Generalized intrinsic symmetry detection

In this paper, we address the problem of detecting partial symmetries in 3D objects. In contrast to previous work, our algorithm is able to match deformed symmetric parts: We first develop an algorithm for the case of approximately isometric deformations, based on matching graphs of surface feature lines that are annotated with intrinsic geometric properties. The sensitivity to non-isometry is controlled by tolerance parameters for each such annotation. Using large tolerance values for some of these annotations and a robust matching of the graph topology yields a more general symmetry detection algorithm that can detect similarities in structures that have undergone strong deformations. This approach for the first time allows for detecting partial intrinsic as well as more general, non-isometric symmetries. We evaluate the recognition performance of our technique for a number synthetic and real-world scanner data sets

Part Description and Segmentation Using Contour, Surface and Volumetric Primitives

The problem of part definition, description, and decomposition is central to the shape recognition systems. The Ultimate goal of segmenting range images into meaningful parts and objects has proved to be very difficult to realize, mainly due to the isolation of the segmentation problem from the issue of representation. We propose a paradigm for part description and segmentation by integration of contour, surface, and volumetric primitives. Unlike previous approaches, we have used geometric properties derived from both boundary-based (surface contours and occluding contours), and primitive-based (quadric patches and superquadric models) representations to define and recover part-whole relationships, without a priori knowledge about the objects or object domain. The object shape is described at three levels of complexity, each contributing to the overall shape. Our approach can be summarized as answering the following question : Given that we have all three different modules for extracting volume, surface and boundary properties, how should they be invoked, evaluated and integrated? Volume and boundary fitting, and surface description are performed in parallel to incorporate the best of the coarse to fine and fine to coarse segmentation strategy. The process involves feedback between the segmentor (the Control Module) and individual shape description modules. The control module evaluates the intermediate descriptions and formulates hypotheses about parts. Hypotheses are further tested by the segmentor and the descriptors. The descriptions thus obtained are independent of position, orientation, scale, domain and domain properties, and are based purely on geometric considerations. They are extremely useful for the high level domain dependent symbolic reasoning processes, which need not deal with tremendous amount of data, but only with a rich description of data in terms of primitives recovered at various levels of complexity

Discovering Regularity in Point Clouds of Urban Scenes

Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of the Fourier transform for the real-time detection of periodicity in building facades. Periodic regularity is discovered online by doing a plane sweep across the scene and analyzing the frequency space of each column in the sweep. The simplicity and online nature of this algorithm allow it to be embedded in scanner hardware, making periodicity detection a built-in feature of future 3D cameras. We demonstrate the usefulness of periodicity in view registration, compression, segmentation, and facade reconstruction. The second algorithm leverages the hierarchical decomposition and locality in space of the wavelet transform to find stochastic parameters for procedural models that succinctly describe vegetation. These procedural models facilitate the generation of virtual worlds for architecture, gaming, and augmented reality. The self-similarity of vegetation can be inferred using multi-resolution analysis to discover the underlying branching patterns. We present a unified framework of these tools, enabling the modeling, transmission, and compression of high-resolution, accurate, and immersive 3D images

Evaluating perceptual maps of asymmetries for gait symmetry quantification and pathology detection

Le mouvement de la marche est un processus essentiel de l'activité humaine et aussi le résultat de nombreuses interactions collaboratives entre les systèmes neurologiques, articulaires et musculo-squelettiques fonctionnant ensemble efficacement. Ceci explique pourquoi une analyse de la marche est aujourd'hui de plus en plus utilisée pour le diagnostic (et aussi la prévention) de différents types de maladies (neurologiques, musculaires, orthopédique, etc.). Ce rapport présente une nouvelle méthode pour visualiser rapidement les différentes parties du corps humain liées à une possible asymétrie (temporellement invariante par translation) existant dans la démarche d'un patient pour une possible utilisation clinique quotidienne. L'objectif est de fournir une méthode à la fois facile et peu dispendieuse permettant la mesure et l'affichage visuel, d'une manière intuitive et perceptive, des différentes parties asymétriques d'une démarche. La méthode proposée repose sur l'utilisation d'un capteur de profondeur peu dispendieux (la Kinect) qui est très bien adaptée pour un diagnostique rapide effectué dans de petites salles médicales car ce capteur est d'une part facile à installer et ne nécessitant aucun marqueur. L'algorithme que nous allons présenter est basé sur le fait que la marche saine possède des propriétés de symétrie (relativement à une invariance temporelle) dans le plan coronal.The gait movement is an essential process of the human activity and also the result of coordinated effort between the neurological, articular and musculoskeletal systems. This motivates why gait analysis is important and also increasingly used nowadays for the (possible early) diagnosis of many different types (neurological, muscular, orthopedic, etc.) of diseases. This paper introduces a novel method to quickly visualize the different parts of the body related to an asymmetric movement in the human gait of a patient for daily clinical. The goal is to provide a cheap and easy-to-use method to measure the gait asymmetry and display results in a perceptually relevant manner. This method relies on an affordable consumer depth sensor, the Kinect. The Kinect was chosen because this device is amenable for use in small, confined area, like a living room. Also, since it is marker-less, it provides a fast non-invasive diagnostic. The algorithm we are going to introduce relies on the fact that a healthy walk has (temporally shift-invariant) symmetry properties in the coronal plane

Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor

For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which describe the geometric shape as well as the composition of the microstructures under consideration and enable distinguishing microstructures with distinct effective material behavior. For this purpose, we propose using Minkowski tensors, in general, and the quadratic normal tensor, in particular, and introduce a computational algorithm applicable to voxel-based microstructure representations. Rooted in the mathematical field of integral geometry, Minkowski tensors associate a tensor to rather general geometric shapes, which make them suitable for a wide range of microstructured material classes. Furthermore, they satisfy additivity and continuity properties, which makes them suitable and robust for large-scale applications. We present a modular algorithm for computing the quadratic normal tensor of digital microstructures. We demonstrate multigrid convergence for selected numerical examples and apply our approach to a variety of microstructures. Strikingly, the presented algorithm remains unaffected by inaccurate computation of the interface area. The quadratic normal tensor may be used for engineering purposes, such as mean field homogenization or as target value for generating synthetic microstructures

Lifting Freehand Concept Sketches into 3D

International audienceWe present the first algorithm capable of automatically lifting real-world, vector-format, industrial design sketches into 3D. Targeting real-world sketches raises numerous challenges due to inaccuracies, use of overdrawn strokes, and construction lines. In particular, while construction lines convey important 3D information, they add significant clutter and introduce multiple accidental 2D intersections. Our algorithm exploits the geometric cues provided by the construction lines and lifts them to 3D by computing their intended 3D intersections and depths. Once lifted to 3D, these lines provide valuable geometric constraints that we leverage to infer the 3D shape of other artist drawn strokes. The core challenge we address is inferring the 3D connectivity of construction and other lines from their 2D projections by separating 2D intersections into 3D intersections and accidental occlusions. We efficiently address this complex combinatorial problem using a dedicated search algorithm that leverages observations about designer drawing preferences , and uses those to explore only the most likely solutions of the 3D intersection detection problem. We demonstrate that our separator outputs are of comparable quality to human annotations, and that the 3D structures we recover enable a range of design editing and visualization applications, including novel view synthesis and 3D-aware scaling of the depicted shape