33,075 research outputs found
Subdivision surface fitting to a dense mesh using ridges and umbilics
Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach
Polygonal Building Segmentation by Frame Field Learning
While state of the art image segmentation models typically output
segmentations in raster format, applications in geographic information systems
often require vector polygons. To help bridge the gap between deep network
output and the format used in downstream tasks, we add a frame field output to
a deep segmentation model for extracting buildings from remote sensing images.
We train a deep neural network that aligns a predicted frame field to ground
truth contours. This additional objective improves segmentation quality by
leveraging multi-task learning and provides structural information that later
facilitates polygonization; we also introduce a polygonization algorithm that
utilizes the frame field along with the raster segmentation. Our code is
available at https://github.com/Lydorn/Polygonization-by-Frame-Field-Learning.Comment: CVPR 2021 - IEEE Conference on Computer Vision and Pattern
Recognition, Jun 2021, Pittsburg / Virtual, United State
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
The persistent cosmic web and its filamentary structure I: Theory and implementation
We present DisPerSE, a novel approach to the coherent multi-scale
identification of all types of astrophysical structures, and in particular the
filaments, in the large scale distribution of matter in the Universe. This
method and corresponding piece of software allows a genuinely scale free and
parameter free identification of the voids, walls, filaments, clusters and
their configuration within the cosmic web, directly from the discrete
distribution of particles in N-body simulations or galaxies in sparse
observational catalogues. To achieve that goal, the method works directly over
the Delaunay tessellation of the discrete sample and uses the DTFE density
computed at each tracer particle; no further sampling, smoothing or processing
of the density field is required.
The idea is based on recent advances in distinct sub-domains of computational
topology, which allows a rigorous application of topological principles to
astrophysical data sets, taking into account uncertainties and Poisson noise.
Practically, the user can define a given persistence level in terms of
robustness with respect to noise (defined as a "number of sigmas") and the
algorithm returns the structures with the corresponding significance as sets of
critical points, lines, surfaces and volumes corresponding to the clusters,
filaments, walls and voids; filaments, connected at cluster nodes, crawling
along the edges of walls bounding the voids. The method is also interesting as
it allows for a robust quantification of the topological properties of a
discrete distribution in terms of Betti numbers or Euler characteristics,
without having to resort to smoothing or having to define a particular scale.
In this paper, we introduce the necessary mathematical background and
describe the method and implementation, while we address the application to 3D
simulated and observed data sets to the companion paper.Comment: A higher resolution version is available at
http://www.iap.fr/users/sousbie together with complementary material.
Submitted to MNRA
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