentation and various shape exploration tasks.

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Functional map networks for analyzing and exploring large shape collections

Shape structure is about the arrangement and relations between shape parts. Structure-aware shape processing goes beyond local geometry and low level processing, and analyzes and processes shapes at a high level. It focuses more on the global inter and intra semantic relations among the parts of shape rather than on their local geometry.With recent developments in easy shape acquisition, access to vast repositories of 3D models, and simple-to-use desktop fabrication possibilities, the study of structure in shapes has become a central research topic in shape analysis, editing, and modeling. A whole new line of structure-aware shape processing algorithms has emerged that base their operation on an attempt to understand such structure in shapes. The algorithms broadly consist of two key phases: an analysis phase, which extracts structural information from input data; and a (smart) processing phase, which utilizes the extracted information for exploration, editing, and synthesis of novel shapes.In this course, we will organize, summarize, and present the key concepts and methodological approaches towards efficient structure-aware shape processing. We discuss common models of structure, their implementation in terms of mathematical formalism and algorithms, and explain the key principles in the context of a number of state-of-the-art approaches. Further, we attempt to list the key open problems and challenges, both at the technical and at the conceptual level, to make it easier for new researchers to better explore and contribute to this topic.Our goal is to both give the practitioner an overview of available structure-aware shape processing techniques, as well as identify future research questions in this important, emerging, and fascinating research area.

/pdf/structure-aware-shape-processing-1evxd0ycj0.pdf

Structure-aware shape processing

3D modeling remains a notoriously difficult task for novices despite significant research effort to provide intuitive and automated systems. We tackle this problem by combining the strengths of two popular domains: sketch-based modeling and procedural modeling. On the one hand, sketch-based modeling exploits our ability to draw but requires detailed, unambiguous drawings to achieve complex models. On the other hand, procedural modeling automates the creation of precise and detailed geometry but requires the tedious definition and parameterization of procedural models. Our system uses a collection of simple procedural grammars, called snippets, as building blocks to turn sketches into realistic 3D models. We use a machine learning approach to solve the inverse problem of finding the procedural model that best explains a user sketch. We use non-photorealistic rendering to generate artificial data for training convolutional neural networks capable of quickly recognizing the procedural rule intended by a sketch and estimating its parameters. We integrate our algorithm in a coarse-to-fine urban modeling system that allows users to create rich buildings by successively sketching the building mass, roof, facades, windows, and ornaments. A user study shows that by using our approach non-expert users can generate complex buildings in just a few minutes.

/pdf/interactive-sketching-of-urban-procedural-models-4gl22idosz.pdf

Interactive sketching of urban procedural models

We propose a method for reconstructing 3D shapes from 2D sketches in the form of line drawings. Our method takes as input a single sketch, or multiple sketches, and outputs a dense point cloud representing a 3D reconstruction of the input sketch(es). The point cloud is then converted into a polygon mesh. At the heart of our method lies a deep, encoder-decoder network. The encoder converts the sketch into a compact representation encoding shape information. The decoder converts this representation into depth and normal maps capturing the underlying surface from several output viewpoints. The multi-view maps are then consolidated into a 3D point cloud by solving an optimization problem that fuses depth and normals across all viewpoints. Based on our experiments, compared to other methods, such as volumetric networks, our architecture offers several advantages, including more faithful reconstruction, higher output surface resolution, better preservation of topology and shape structure.

3D Shape Reconstruction from Sketches via Multi-view Convolutional Networks

Sketching in immersive 3D virtual reality (VR) environments has great potential for a variety of interactive 3D design applications. Precisely sketching the intended strokes in mid-air, however, can be a challenge. In this paper, we present a set of controlled studies to analyze the factors affecting human ability to sketch freely in a 3D VR environment. In our first study, we directly compare traditional sketching on a physical surface to sketching in VR, with and without a physical surface to rest the stylus on. Our results indicate that the lack of a physical drawing surface is a major cause of inaccuracies in VR drawing, and that the effect is dependent on the orientation of the drawing surface. In a second experiment, we evaluate the extent to which visual guidance can compensate for the loss of sketching precision in VR. We found that while additional visual guidance improves positional accuracy, it can be detrimental to the aesthetic quality of strokes. We conclude by distilling our experimental findings into design guidelines for sketching tools in immersive 3D environments.

Experimental Evaluation of Sketching on Surfaces in VR

True2Form is a sketch-based modeling system that reconstructs 3D curves from typical design sketches. Our approach to infer 3D form from 2D drawings is a novel mathematical framework of insights derived from perception and design literature. We note that designers favor viewpoints that maximally reveal 3D shape information, and strategically sketch descriptive curves that convey intrinsic shape properties, such as curvature, symmetry, or parallelism. Studies indicate that viewers apply these properties selectively to envision a globally consistent 3D shape. We mimic this selective regularization algorithmically, by progressively detecting and enforcing applicable properties, accounting for their global impact on an evolving 3D curve network. Balancing regularity enforcement against sketch fidelity at each step allows us to correct for inaccuracy inherent in free-hand sketching. We perceptually validate our approach by showing agreement between our algorithm and viewers in selecting applicable regularities. We further evaluate our solution by: reconstructing a range of 3D models from diversely sourced sketches; comparisons to prior art; and visual comparison to both ground-truth and 3D reconstructions by designers.

https://hal.inria.fr/hal-01060850/document

True2Form: 3D curve networks from 2D sketches via selective regularization

A method is for estimating a three-dimensional (3D) representation of a set of two-dimensional (2D) curves of a concept drawing, the estimate of the 3D representation corresponding to a 3D object underlying the concept drawing. The method comprises: obtaining a representation of a set of 2D curves a concept drawing that represent a 3D object underlying the concept drawing; determining an energy function based on the set of 2D curves, the energy function comprising one or more terms, each term reflective of a preference for a 3D representation based on a characteristic of the 2D curves which reflects how concept drawings are commonly perceived to represent 3D objects; and performing an optimization which minimizes the energy function to thereby determine the 3D representation.

Baoxuan Xu

Papers

True2Form: 3D curve networks from 2D sketches via selective regularization

Methods and systems for estimating three-dimensional information from two-dimensional concept drawings