Invariant crease lines for topological and structural analysis of tensor fields

We introduce a versatile framework for characterizing and extracting salient structures in three-dimensional symmetric second-order tensor fields. The key insight is that degenerate lines in tensor fields, as defined by the standard topological approach, are exactly crease (ridge and valley) lines of a particular tensor invariant called mode. This reformulation allows us to apply well-studied approaches from scientific visualization or computer vision to the extraction of topological lines in tensor fields. More generally, this main result suggests that other tensor invariants, such as anisotropy measures like fractional anisotropy (FA), can be used in the same framework in lieu of mode to identify important structural properties in tensor fields. Our implementation addresses the specific challenge posed by the non-linearity of the considered scalar measures and by the smoothness requirement of the crease manifold computation. We use a combination of smooth reconstruction kernels and adaptive refinement strategy that automatically adjust the resolution of the analysis to the spatial variation of the considered quantities. Together, these improvements allow for the robust application of existing ridge line extraction algorithms in the tensor context of our problem. Results are proposed for a diffusion tensor MRI dataset, and for a benchmark stress tensor field used in engineering research.     

3D posture estimation using geodesic distance maps

This paper presents a novel technique for three-dimensional (3D) human motion capture using a set of two non-calibrated cameras. The user’s five extremities (head, hands and feet) are extracted, labeled and tracked after silhouette segmentation. As they are the minimal number of points that can be used in order to enable whole body gestural interaction, we will henceforth refer to these features as crucial points. Features are subsequently labelled using 3D triangulation and inter-image tracking. The crucial point candidates are defined as the local maxima of the geodesic distance with respect to the center of gravity of the actor region that lie on the silhouette boundary. Due to its low computational complexity, the system can run at real-time paces on standard personal computers, with an average error rate range between 4% and 9% in realistic situations, depending on the context and segmentation quality.

Objective quantification of acetylcholine receptor aggregation using fast Fourier transforms

A new approach for objectively analyzing the aggregation of acetylcholine receptors (AChRs) through power spectrum analysis derived from fast Fourier transform (FFT) of images has been developed. Presently, detection of AChR aggregates at neuromuscular junctions is not easily accomplished. Though the formation of AChR clusters results in periodic gray-level variations that differ with time, no study reporting their correlation with frequency information in the Fourier domain for aggregates' detection purposes exists. To this end, we processed time-lapse images of AChR aggregates' formation on murine myotubes to extract peak values of power spectra. To validate interpretation of the Fourier spectra analysis, a computer routine was developed to semi-automatically count AChR aggregates. We found: (1) logarithmic maxima of Fourier spectra correlated significantly with experimentation time; (2) cluster count correlated significantly with time only after clusters were discernable from images, signifying that this method heavily depended on definitive growth data and thresholding values; (3) exponents of Fourier maxima versus time and cluster count versus time profiles during this phase compared favorably, indicating that both methods were analyzing identical cluster growth rates. Our observations suggest that analysis via FFT power spectrum is sensitive and robust enough to automatically quantify AChR aggregates.     

Exploiting eye–hand coordination to detect grasping movements

Human beings are very skillful at reaching for and grasping objects under multiple conditions, even when faced with an object's wide variety of positions, locations, structures and orientations. This natural ability, controlled by the human brain, is called eye–hand coordination. To understand this behavior it is necessary to study both eye and hand movements simultaneously. This paper proposes a novel approach to detect grasping movements by means of computer vision techniques. This solution fuses two viewpoints, one viewpoint which is obtained from an eye-tracker capturing the user's perspective and a second viewpoint which is captured by a wearable camera attached to a user's wrist. Utilizing information from these two viewpoints it is possible to characterize multiple hand movements in conjunction with eye-gaze movements through a Hidden–Markov Model framework. This paper shows that combining these two sources makes it possible to detect hand gestures using only the objects contained in the scene even without markers on the surface of the objects. In addition, it is possible to detect which is the desired object before the user can actually grasp said object.     

Finite Volume Time Domain modelling of microwave breakdown and plasma formation in a metallic aperture

The modelling of plasma formation during microwave breakdown is a difficult task because of the strong non-linear coupling between Maxwell?s equations and plasma equations, and of the large plasma density gradients that form during breakdown. An original Finite Volume Time Domain (FVTD) method has been developed to solve Maxwell?s equations coupled with a simplified fluid plasma model and is described in this paper. This method is illustrated with the study of the shielding of a metallic aperture by the plasma generated by an incident high power electromagnetic wave. Typical results obtained with the FVTD method for this shielding problem are shown.     

Selecting Significant Effects in Factorial Designs Taking Type II Errors into Account

When analysing the effects of a factorial design, it is customary to take into account the probability of making a Type I error (the probability of considering an effect significant when it is non‐significant), but not to consider the probability of making a Type II error (the probability of considering an effect as non‐significant when it is significant). Making a Type II error, however, may lead to incorrect decisions regarding the values that the factors should take or how subsequent experiments should be conducted. In this paper, we introduce the concept of minimum effect size of interest and present a visualization method for selecting the critical value of the effects, the threshold value above which an effect should be considered significant, which takes into account the probability of Type I and Type II errors. Copyright © 2006 John Wiley & Sons, Ltd.     

On the probabilistic-deterministic transition involved in a fragmentation process of brittle materials

Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass and rocks. The main mechanism used to explain the change of the number of fragments with stress rate is a shielding phenomenon. However, under quasi-static loading conditions, a weakest link hypothesis may be applicable. Therefore, depending on the local strain or stress rate, different fragmentation regimes are observed. One regime corresponds to single fragmentation for which a probabilistic approach is needed. Conversely, the multiple fragmentation regime may be described by a deterministic approach. The transition between the two fragmentation regimes is discussed for high performance concrete, glass and SiC ceramics.     

A review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot

The estimation of camera egomotion is an old problem in computer vision. Since the 1980s, many approaches based on both the discrete and the differential epipolar constraint have been proposed. The discrete case is used mainly in self-calibrated stereoscopic systems, whereas the differential case deals with a single moving camera. This article surveys several methods for 3D motion estimation unifying the mathematics convention which are then adapted to the common case of a mobile robot moving on a plane. Experimental results are given on synthetic data covering more than 0.5 million estimations. These surveyed algorithms have been programmed and are available on the Internet.     

Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing

Complex geometric features such as oriented points, lines or 3D frames are increasingly used in image processing and computer vision. However, processing these geometric features is far more difficult than processing points, and a number of paradoxes can arise. We establish in this article the basic mathematical framework required to avoid them and analyze more specifically three basic problems: (1) what is a random distribution of features, (2) how to define a distance between features, (3) and what is the “mean feature” of a number of feature measurements? We insist on the importance of an invariance hypothesis for these definitions relative to a group of transformations that models the different possible data acquisitions. We develop general methods to solve these three problems and illustrate them with 3D frame features under rigid transformations. The first problem has a direct application in the computation of the prior probability of a false match in classical model-based object recognition algorithms. We also present experimental results of the two other problems for the statistical analysis of anatomical features automatically extracted from 24 three-dimensional images of a single patient's head. These experiments successfully confirm the importance of the rigorous requirements presented in this article.     

Distributed machining control and monitoring using smart sensors/actuators

The study of smart sensors and actuators led, during the past few years, to the development of facilities which improve traditional sensors and actuators in a necessary way to automate production systems. In another context, many studies have been carried out aimed at defining a decisional structure for production activity control and the increasing need of reactivity leads to the autonomization of decisional levels close to the operational system. We study in this paper the natural convergence between these two approaches and we propose an integration architecture, dealing with machine tool and machining control, that enables the exploitation of distributed smart sensors and actuators in the decisional system.