11 research outputs found
Doctor of Philosophy
dissertationIn this dissertation, we advance the theory and practice of verifying visualization algorithms. We present techniques to assess visualization correctness through testing of important mathematical properties. Where applicable, these techniques allow us to distinguish whether anomalies in visualization features can be attributed to the underlying physical process or to artifacts from the implementation under verification. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. The contributions of this dissertation are manifold. We derive the mathematical framework for the expected behavior of several visualization algorithms, and compare them to experimentally observed results in the selected codes. In the Computational Science & Engineering community CS&E, this technique is know as the Method of Manufactured Solution (MMS). We apply MMS to the verification of geometrical and topological properties of isosurface extraction algorithms, and direct volume rendering. We derive the convergence of geometrical properties of isosurface extraction techniques, such as function value and normals. For the verification of topological properties, we use stratified Morse theory and digital topology to design algorithms that verify topological invariants. In the case of volume rendering algorithms, we provide the expected discretization errors for three different error sources. The results of applying the MMS is another important contribution of this dissertation. We report unexpected behavior for almost all implementations tested. In some cases, we were able to find and fix bugs that prevented the correctness of the visualization algorithm. In particular, we address an almost 2 0 -year-old bug with the core disambiguation procedure of Marching Cubes 33, one of the first algorithms intended to preserve the topology of the trilinear interpolant. Finally, an important by-product of this work is a range of responses practitioners can expect to encounter with the visualization technique under verification
Progressive Wasserstein Barycenters of Persistence Diagrams
This paper presents an efficient algorithm for the progressive approximation
of Wasserstein barycenters of persistence diagrams, with applications to the
visual analysis of ensemble data. Given a set of scalar fields, our approach
enables the computation of a persistence diagram which is representative of the
set, and which visually conveys the number, data ranges and saliences of the
main features of interest found in the set. Such representative diagrams are
obtained by computing explicitly the discrete Wasserstein barycenter of the set
of persistence diagrams, a notoriously computationally intensive task. In
particular, we revisit efficient algorithms for Wasserstein distance
approximation [12,51] to extend previous work on barycenter estimation [94]. We
present a new fast algorithm, which progressively approximates the barycenter
by iteratively increasing the computation accuracy as well as the number of
persistent features in the output diagram. Such a progressivity drastically
improves convergence in practice and allows to design an interruptible
algorithm, capable of respecting computation time constraints. This enables the
approximation of Wasserstein barycenters within interactive times. We present
an application to ensemble clustering where we revisit the k-means algorithm to
exploit our barycenters and compute, within execution time constraints,
meaningful clusters of ensemble data along with their barycenter diagram.
Extensive experiments on synthetic and real-life data sets report that our
algorithm converges to barycenters that are qualitatively meaningful with
regard to the applications, and quantitatively comparable to previous
techniques, while offering an order of magnitude speedup when run until
convergence (without time constraint). Our algorithm can be trivially
parallelized to provide additional speedups in practice on standard
workstations. [...
Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)
This paper presents a computational framework for the Principal Geodesic
Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated
Principal Component Analysis (PCA) framework [87] to the Wasserstein metric
space of merge trees [92]. We formulate MT-PGA computation as a constrained
optimization problem, aiming at adjusting a basis of orthogonal geodesic axes,
while minimizing a fitting energy. We introduce an efficient, iterative
algorithm which exploits shared-memory parallelism, as well as an analytic
expression of the fitting energy gradient, to ensure fast iterations. Our
approach also trivially extends to extremum persistence diagrams. Extensive
experiments on public ensembles demonstrate the efficiency of our approach -
with MT-PGA computations in the orders of minutes for the largest examples. We
show the utility of our contributions by extending to merge trees two typical
PCA applications. First, we apply MT-PGA to data reduction and reliably
compress merge trees by concisely representing them by their first coordinates
in the MT-PGA basis. Second, we present a dimensionality reduction framework
exploiting the first two directions of the MT-PGA basis to generate
two-dimensional layouts of the ensemble. We augment these layouts with
persistence correlation views, enabling global and local visual inspections of
the feature variability in the ensemble. In both applications, quantitative
experiments assess the relevance of our framework. Finally, we provide a
lightweight C++ implementation that can be used to reproduce our results
Fuelling the zero-emissions road freight of the future: routing of mobile fuellers
The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios