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A Barcode Shape Descriptor for Curve Point Cloud Data [article]

Anne Collins, Afra Zomorodian, Gunnar Carlsson, Leonidas Guibas
2004 Symposium Point-Based Graphics : [Proceedings]  
In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data.  ...  Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology.We also provide a metric over the space of barcodes, enabling fast comparison  ...  Introduction In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data.  ... 
doi:10.2312/spbg/spbg04/181-191 fatcat:kp6nekawmnap5nptbsbqvvkary

A barcode shape descriptor for curve point cloud data

Anne Collins, Afra Zomorodian, Gunnar Carlsson, Leonidas J. Guibas
2004 Computers & graphics  
In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD).  ...  Our shape descriptor, called a barcode, is based on a blend of techniques from differential geometry and algebraic topology.  ...  Introduction In this paper, we present a complete computational pipeline for extracting a compact shape descriptor for curve point cloud data (PCD).  ... 
doi:10.1016/j.cag.2004.08.015 fatcat:p6s3s7p7snfkll4hrch3f6vpva

The shape of cancer relapse: Topological data analysis predicts recurrence in paediatric acute lymphoblastic leukaemia [article]

Salvador Chulian, Bernadette J. Stolz, Alvaro Martinez-Rubio, Cristina Blazquez Goni, Juan Francisco Rodriguez Gutierrez, Teresa Caballero Velazquez, Agueda Molinos Quintana, Manuel Ramirez Orellana, Ana Castillo Robleda, Jose Luis Fuster Soler, Alfredo Minguela Puras, Maria Victoria Martinez Sanchez (+3 others)
2021 medRxiv   pre-print
At present, patients' risk of relapse are assessed by projecting high-dimensional flow cytometry data onto a subset of biomarkers and manually estimating the shape of this reduced data.  ...  We combine these fully unsupervised analyses with machine learning to identify features in the pre-treatment data that are prognostic for risk of relapse.  ...  We would also like to acknowledge Heather Harrington (Centre for Topological Data Analysis, Mathematical Institute, Oxford) for helpful discussions.  ... 
doi:10.1101/2021.12.22.21268233 fatcat:zjtdsadvifcclmyjusouomwmwi

Pore-geometry recognition: on the importance of quantifying similarity in nanoporous materials [article]

Yongjin Lee, Senja D. Barthel, Paweł Dłotko, S. Mohamad Moosavi, Kathryn Hess, Berend Smit
2017 arXiv   pre-print
Here we develop a pore recognition approach to quantify similarity of pore structures and classify them using topological data analysis (3,4).  ...  big-data science.  ...  For a fixed non-negative real number r, the Vietoris-Rips complex of a point cloud is constructed as follows from the collection of balls of radius r centered at the points of the point cloud.  ... 
arXiv:1701.06953v1 fatcat:32qyjytpqzaingjowdbrcpqwai

The persistent homology mathematical framework provides enhanced genotype-to-phenotype associations for plant morphology

Mao Li, Margaret Frank, Viktoriya Coneva, Washington Mio, Daniel H Chitwood, Christopher N. Topp
2018 Plant Physiology  
Landmarks (Weight et al., 2008; Chitwood et al., 2016) and pseudolandmarks (Langlade et al., 2005) rely on homologous points that collectively represent shapes.  ...  Elliptical Fourier descriptors (Kuhl and Giardina, 1982; Chitwood, 2014a) are a continuous representation of a closed contour that treats outlines as a wave and approximates their features as a harmonic  ...  Our pipeline for converting 2D plant imaging data into persistence barcodes involves four main steps: extracting point clouds from images, converting point clouds to functions, forming filtrations, and  ... 
doi:10.1104/pp.18.00104 pmid:29871979 fatcat:5yywkdapdrhohfsevhjihefro4

Geometric Landscapes for Material Discovery within Energy-Structure-Function Maps

Seyed Mohamad Moosavi, Henglu Xu, Linjiang Chen, Andrew Cooper, Berend Smit
2020 Chemical Science  
Fig. 1 1 Calculation steps for computing the persistent homology barcodes for a porous molecular crystal. First, a point cloud is sampled on the pore surface of the material.  ...  Then, the persistent homology barcodes are computed for this point cloud. The figure on the right is the persistent diagram of the barcodes of the material computed up to the second dimension.  ... 
doi:10.1039/d0sc00049c pmid:34094069 pmcid:PMC8159328 fatcat:vzk4ugmmprhtxgfxedvkvdaruu

Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors

Oliver Vipond, Joshua A Bull, Philip S Macklin, Ulrike Tillmann, Christopher W Pugh, Helen M Byrne, Heather A Harrington
2021 Proceedings of the National Academy of Sciences of the United States of America  
Quantification of heterogeneous and noisy data-often with outliers, artifacts, and mislabeled points-such as those from tissues, remains a challenge.  ...  The mathematical field that extracts information from the shape of data, topological data analysis (TDA), has expanded its capability for analyzing real-world datasets in recent years by extending theory  ...  A dvances in topological data analysis (TDA), an emerging field of mathematics that studies shape within datasets, offer novel descriptors of spatial data that have the potential to inform histological  ... 
doi:10.1073/pnas.2102166118 pmid:34625491 pmcid:PMC8522280 fatcat:xnax7gbvzncwnhvse33dxjog4i

Persistent topology of protein space [article]

W. Hamilton, J.E. Borgert, T. Hamelryck, J.S. Marron
2021 arXiv   pre-print
In particular, we use alpha shape filtrations to compare a topological representation of the data with a different representation that makes use of knot-theoretic ideas.  ...  Protein fold classification is a classic problem in structural biology and bioinformatics. We approach this problem using persistent homology.  ...  Recall that the Voronoi cell of a point in a point cloud 1 , 2 , ..., is the set = { : | − | ≤ | − | for ≠ }.  ... 
arXiv:2102.06768v2 fatcat:u6wnzehxkvfpnbqvmbvzrjs4gm

Diagnosis of Pediatric Obstructive Sleep Apnea via Face Classification with Persistent Homology and Convolutional Neural Networks [article]

Milad Kiaee, Adam B Kashlak, Jisu Kim, Giseon Heo
2019 arXiv   pre-print
In this comparative study, we consider both persistent homology and geometric shape analysis from the field of computational topology as well as convolutional neural networks, a powerful method from deep  ...  The gold standard for diagnosis is an overnight sleep study, which is often unobtainable by many potentially suffering from this condition.  ...  In other words, the manifold was transformed to a topological descriptors on each data set: point clouds and curves.  ... 
arXiv:1911.05628v1 fatcat:mdbzlwswn5bjvnqo2axiwvgdri

Foreword to the Special Section on Shape Modeling International 2020

David Bommes, Nico Pietroni, Ruizhen Hu
2020 Computers & graphics  
Zhang et al. [16] Subdivision II • Multi-sided implicit surfacing with I-patches, A. Sipos et al. [17] • Data-driven quasi-interpolant spline surfaces for point cloud ap- proximation , A.  ...  Machchhar et al. [20] • Automatically Modeling Piecewise Planar Furniture Shapes from Unorganized Point Cloud , J. Zhao et al. [21] • Co-skeletons: Consistent Curve Skeletons for Shape Families , Z.  ...  Her research interests are in computer graphics, with a recent focus on applying machine learning to advance the understanding and generative modeling of visual data including 3D shapes and indoor scenes  ... 
doi:10.1016/j.cag.2020.07.005 pmid:32834191 pmcid:PMC7368407 fatcat:zkzdgxialbhajpgf4t44bnvqxu

Topological Time Series Analysis

Jose A. Perea
2019 Notices of the American Mathematical Society  
Thus far we have that the Betti numbers capture the homology of a space, yielding succinct shape descriptors for its topology.  ...  show in [5] that, given time series data, effective classifiers can be trained on features from the barcodes of sliding window point clouds, with the goal of automatically segmenting a system into different  ... 
doi:10.1090/noti1869 fatcat:ie77img6qzefpoqukenefvulf4

Persistent homology and the branching topologies of plants

Mao Li, Keith Duncan, Christopher N. Topp, Daniel H. Chitwood
2017 American Journal of Botany  
Shapes can also be viewed as waves that form a closed contour, to which a Fourier-based decomposition technique, elliptical Fourier descriptors (EFDs), can be applied ( Kuhl and Giardina, 1982 ) .  ...  shape as a multicoordinate object.  ...  Consider a set of points-for example, stomata on a leaf, locations of trees imaged by satellite across large swaths of land ( Mander et al., 2017 ) , or point cloud data from an agricultural fi eld as  ... 
doi:10.3732/ajb.1700046 pmid:28341629 fatcat:ldtqk4yosngkdjkxjb4kbwgci4

Persistence Barcodes for Shapes [article]

Gunnar Carlssony, Afra Zomorodian, Anne Collins, Leonidas Guibas
2004 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
Applying persistent homology, we obtain a shape descriptor, called a barcode, that is a finite union of intervals.  ...  We define a metric over the space of such intervals, arriving at a continuous invariant that reflects the geometric properties of shapes.  ...  Such a set of points, commonly called point cloud data or PCD for short, is a discrete topological space.  ... 
doi:10.2312/sgp/sgp04/127-138 fatcat:k4uqci3dancm3bwe64dbn376tu

A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science [article]

Lander Ver Hoef and Henry Adams and Emily J. King and Imme Ebert-Uphoff
2022 arXiv   pre-print
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science.  ...  To this end, we frame our discussion around a guiding example of classifying satellite images from the Sugar, Fish, Flower, and Gravel Dataset produced for the study of mesocale organization of clouds  ...  cloud of data points (Carlsson 2009) .  ... 
arXiv:2207.10552v1 fatcat:skdidlxdube5lgb3jp6mxuybou

Topological Data Analysis for Eye Fundus Image Quality Assessment

Gener José Avilés-Rodríguez, Juan Iván Nieto-Hipólito, María de los Ángeles Cosío-León, Gerardo Salvador Romo-Cárdenas, Juan de Dios Sánchez-López, Patricia Radilla-Chávez, Mabel Vázquez-Briseño
2021 Diagnostics  
Then, 30 vectorized topological descriptors were calculated from each image and used as input to a classification algorithm.  ...  Performance results on the validation subset showed a global accuracy of 0.932, precision of 0.912 for label "quality" and 0.952 for label "no quality", recall of 0.932 for label "quality" and 0.912 for  ...  Acknowledgments: The authors acknowledge the financial support from Universidad Autónoma de Baja California, the MyDCI graduate program, and the Mexican Consejo Nacional de Ciencia y Tecnología (CONACYT) for  ... 
doi:10.3390/diagnostics11081322 fatcat:inzcshfzmffofpaseeube73ney
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