Florence Nicol

Functional Decomposition for Bundled Simplification of Trail Sets

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.

Adaptive Simulated Annealing with Homogenization for Aircraft Trajectory Optimization

In air traffic management, most optimization procedures are commonly based on deterministic modeling and do not take into account the uncertainties on environmental conditions (e.g., wind) and on air traffic control operations. However, aircraft performances in a real-world context are highly sensitive to these uncertainties. The aim of this work is twofold. First, we provide some numerical evidence of the sensitivity of fuel consumption and flight duration with respect to random fluctuations of the wind and the air traffic control operations. Second, we develop a global stochastic optimization procedure for general aircraft performance criteria. Since we consider general (black-box) cost functions, we develop a derivative-free optimization procedure: noisy simulated annealing (NSA).

On the Geodesic Distance in Shapes K-means Clustering

In this paper, the problem of clustering rotationally invariant shapes is studied and a solution using Information Geometry tools is provided. Landmarks of a complex shape are defined as probability densities in a statistical manifold. Then, in the setting of shapes clustering through a K-means algorithm, the discriminative power of two different shapes distances are evaluated. The first, derived from Fisher–Rao metric, is related with the minimization of information in the Fisher sense and the other is derived from the Wasserstein distance which measures the minimal transportation cost. A modification of the K-means algorithm is also proposed which allows the variances to vary not only among the landmarks but also among the clusters.

Von Mises-like probability density functions on surfaces

Directional densities were introduced in the pioneering work of von Mises, with the definition of a rotationally invariant probability distribution on the circle. It was further generalized to more complex objects like the torus or the hyperbolic space. The purpose of the present work is to give a construction of equivalent objects on surfaces with genus larger than or equal to 2, for which an hyperbolic structure exists. Although the directional densities on the torus were introduced by several authors and are closely related to the original von Mises distribution, allowing more than one hole is challenging as one cannot simply add more angular coordinates. The approach taken here is to use a wrapping as in the case of the circular wrapped Gaussian density, but with a summation taken over all the elements of the group that realizes the surface as a quotient of the hyperbolic plane.

Entropy minimizing curves with application to flight path design and clustering

Air traffic management (ATM) aims at providing companies with a safe and ideally optimal aircraft trajectory planning. Air traffic controllers act on flight paths in such a way that no pair of aircraft come closer than the regulatory separation norms. With the increase of traffic, it is expected that the system will reach its limits in a near future: a paradigm change in ATM is planned with the introduction of trajectory based operations. In this context, sets of well separated flight paths are computed in advance, tremendously reducing the number of unsafe situations that must be dealt with by controllers. Unfortunately, automated tools used to generate such plannings generally issue trajectories not complying with operational practices or even flight dynamics. In this paper, a mean of producing realistic air routes from the output of an automated trajectory design tool is investigated. For that purpose, the entropy of a system of curves is first defined and a mean of iteratively minimizing it is presented.The resulting curves form a route network that is suitable for use in a semi-automated ATM system with human in the loop. The tool introduced in this work is quite versatile and may be applied also to unsupervised classification of curves: an example is given for the french traffic.

Entropy Minimizing Curves with Application to Automated Flight Path Design

Air traffic management (ATM) aims at providing companies with a safe and ideally optimal aircraft trajectory planning. Air traffic controllers act on flight paths in such a way that no pair of aircraft come closer than the regulatory separation norm. With the increase of traffic, it is expected that the system will reach its limits in a near future: a paradigm change in ATM is planned with the introduction of trajectory based operations. This paper investigate a mean of producing realistic air routes from the output of an automated trajectory design tool. For that purpose, an entropy associated with a system of curves is defined and a mean of iteratively minimizing it is presented. The network produced is suitable for use in a semi-automated ATM system with human in the loop.