3,363 research outputs found
A topological approach for segmenting human body shape
Segmentation of a 3D human body, is a very challenging problem in applications exploiting human scan data. To tackle this problem, the paper proposes a topological approach based on the discrete Reeb graph (DRG) which is an extension of the classical Reeb graph to handle unorganized clouds of 3D points. The essence of the approach concerns detecting critical nodes in the DRG, thereby permitting the extraction of branches that represent parts of the body. Because the human body shape representation is built upon global topological features that are preserved so long as the whole structure of the human body does not change, our approach is quite robust against noise, holes, irregular sampling, frame change and posture variation. Experimental results performed on real scan data demonstrate the validity of our method
A discrete Reeb graph approach for the segmentation of human body scans
Segmentation of 3D human body (HB) scan is a very challenging problem in applications exploiting human scan data. To tackle this problem, we propose a topological approach based on discrete Reeb graph (DRG) which is an extension of the classical Reeb graph to unorganized cloud of 3D points. The essence of the approach is detecting critical nodes in the DRG thus permitting the extraction of branches that represent the body parts. Because the human body shape representation is built upon global topological features that are preserved so long as the whole structure of the human body does not change, our approach is quite robust against noise, holes, irregular sampling, moderate reference change and posture variation. Experimental results performed on real scan data demonstrate the validity of our method
Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methods
Automatic Extraction of road network from satellite images is a goal that can
benefit and even enable new technologies. Methods that combine machine learning
(ML) and computer vision have been proposed in recent years which make the task
semi-automatic by requiring the user to provide curated training samples. The
process can be fully automatized if training samples can be produced
algorithmically. Of course, this requires a robust algorithm that can
reconstruct the road networks from satellite images reliably so that the output
can be fed as training samples. In this work, we develop such a technique by
infusing a persistence-guided discrete Morse based graph reconstruction
algorithm into ML framework.
We elucidate our contributions in two phases. First, in a semi-automatic
framework, we combine a discrete-Morse based graph reconstruction algorithm
with an existing CNN framework to segment input satellite images. We show that
this leads to reconstructions with better connectivity and less noise. Next, in
a fully automatic framework, we leverage the power of the discrete-Morse based
graph reconstruction algorithm to train a CNN from a collection of images
without labelled data and use the same algorithm to produce the final output
from the segmented images created by the trained CNN. We apply the
discrete-Morse based graph reconstruction algorithm iteratively to improve the
accuracy of the CNN. We show promising experimental results of this new
framework on datasets from SpaceNet Challenge.Comment: 26 pages, 13 figures, ACM SIGSPATIAL 201
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
Surface networks
© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou
Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph
We present a SE(3)-equivariant graph neural network (GNN) approach that
directly predicting the formation factor and effective permeability from
micro-CT images. FFT solvers are established to compute both the formation
factor and effective permeability, while the topology and geometry of the pore
space are represented by a persistence-based Morse graph. Together, they
constitute the database for training, validating, and testing the neural
networks. While the graph and Euclidean convolutional approaches both employ
neural networks to generate low-dimensional latent space to represent the
features of the micro-structures for forward predictions, the SE(3) equivariant
neural network is found to generate more accurate predictions, especially when
the training data is limited. Numerical experiments have also shown that the
new SE(3) approach leads to predictions that fulfill the material frame
indifference whereas the predictions from classical convolutional neural
networks (CNN) may suffer from spurious dependence on the coordinate system of
the training data. Comparisons among predictions inferred from training the CNN
and those from graph convolutional neural networks (GNN) with and without the
equivariant constraint indicate that the equivariant graph neural network seems
to perform better than the CNN and GNN without enforcing equivariant
constraints
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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