Florida
State University
Data Science Publications

Washington Mio
Roger W. Roberts Professor in Mathematics
Department of Mathematics
Florida State University

Geometric and Topological Data Analysis & Applications

  • Stability and Approximations for Decorated Reeb Spaces
J. Curry, W. Mio, T. Needham, O.B. Okutan, F. Russold
Symposium on Computational Geometry (SoCG), Athens, Greece, June 2024
Preprint: arXiv:2312.01982
  • On Metrics for Analysis of Functional Data on Geometric Domains
S. Anbouhi, W. Mio, O.B. Okutan
Submitted for publication, 2023
Preprint: arXiv:2309.10907, early version: arXiv:2208.04782
  • Topologically Attributed Graphs for Shape Discrimination
J. Curry, W. Mio, T. Needham, O.B. Okutan, F. Russold
Workshop on Topology, Algebra and Geometry in Machine Learning (TAGML), 40th International Conference on Machine Learning (ICML 2023)
Preprint: arXiv:2306.17805
  • Convergence of Leray Cosheaves for Decorated Mapper Graphs
J. Curry, W. Mio, T. Needham, O.B. Okutan, F. Russold
Abstract, Young Researchers Forum (YRF), 39th International Symposium on Computational Geometry, SoCG 2023
Preprint: arXiv:2303.00130
  • Correspondence Modules and Persistence Sheaves: A Unifying Perspective on One-Parameter Persistent Homology
H. Hang and W. Mio
Japan Journal of Industrial and Applied Mathematics (2022). 10.1007/s13160-022-00517-y
Preprint: arXiv:2006.08557
  • Decorated Merge Trees for Persistent Topology
J. Curry, H. Hang, W. Mio, T. Needham, O.B. Okutan
J Appl. and Comput. Topology (2022). https://doi.org/10.1007/s41468-022-00089-3
Preprint: arXiv:2103.15804v4
  • Detecting Carbon Nanotube Orientation with Topological Data Analysis of Scanning Electron Micrographs
L. Dong, H. Hang, J.G. Park, W. Mio, R. Liang
Nanomaterials (2022), 12(8), 1251. https://doi.org/10.3390/nano12081251
Preprint: arXiv:2108.04375
  • Geometric and Topological Approaches to Shape Variation in Ginkgo Leaves
L. Mander, M. Bauer, H. Hang, W. Mio
R Soc Open Sci. 2021, 8(11): 210978. doi: 10.1098/rsos.210978
Preprint: bioRxiv:2020.10.23.352476v4
H. Hang, F. Mémoli, W. Mio
J Appl. and Comput. Topology (2019). https://doi.org/10.1007/s41468-019-00037-8
Preprint: arXiv:1811.06613
S. Cellat, Y. Fan, W. Mio, G. Ökten
J. Comput. Appl. Math. 348 (2019), 120-129, https://doi.org/10.1016/j.cam.2018.08.043
M. Li, M. H. Frank, V. Coneva, W. Mio, D. Chitwood, C. Topp
Plant Physiology, 2018, https://doi.org/10.1104/pp.18.00104
Preprint: bioRxiv, doi: https://doi.org/10.1101/104141
D. H. Díaz Martínez, F. Mémoli, W. Mio
Appl. Comput. Harmon. Anal. (2018), https://doi.org/10.1016/j.acha.2018.03.003
Preprint: arXiv:1509.04632v2
D. H. Díaz Martínez, C. H. Lee, P. T. Kim, W. Mio
Appl. Comput. Harmon. Anal. (2018), https://doi.org/10.1016/j.acha.2018.01.003
Preprint: arXiv:1605.04955v2
J. B. Cole, M. Manyama, J. R. Larson, D. K. Liberton, T. M. Ferrara, S. L. Riccardi, M. Li, W. Mio, O. D. Klein, S. A. Santorico, B. Hallgrimsson, R. A. Spritz
Genetics 205 (2017), 967-978. doi: 10.1534/genetics.116.193185
A. Bucksch, A. Atta-Boateng, A. F. Azihou, M. A. Balduzzi, D. Battogtokh, A. Baumgartner, B. M. Binder, S. Braybrook, C. Chang, V. Coneva, T. DeWitt, A. Fletcher, M. Gehan, D. H. Diaz Martinez, L. Hong, A. Iyer-Pascuzzi, L. L. Klein, S. A. Leiboff, M. Li, J. Lynch, A. Maizel, J. N. Maloof, R.J.C. Markelz, C. Martinez, L.A. Miller, W. Mio, W. Palubicki, H. Poorter, C. Pradal, C. Price, E. Puttonen, J. Reese, R. Rellan-Alvarez, E. P. Spalding, E. E. Sparks, C. N. Topp, J. H. Williams, D. H. Chitwood
Frontiers in Plant Science (2017) 8:900. doi: 10.3389/fpls.2017.00900
L. Mander, S. C. Dekker, M. Li, W. Mio, S. W. Punyasena, T. M. Lenton
Royal Society Open Science 4, 160443 (2017). http://dx.doi.org/10.1098/rsos.160443
M. Li, J. B. Cole, M. Manyama, J. Larson, J. J. Bannister, D. K. Liberton, S. L. Ricardi, T. M. Ferrara, S. A. Santorico, N. D. Korkert, R. A. Spritz, W. Mio, B. Hallgrimsson
Journal of Anatomy, 2017. doi: 10.1111/joa.12576
J. R. Shaffer, E. Orlova, M. K. Lee, E. J. Leslie, Z. D. Raffensperger, C. L. Heike, M. L. Cunningham, J. T. Hecht, C. H. Kau, N. L. Nidey, L. M. Moreno, G. L. Wehby, J. C. Murray, C. A. Laurie, C. C. Laurie, J. Cole, T. Ferrara, S. Santorico, O. Klein, W. Mio, E. Feingold, B. Hallgrimsson, R. A. Spritz, M. L. Marazita, S. M. Weinberg
PLoS Genet 12(8) (2016): e1006149. doi:10.1371/journal.pgen.1006149
J. Cole, M. F. Manyama, J. R. Larson, D. K. Liberton, T. M. Ferrara, S. L. Riccardi, M. Li, W Mio, O. D. Klein, S. A. Santorico, B. Hallgrimsson, R. A. Spritz
PLoS Genet 12(8) (2016): e1006174. doi:10.1371/journal.pgen.1006174
D. Jia, Q. Xu, Q. Xie, W. Mio, W-M. Deng
Scientific Reports 6 (2015), doi:10.1038/srep18850
B. Hallgrimsson, C. J. Percival, R. Green, N. M. Young, W. Mio, R. Marcucio
In Craniofacial Development, Current Topics in Developmental Biology, Vol. 115 (2015), 561-597. https://doi.org/10.1016/bs.ctdb.2015.09.003
D. Hu, N. Young, Q. Xu, H. Jamniczky, R. M. Green, W. Mio, R. S. Marcucio, B. Hallgrimsson
Developmental Dynamics (Special issue: Evolution & Morphological Diversity) 244(9) (2015), 1133-1143
Q. Xu, H. Jamniczky, D. Hu, R. M. Green, R. S. Marcucio, B. Hallgrimsson, W. Mio
Evolutionary Biology 42(3) (2015), 379-386.
B. Hallgrimsson, W. Mio, R. Marcucio, R. Spritz
PLOS Genetics 10:e1004724, 2014.
J. Bates and W. Mio
Journal of Mathematical Imaging and Vision 50 (2014), 53-59.
L. Mander, M. Li, W. Mio, C. Fowlkes, S. Punyasena
Proc. Royal Soc. B: Biological Sciences 280 (2013), 20131905.
D. H. Diaz Martinez, F. Mémoli, W. Mio
Proc. Geometric Science of Information (Paris, France, 2013), LNCS 8085, 794-801, Springer, 2013.
J. Stinchcombe, Function-Valued Traits Working Group, M. Kirkpatrick
Trends in Ecology and Evolution (TREE) 27(11) (2012), 637-647
M. Rivera, O. Dalmau, W. Mio, A. Ramirez-Manzanares
The Computer Journal 55(3) (2012), 313-324.
R. Mueller, J. Ma, Z. Yan, C. Grimm, W. Mio
International Mechanical Engineering Congress and Exposition (ASME), Denver, CO, 2011.
  • Shape Space Analysis of Structures in Bat Biosonars
R. Mueller, L. Cai, C. Grimm, W. Mio
The Journal of the Acoustic Society of America, 129(4) (2011), 2507.
  • A Hybrid PCA-LDA Model for Dimension Reduction
N. Zhao, W. Mio, X. Liu
International Joint Conference on Neural Networks (IJCNN), San Jose, CA, 2011.
  • Spectral Signatures of Point Clouds and Applications to Detection of Alzheimer's Disease Through Neuroimaging
J. Bates, D. Pafundi, P. Kanel, X. Liu, W. Mio
International Symposium on Biomedical Imaging (ISBI), Chicago IL, 2011.
  • Spatial Sampling for Image Segmentation
M. Rivera, O. Dalmau, W. Mio
25th International Symposium on Computer and Information Science (ISCIS), The Royal Society, London, 2010.
  • A Model of Volumetric Shape for the Analysis of Longitudinal Alzheimer's Disease Data
Xinyang Liu, Xiuwen Liu, Y. Shi, P. Thompson, W. Mio
European Conference on Computer Vision (ECCV), Heraklion, Greece, 2010.
  • Learning Metrics for Shape Classification and Discrimination
Y. Fan, D. Houle, W. Mio
International Conference on Pattern Recognition (ICPR), Istanbul, Turkey, 2010.
  • Scale-Space Spectral Representation of Shape
J. Bates, X. Liu, W. Mio
International Conference on Pattern Recognition (ICPR), Istanbul, Turkey, 2010.
  • A Riemannian Model of Regional Degeneration of the Hippocampus in Alzheimer's Disease
X. Liu, Y. Shi, Y. Wang, P.M. Thompson, W. Mio
International Symposium on Biomedical Imaging (ISBI), Rotterdam, Netherlands, 2010.
X. Liu, Y. Shi, I. Dinov, W. Mio
International Journal of Computer Vision 89(1), 2010.
  • Mapping Hippocampal Atrophy with a Multi-Scale Model of Shape
Xinyang Liu, Y. Shi, J. Morra, Xiuwen Liu, P. Thompson, W. Mio
IEEE International Symposium on Biomedical Imaging (ISBI), Boston, MA, 2009.
  • Registration of Contours of Brain Structures Through a Heat-Kernel Representation of Shape
J. Bates, Y. Wang. X. Liu, W. Mio
IEEE International Symposium on Biomedical Imaging (ISBI), Boston, MA, 2009.
  • Spherical Representations of Shape Using Parametrizations with Minimal Distortion
Q. Yue, Y. Wang, X. Liu, W. Mio
IEEE International Symposium on Biomedical Imaging (ISBI), Boston, MA, 2009.
  • Image Retrieval Based on Intrinsic Spectral Histogram Representation
Y. Zhu, X. Liu, W. Mio
International Joint Conference on Neural Networks (IJCNN), Atlanta, GA, 2009.
  • Optimal Dimension Reduction for Image Retrieval with Correlation Metrics
Y. Zhu, W. Mio, X. Liu
International Joint Conference on Neural Networks (IJCNN), Atlanta, GA, 2009.
  • Geodesic Shape Spaces of Surfaces of Genus Zero
Xiuwen Liu, Washington Mio, Yonggang Shi, Ivo Dinov
MICCAI Workshop on Mathematical Foundations of Computational Anatomy, New York, NY, 2008.
Xinyang Liu, W. Mio, Y. Shi, I. Dinov, Xiuwen Liu, N. Lepore, F. Lepore, M. Fortin, P. Voss, M. Lassonde, P. Thompson
International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), New York, NY, 2008.
  • Transductive Optimal Component Analysis
Y. Zhu, Y. Wu, X. Liu, W. Mio
International Conference on Pattern Recognition (ICPR), Tampa, FL, 2008.
  • Kernel Functions for Robust 3D Surface Registration with Spectral Embeddings
X. Liu, A. Donate, M. Jemison, W. Mio
International Conference on Pattern Recognition (ICPR), Tampa, FL, 2008.
  • Optimal Factor Analysis and Applications to Content-Based Image Retrieval
Y. Zhu, W. Mio, X. Liu
Computer Vision and Computer Graphics: Theory and Applications, J. Braz, A. Ranchordas, H. Araujo, J. Pereira (Eds.), Communications in Computer and Information Sciences, Springer, vol. 21 (2009), 164--176.
W. Mio, J. C. Bowers, and X. Liu
International Journal of Computer Vision, 82(1), 2009, 96-112.
  • Modeling Brain Anatomy with 3D Arrangements of Curves
W. Mio, J. C. Bowers, M. Hurdal, and X. Liu
ICCV workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), Rio de Janeiro, Brazil, 2007.
  • Learning Representations for Object Recognition Using Multi-Stage Optimal Component Analysis
Y. Wu, X. Liu, and W. Mio
Neural Networks 21 (2008), 214-221.
  • Two-Stage Optimal Component Analysis via Dimensional Reduction
Y. Wu, X. Liu, W. Mio, K. Gallivan
Computer Vision and Image Understanding 110 (2008), 91-101.
  • Scalable Optimal Linear Representation for Face and Object Recognition
Y. Wu, X. Liu, and W. Mio
International Conference on Machine Learning and Applications (ICMLA), Cincinnati, OH, 2007.
  • Multi-Stage Optimal Component Analysis
Y. Wu, X. Liu, and W. Mio
International Joint Conference on Machine Neural Networks (IJCNN), Orlando, FL, 2007, 2545-2550.
  • Parametrization, Alignment and Shape of Spherical Surfaces
X. Liu, J. Bowers, and W. Mio
Proc. 2nd International Conference on Computer Vision Theory and Applications (VISAPP, Barcelona, Spain) vol. 1, 2007, 199-206.
  • A Learning Approach to Content-Based Image Categorization and Retrieval
W. Mio. Y. Zhu, and X. Liu
Proc. 2nd International Conference on Computer Vision Theory and Applications (VISAPP, Barcelona, Spain) vol. 2, 2007, 36-43.
  • Landmark Representation of Shapes and Fisher-Rao Geometry
W. Mio and X. Liu
Proc. 13th International Conference on Image Processing (ICIP), Atlanta, GA, 2006.
  • Splitting Factor Analysis and Multi-Class Boosting
X. Liu and W. Mio
Proc. 13th International Conference on Image Processing (ICIP), Atlanta, GA, 2006.

  • Recognition Using Rapid Classification Trees
K. Haynes, X. Liu, and W. Mio
Proc. 13th International Conference on Image Processing (ICIP), Atlanta, GA, 2006.
  • Two-Stage Optimal Component Analysis
Y. Wu, X. Liu, W. Mio, and K. Gallivan
Proc. 13th International Conference on Image Processing (ICIP), Atlanta, GA, 2006, 2041-2044.
  • Riemnnian Structures on Shape Spaces: a Framework for Statistical Inferences
S. Joshi, D. Kaziska, A. Srivastava, and W. Mio
In Statistics and Analysis of Shapes; eds. H. Krim and A. Yezzi, Birkhauser, Boston, 2006.
W. Mio, A. Srivastava, and S. Joshi
International Journal of Computer Vision, 73(3), 307-324, 2007.
  • A Computational Approach to Fisher Information Geometry with Applications to Image Analysis
W. Mio, D. Badlyans, and X. Liu
Proc. of EMMCVPR 2005 (St. Augustine, FL), Lecture Notes in Computer Science 3757 (2005), 18-33.
  • Kernel Methods for Nonlinear Discriminative Data Analysis
X. Liu and W. Mio
Proc. of 5th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), St. Augustine, FL, 2005.
  • 3D Curve Interpolation and Object Reconstruction
S. Baloch, H. Krim, W. Mio, and A. Srivastava
Proc. of the International Conference on Image Processing (ICIP), Genoa, Italy, 2005 .
  • Elastic Shape Models for Interpolations of Curves in Image Sequences
S. Joshi, A. Srivastava, and W. Mio
Proc. of the Conference on Information Processing in Medical Imaging (IPMI), Glenwood Springs, CO, 2005.
  • Non-Parametric Information Geometry and Multi-Scale Models of Texture
W. Mio, D. Badlyans, and X. Liu
Proc. 13th European Signal Processing Conference (EUSIPCO), Antalya, Turkey, 2005.
  • Nonlinearity and Optimal Component Analysis
W. Mio, Q. Zhang, and X. Liu
Proc. of the International Joint Conference on Neural Networks (IJCNN), Montreal, Canada, 2005.
  • Contour Inferences for Image Understanding
W. Mio, A. Srivastava, and X. Liu
International Journal of Computer Vision 69 (2006), 137-144.
  • Elastic-String Models for Representation and Analysis of Planar Shapes
W. Mio and A. Srivastava
Proceedings of the IEEE Computer Society International Conference on Computer Vision and Pattern Recognition (CVPR), Washington, DC, 2004.
  • Learning and Bayesian Shape Extraction for Object Recognition
W. Mio, A. Srivastava, and X. Liu
Proceedings of the 8th European Conference on Computer Vision (ECCV), Prague, Czech Republic, 2004.
  • Hierarchical Organization of Shapes for Efficient Retrieval
S. Joshi, A. Srivastava, W. Mio, and X. Liu
Proceedings of the 8th European Conference on Computer Vision (ECCV), Prague, Czech Republic, 2004.
  • Statistical Shape Analysis: Clustering, Learning and Testing
A. Srivastava, S. Joshi, W. Mio, and X. Liu
IEEE Trans. Pattern Analysis and Machine Intelligence 27 (2005), 590-602.
  • Some Approaches to Shape Analysis
A. Srivastava and W. Mio
Proc. 12th Europena Conference on Signal Processing (EUSIPCO), Vienna, Austria, 2004.
  • Computational Approaches to a Statistical Theory of Shapes
A. Srivastava, W. Mio, X. Liu, and E. Klassen
Proc. 17th Annual Conference on Neural Information Processing Systems (NIPS), Vancouver, Canada, 2003.
  • Geometric Analysis of Constrained Curves for Image Understanding
A. Srivastava, W. Mio, E. Klassen, and X. Liu
Proc. 2nd IEEE International Workshop on Variational, Geometric and Level-Set Methods in Computer Vision (VLSM), Nice, France, 2003.
  • Geometric Analysis of Continuous, Planar Shapes
A. Srivastava, W. Mio, E. Klassen, and S. Joshi
Proc. 4th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Lisbon, Portugal, 2003.
  • Interpolations with Elasticae in Euclidean Spaces
W. Mio, A. Srivastava, and E. Klassen     (pdf)
Quarterly of Applied Mathematics 62 (2004), 359-378.
  • Analysis of Planar Shapes Using Geodesic Paths in Shape Spaces
E. Klassen, A. Srivastava, W. Mio, and S. Joshi
IEEE Trans. Pattern Analysis and Machine Intelligence 26 (2004), 372-383.