2,890 research outputs found
Topological descriptors for 3D surface analysis
We investigate topological descriptors for 3D surface analysis, i.e. the
classification of surfaces according to their geometric fine structure. On a
dataset of high-resolution 3D surface reconstructions we compute persistence
diagrams for a 2D cubical filtration. In the next step we investigate different
topological descriptors and measure their ability to discriminate structurally
different 3D surface patches. We evaluate their sensitivity to different
parameters and compare the performance of the resulting topological descriptors
to alternative (non-topological) descriptors. We present a comprehensive
evaluation that shows that topological descriptors are (i) robust, (ii) yield
state-of-the-art performance for the task of 3D surface analysis and (iii)
improve classification performance when combined with non-topological
descriptors.Comment: 12 pages, 3 figures, CTIC 201
Multiscale Fractal Descriptors Applied to Nanoscale Images
This work proposes the application of fractal descriptors to the analysis of
nanoscale materials under different experimental conditions. We obtain
descriptors for images from the sample applying a multiscale transform to the
calculation of fractal dimension of a surface map of such image. Particularly,
we have used the}Bouligand-Minkowski fractal dimension. We applied these
descriptors to discriminate between two titanium oxide films prepared under
different experimental conditions. Results demonstrate the discrimination power
of proposed descriptors in such kind of application
Efficient Image-Space Extraction and Representation of 3D Surface Topography
Surface topography refers to the geometric micro-structure of a surface and
defines its tactile characteristics (typically in the sub-millimeter range).
High-resolution 3D scanning techniques developed recently enable the 3D
reconstruction of surfaces including their surface topography. In his paper, we
present an efficient image-space technique for the extraction of surface
topography from high-resolution 3D reconstructions. Additionally, we filter
noise and enhance topographic attributes to obtain an improved representation
for subsequent topography classification. Comprehensive experiments show that
the our representation captures well topographic attributes and significantly
improves classification performance compared to alternative 2D and 3D
representations.Comment: Initial version of the paper accepted at the IEEE ICIP Conference
201
Persistence Bag-of-Words for Topological Data Analysis
Persistent homology (PH) is a rigorous mathematical theory that provides a
robust descriptor of data in the form of persistence diagrams (PDs). PDs
exhibit, however, complex structure and are difficult to integrate in today's
machine learning workflows. This paper introduces persistence bag-of-words: a
novel and stable vectorized representation of PDs that enables the seamless
integration with machine learning. Comprehensive experiments show that the new
representation achieves state-of-the-art performance and beyond in much less
time than alternative approaches.Comment: Accepted for the Twenty-Eight International Joint Conference on
Artificial Intelligence (IJCAI-19). arXiv admin note: substantial text
overlap with arXiv:1802.0485
Fractal descriptors based on the probability dimension: a texture analysis and classification approach
In this work, we propose a novel technique for obtaining descriptors of
gray-level texture images. The descriptors are provided by applying a
multiscale transform to the fractal dimension of the image estimated through
the probability (Voss) method. The effectiveness of the descriptors is verified
in a classification task using benchmark over texture datasets. The results
obtained demonstrate the efficiency of the proposed method as a tool for the
description and discrimination of texture images.Comment: 7 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1205.282
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Texture descriptor combining fractal dimension and artificial crawlers
Texture is an important visual attribute used to describe images. There are
many methods available for texture analysis. However, they do not capture the
details richness of the image surface. In this paper, we propose a new method
to describe textures using the artificial crawler model. This model assumes
that each agent can interact with the environment and each other. Since this
swarm system alone does not achieve a good discrimination, we developed a new
method to increase the discriminatory power of artificial crawlers, together
with the fractal dimension theory. Here, we estimated the fractal dimension by
the Bouligand-Minkowski method due to its precision in quantifying structural
properties of images. We validate our method on two texture datasets and the
experimental results reveal that our method leads to highly discriminative
textural features. The results indicate that our method can be used in
different texture applications.Comment: 12 pages 9 figures. Paper in press: Physica A: Statistical Mechanics
and its Application
Classification of lung disease in HRCT scans using integral geometry measures and functional data analysis
A framework for classification of chronic lung disease from high-resolution CT scans is presented. We use a set of features which measure the local morphology and topology of the 3D voxels within the lung parenchyma and apply functional data classification to the extracted features. We introduce the measures, Minkowski functionals, which derive from integral geometry and show results of classification on lungs containing various stages of chronic lung disease: emphysema, fibrosis and honey-combing. Once trained, the presented method is shown to be efficient and specific at characterising the distribution of disease in HRCT slices
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
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