### Eigenmode Compression for Modal Sound Models

"... vertices, and consumes 186 MB. By approximating each eigenmode with moving least squares (MLS), and nonlinearly optimizing the control points (shown in white), we compressed the entire model down to 3.1 MB—a 60:1 compression ratio—with negligible audible difference. (Middle) mode #17 (2.67 kHz, 276 ..."

Abstract
- Add to MetaCart

vertices, and consumes 186 MB. By approximating each eigenmode with moving least squares (MLS), and nonlinearly optimizing the control points (shown in white), we compressed the entire model down to 3.1 MB—a 60:1 compression ratio—with negligible audible difference. (Middle) mode #17 (2.67 kHz, 276 MLS control points), (Right) mode #53 (5.21 kHz, 610 MLS control points). We propose and evaluate a method for significantly compressing modal sound models, thereby making them far more practical for audiovisual applications. The dense eigenmode matrix, needed to compute the sound model’s response to contact forces, can consume tens to thousands of megabytes depending on mesh resolution and mode count. Our eigenmode compression pipeline is based on non-linear optimization of Moving Least Squares (MLS) approxima-tions. Enhanced compression is achieved by exploiting symmetry both within and between eigenmodes, and by adaptively assigning per-mode error levels based on human perception of the far-field pressure amplitudes. Our method provides smooth eigenmode ap-proximations, and efficient random access. We demonstrate that, in many cases, hundredfold compression ratios can be achieved with-out audible degradation of the rendered sound.

### Characterization of Partial Intrinsic Symmetries

"... Abstract. We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry pro-cessing algorithms. Our goal is to compute all “significant ” symmetry information of the shape, ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry pro-cessing algorithms. Our goal is to compute all “significant ” symmetry information of the shape, which we define as r-symmetries, i.e., we re-port all isometric self-maps within subsets of the shape that contain at least an intrinsic circle or radius r. By specifying r, the user has direct control over the scale at which symmetry should be detected. Unlike previous techniques, we do not rely on feature points, voting or proba-bilistic schemes. Rather than that, we bound computational efforts by splitting our algorithm into two phases. The first detects infinitesimal r-symmetries directly using a local differential analysis, and the sec-ond performs direct matching for the remaining discrete symmetries. We show that our algorithm can successfully characterize and extract intrinsic symmetries from a number of example shapes.

### Training through Observations Action Map Predictions

"... 1 reading a book using a laptop watching TV reading a book Figure 1: We predict regions in 3D scenes where actions are likely to take place. We start by scanning the geometry of real environments using RGB-D sensors and reconstructing a dense 3D mesh (left). We then observe and track people as they ..."

Abstract
- Add to MetaCart

1 reading a book using a laptop watching TV reading a book Figure 1: We predict regions in 3D scenes where actions are likely to take place. We start by scanning the geometry of real environments using RGB-D sensors and reconstructing a dense 3D mesh (left). We then observe and track people as they interact with the captured environments (mid-left). We use these observations to train a classifier which allows us to infer the likelihood of actions occurring in regions of new, unobserved scenes. We call these predictions action maps and we demonstrate that we are able to deduce action maps for previously unobserved real and virtual scenes (see mid-right and right, respectively). With modern computer graphics, we can generate enormous amounts of 3D scene data. It is now possible to capture high-quality 3D representations of large real-world environments. Large shape and scene databases, such as the Trimble 3D Warehouse, are publicly accessible and constantly growing. Unfortunately, while a great amount of 3D content exists, most of it is detached from the semantics and functionality of the objects it represents. In this paper, we present a method to establish a correlation between the geometry and the functionality of 3D environments. Using RGB-D sensors, we capture dense 3D reconstructions of real-world scenes, and observe and track people as they interact with the environment. With these observations, we train a classifier which can transfer interaction knowledge to unobserved 3D scenes. We predict a like-lihood of a given action taking place over all locations in a 3D en-vironment and refer to this representation as an action map over the scene. We demonstrate prediction of action maps in both 3D scans and virtual scenes. We evaluate our predictions against ground truth annotations by people, and present an approach for characterizing 3D scenes by functional similarity using action maps.

### Symmetry Detection in Large Scale City Scans

, 2012

"... In this report we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which was limited to data sets of a few hundred megabytes maximum, our method scales to very large scenes. We map the detection problem to a nearest-neighbor s ..."

Abstract
- Add to MetaCart

In this report we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which was limited to data sets of a few hundred megabytes maximum, our method scales to very large scenes. We map the detection problem to a nearest-neighbor search in a low-dimensional feature space, followed by a cascade of tests for geometric clustering of potential matches. Our algorithm robustly handles noisy real-world scanner data, obtaining a recognition performance comparable to state-of-the-art methods. In practice, it scales linearly with the scene size and achieves a high absolute throughput, processing half a terabyte of raw scanner data over night on a dual socket commodity PC.

### b. Estimated Structure a2. Training Data d. Fused Result c2. Completed With Database c1. Completed With Symmetry

"... Figure 1: Given an incomplete point scan with occlusions (a1), our method leverages training data (a2) to estimate the structure of the underlying shape, including parts and symmetries (b). Our inference algorithm is capable of discovering the major symmetries, despite the occlusion of symmetric cou ..."

Abstract
- Add to MetaCart

Figure 1: Given an incomplete point scan with occlusions (a1), our method leverages training data (a2) to estimate the structure of the underlying shape, including parts and symmetries (b). Our inference algorithm is capable of discovering the major symmetries, despite the occlusion of symmetric counterparts. The estimated structure is used to augment the point cloud with additional points from symmetry (c1) and database (c2) priors, which are further fused to produce the final completed point cloud (d). Note how the final result leverages symmetry whenever possible for self-completion (e.g., stem, armrests), and falls back to database information transfer in case all symmetric parts are occluded (e.g., back). Acquiring 3D geometry of an object is a tedious and time-consuming task, typically requiring scanning the surface from multiple view-points. In this work we focus on reconstructing complete geometry from a single scan acquired with a low-quality consumer-level scan-ning device. Our method uses a collection of example 3D shapes to build structural part-based priors that are necessary to complete the shape. In our representation, we associate a local coordinate system to each part and learn the distribution of positions and orien-tations of all the other parts from the database, which implicitly also defines positions of symmetry planes and symmetry axes. At the

### Article Unsupervised Object Modeling and Segmentation with Symmetry Detection for Human Activity Recognition

"... www.mdpi.com/journal/symmetry ..."

(Show Context)
### Adobe

"... drawing 1 drawing 2 fixed hinge slide slide slide proxies 1 proxies 2 global junction-graph junction arrows animated transitions Figure 1: We present a system to interpret concept sketches. Starting from input sketches (drawings 1 and 2) and rough geometry proxies, we automatically extract consisten ..."

Abstract
- Add to MetaCart

drawing 1 drawing 2 fixed hinge slide slide slide proxies 1 proxies 2 global junction-graph junction arrows animated transitions Figure 1: We present a system to interpret concept sketches. Starting from input sketches (drawings 1 and 2) and rough geometry proxies, we automatically extract consistent proxy correspondence across the views and a global junction-graph encoding inter-proxy connections. The user can then interactively change view and/or manipulate junctions (based on arrow handles), or browse through animated transition sequences. The key observation is that consistent inter-part relations can be inferred even based on largely inconsistent geometry information. Concept sketches are popularly used by designers to convey pose and function of products. Understanding such sketches, however, requires special skills to form a mental 3D representation of the product geometry by linking parts across the different sketches and imagining the intermediate object configurations. Hence, the sketches can remain inaccessible to many, especially non-designers. We present a system to facilitate easy interpretation and exploration of concept sketches. Starting from crudely specified incomplete geometry, often inconsistent across the different views, we propose a globally-coupled analysis to extract part correspondence and inter-part junction information that best explain the different sketch views. The user can then interactively explore the abstracted object to gain better understanding of the product functions. Our key technical contribution is performing shape analysis without access to any coherent 3D geometric model by reasoning in the space of inter-part relations. We evaluate our system on various concept sketches obtained from popular product design books and websites.

### *Highlights (for review) Fast global and partial reflective symmetry analyses using boundary surfaces of mechanical components

, 2014

"... Axisymmetry and planar reflective symmetry properties of mechanical components can be used throughout a product development process to restructure the modeling process of a component, simplify the computation of tool pathtrajectories, assembly trajectories, etc. To thisend, the restructured geometri ..."

Abstract
- Add to MetaCart

(Show Context)
Axisymmetry and planar reflective symmetry properties of mechanical components can be used throughout a product development process to restructure the modeling process of a component, simplify the computation of tool pathtrajectories, assembly trajectories, etc. To thisend, the restructured geometric model of such components must be at least as accurate as the manufacturing processes used to produce them, likewise their symmetry properties must be extracted with the same level of accuracy to preserve the accuracy of their geometric model. The proposed symmetry analysis is performed on a B-Rep CAD model through a divide-and-conquer approach over the boundary of a component with faces as atomic entities. As a result, it is possible to identify rapidly all global symmetry planes and axisymmetry as well as local symmetries. Also, the corresponding algorithm is fast enough to be inserted in CAD/CAM operators as part of interactive modeling processes,

### The Visual Computer (2013, to appear) Scalar Field Visualization via Extraction of Symmetric Structures

"... Abstract Identifying symmetry in scalar fields is a recent area of research in scientific visualization and computer graphics communities. Symmetry detection techniques based on abstract representations of the scalar field use only limited geometric information in their analysis. Hence they may not ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract Identifying symmetry in scalar fields is a recent area of research in scientific visualization and computer graphics communities. Symmetry detection techniques based on abstract representations of the scalar field use only limited geometric information in their analysis. Hence they may not be suited for applications that study the geometric properties of the regions in the domain. On the other hand, methods that accumulate local evidence of symmetry through a voting procedure have been successfully used for detecting geometric symmetry in shapes. We extend such a technique to scalar fields and use it to detect geometrically symmetric regions in synthetic as well as real-world datasets. Identifying symmetry in the scalar field can significantly improve visualization and interactive exploration of the data. We demonstrate different applications of the symmetry detection method to scientific visualization: query-based exploration of scalar fields, linked selection in symmetric regions for interactive visualization, and classification of geometrically symmetric regions and its application to anomaly detection.

### TAU

"... 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 sha ..."

Abstract
- Add to MetaCart

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 lo-cal 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 informa-tion from input data; and a (smart) processing phase, which utilizes the extracted information for exploration, editing, and synthesis of novel shapes. In this survey paper, we 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 con-text 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. 1