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Documents authored by Chen, Chao

Document
DOI: 10.4230/LIPIcs.SoCG.2022.64
GPU Computation of the Euler Characteristic Curve for Imaging Data

Authors: Fan Wang, Hubert Wagner, and Chao Chen

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Persistent homology is perhaps the most popular and useful tool offered by topological data analysis - with point-cloud data being the most common setup. Its older cousin, the Euler characteristic curve (ECC) is less expressive - but far easier to compute. It is particularly suitable for analyzing imaging data, and is commonly used in fields ranging from astrophysics to biomedical image analysis. These fields are embracing GPU computations to handle increasingly large datasets. We therefore propose an optimized GPU implementation of ECC computation for 2D and 3D grayscale images. The goal of this paper is twofold. First, we offer a practical tool, illustrating its performance with thorough experimentation - but also explain its inherent shortcomings. Second, this simple algorithm serves as a perfect backdrop for highlighting basic GPU programming techniques that make our implementation so efficient - and some common pitfalls we avoided. This is intended as a step towards a wider usage of GPU programming in computational geometry and topology software. We find this is particularly important as geometric and topological tools are used in conjunction with modern, GPU-accelerated machine learning frameworks.
Cite as

Fan Wang, Hubert Wagner, and Chao Chen. GPU Computation of the Euler Characteristic Curve for Imaging Data. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{wang_et_al:LIPIcs.SoCG.2022.64,
  author =	{Wang, Fan and Wagner, Hubert and Chen, Chao},
  title =	{{GPU Computation of the Euler Characteristic Curve for Imaging Data}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.64},
  URN =		{urn:nbn:de:0030-drops-160724},
  doi =		{10.4230/LIPIcs.SoCG.2022.64},
  annote =	{Keywords: topological data analysis, Euler characteristic, Euler characteristic curve, Betti curve, persistent homology, algorithms, parallel programming, algorithm engineering, GPU programming, imaging data}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.11
Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study

Authors: Andrew Aukerman, Mathieu Carrière, Chao Chen, Kevin Gardner, Raúl Rabadán, and Rami Vanguri

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
Persistent homology is a common tool of topological data analysis, whose main descriptor, the persistence diagram, aims at computing and encoding the geometry and topology of given datasets. In this article, we present a novel application of persistent homology to characterize the spatial arrangement of immune and epithelial (tumor) cells within the breast cancer immune microenvironment. More specifically, quantitative and robust characterizations are built by computing persistence diagrams out of a staining technique (quantitative multiplex immunofluorescence) which allows us to obtain spatial coordinates and stain intensities on individual cells. The resulting persistence diagrams are evaluated as characteristic biomarkers of cancer subtype and prognostic biomarker of overall survival. For a cohort of approximately 700 breast cancer patients with median 8.5-year clinical follow-up, we show that these persistence diagrams outperform and complement the usual descriptors which capture spatial relationships with nearest neighbor analysis. This provides new insights and possibilities on the general problem of building (topology-based) biomarkers that are characteristic and predictive of cancer subtype, overall survival and response to therapy.
Cite as

Andrew Aukerman, Mathieu Carrière, Chao Chen, Kevin Gardner, Raúl Rabadán, and Rami Vanguri. Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aukerman_et_al:LIPIcs.SoCG.2020.11,
  author =	{Aukerman, Andrew and Carri\`{e}re, Mathieu and Chen, Chao and Gardner, Kevin and Rabad\'{a}n, Ra\'{u}l and Vanguri, Rami},
  title =	{{Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.11},
  URN =		{urn:nbn:de:0030-drops-121695},
  doi =		{10.4230/LIPIcs.SoCG.2020.11},
  annote =	{Keywords: Topological data analysis, persistence diagrams}
}
Document
Multimedia Contribution
DOI: 10.4230/LIPIcs.SoCG.2017.65
Cardiac Trabeculae Segmentation: an Application of Computational Topology (Multimedia Contribution)

Authors: Chao Chen, Dimitris Metaxas, Yusu Wang, and Pengxiang Wu

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
In this video, we present a research project on cardiac trabeculae segmentation. Trabeculae are fine muscle columns within human ventricles whose both ends are attached to the wall. Extracting these structures are very challenging even with state-of-the-art image segmentation techniques. We observed that these structures form natural topological handles. Based on such observation, we developed a topological approach, which employs advanced computational topology methods and achieve high quality segmentation results.
Cite as

Chao Chen, Dimitris Metaxas, Yusu Wang, and Pengxiang Wu. Cardiac Trabeculae Segmentation: an Application of Computational Topology (Multimedia Contribution). In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 65:1-65:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.SoCG.2017.65,
  author =	{Chen, Chao and Metaxas, Dimitris and Wang, Yusu and Wu, Pengxiang},
  title =	{{Cardiac Trabeculae Segmentation: an Application of Computational Topology}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{65:1--65:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.65},
  URN =		{urn:nbn:de:0030-drops-72429},
  doi =		{10.4230/LIPIcs.SoCG.2017.65},
  annote =	{Keywords: image segmentation, trabeculae, persistent homology, homology localization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1343
Quantifying Homology Classes

Authors: Chao Chen and Daniel Freedman

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
We develop a method for measuring homology classes. This involves three problems. First, we define the size of a homology class, using ideas from relative homology. Second, we define an optimal basis of a homology group to be the basis whose elements' size have the minimal sum. We provide a greedy algorithm to compute the optimal basis and measure classes in it. The algorithm runs in $O(\beta^4 n^3 log^2 n)$ time, where $n$ is the size of the simplicial complex and $\beta$ is the Betti number of the homology group. Third, we discuss different ways of localizing homology classes and prove some hardness results.
Cite as

Chao Chen and Daniel Freedman. Quantifying Homology Classes. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 169-180, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{chen_et_al:LIPIcs.STACS.2008.1343,
  author =	{Chen, Chao and Freedman, Daniel},
  title =	{{Quantifying Homology Classes}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{169--180},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1343},
  URN =		{urn:nbn:de:0030-drops-13434},
  doi =		{10.4230/LIPIcs.STACS.2008.1343},
  annote =	{Keywords: Computational Topology, Computational Geometry, Homology, Persistent Homology, Localization, Optimization}
}
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