7,367 research outputs found
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform
designed for topological data analysis in scientific visualization. TTK
provides a unified, generic, efficient, and robust implementation of key
algorithms for the topological analysis of scalar data, including: critical
points, integral lines, persistence diagrams, persistence curves, merge trees,
contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots,
Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due
to a tight integration with ParaView. It is also easily accessible to
developers through a variety of bindings (Python, VTK/C++) for fast prototyping
or through direct, dependence-free, C++, to ease integration into pre-existing
complex systems. While developing TTK, we faced several algorithmic and
software engineering challenges, which we document in this paper. In
particular, we present an algorithm for the construction of a discrete gradient
that complies to the critical points extracted in the piecewise-linear setting.
This algorithm guarantees a combinatorial consistency across the topological
abstractions supported by TTK, and importantly, a unified implementation of
topological data simplification for multi-scale exploration and analysis. We
also present a cached triangulation data structure, that supports time
efficient and generic traversals, which self-adjusts its memory usage on demand
for input simplicial meshes and which implicitly emulates a triangulation for
regular grids with no memory overhead. Finally, we describe an original
software architecture, which guarantees memory efficient and direct accesses to
TTK features, while still allowing for researchers powerful and easy bindings
and extensions. TTK is open source (BSD license) and its code, online
documentation and video tutorials are available on TTK's website
Contains and Inside relationships within combinatorial Pyramids
Irregular pyramids are made of a stack of successively reduced graphs
embedded in the plane. Such pyramids are used within the segmentation framework
to encode a hierarchy of partitions. The different graph models used within the
irregular pyramid framework encode different types of relationships between
regions. This paper compares different graph models used within the irregular
pyramid framework according to a set of relationships between regions. We also
define a new algorithm based on a pyramid of combinatorial maps which allows to
determine if one region contains the other using only local calculus.Comment: 35 page
Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction
A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails
AlSub: Fully Parallel and Modular Subdivision
In recent years, mesh subdivision---the process of forging smooth free-form
surfaces from coarse polygonal meshes---has become an indispensable production
instrument. Although subdivision performance is crucial during simulation,
animation and rendering, state-of-the-art approaches still rely on serial
implementations for complex parts of the subdivision process. Therefore, they
often fail to harness the power of modern parallel devices, like the graphics
processing unit (GPU), for large parts of the algorithm and must resort to
time-consuming serial preprocessing. In this paper, we show that a complete
parallelization of the subdivision process for modern architectures is
possible. Building on sparse matrix linear algebra, we show how to structure
the complete subdivision process into a sequence of algebra operations. By
restructuring and grouping these operations, we adapt the process for different
use cases, such as regular subdivision of dynamic meshes, uniform subdivision
for immutable topology, and feature-adaptive subdivision for efficient
rendering of animated models. As the same machinery is used for all use cases,
identical subdivision results are achieved in all parts of the production
pipeline. As a second contribution, we show how these linear algebra
formulations can effectively be translated into efficient GPU kernels. Applying
our strategies to , Loop and Catmull-Clark subdivision shows
significant speedups of our approach compared to state-of-the-art solutions,
while we completely avoid serial preprocessing.Comment: Changed structure Added content Improved description
Efficient Representation of Computational Meshes
We present a simple yet general and efficient approach to representation of
computational meshes. Meshes are represented as sets of mesh entities of
different topological dimensions and their incidence relations. We discuss a
straightforward and efficient storage scheme for such mesh representations and
efficient algorithms for computation of arbitrary incidence relations from a
given initial and minimal set of incidence relations. The general
representation may harbor a wide range of computational meshes, and may also be
specialized to provide simple user interfaces for particular meshes, including
simplicial meshes in one, two and three space dimensions where the mesh
entities correspond to vertices, edges, faces and cells. It is elaborated on
how the proposed concepts and data structures may be used for assembly of
variational forms in parallel over distributed finite element meshes.
Benchmarks are presented to demonstrate efficiency in terms of CPU time and
memory usage
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