• 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
Foundations of Data Science, accepted for publication, 2024
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

• A Topological Study of Functional Data and Fréchet Functions of Metric Measure Spaces

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

• Learning Shape Metrics with Monte Carlo Optimization

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

• The Persistent Homology Mathematical Framework Provides Enhanced Genotype-to-Phenotype Associations for Plant Morphology

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

• The Shape of Data and Probability Measures

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

• Probing the Geometry of Data with Diffusion Fréchet Functions

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

• Human Facial Shape and Size Heritability and Genetic Correlations

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

• Morphological Plant Modeling: Unleashing Geometric and Topological Potential Within the Plant Sciences

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

• A Morphometric Analysis of Vegetation Patterns in Dryland Ecosystems

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

• Rapid Automated Landmarking for Morphometric Analysis of Three Dimensional Facial Scans

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

• Genome-Wide Association Study Reveals Multiple Loci Influencing Normal Human Facial Morphology

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

• Genomewide Association Study of Facial Variation in African Children Identifies Association of SCHIP1 and PDE8A with Facial Size

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

• Automatic Stage Identification of Drosophila Egg Chamber Based on DAPI Images

D. Jia, Q. Xu, Q. Xie, W. Mio, W-M. Deng
Scientific Reports 6 (2015), doi:10.1038/srep18850

• Morphometrics, 3D Imaging, and Craniofacial Development

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

• Signals From the Brain Induce Variation in Avian Facial Shape

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

• Correlations Between the Morphology of Sonic Hedgehog Expression Domains and Embryonic Craniofacial Shape

Q. Xu, H. Jamniczky, D. Hu, R. M. Green, R. S. Marcucio, B. Hallgrimsson, W. Mio
Evolutionary Biology 42(3) (2015), 379-386.

• Let's Face It - Complex Traits Are Just Not That Simple

B. Hallgrimsson, W. Mio, R. Marcucio, R. Spritz
PLOS Genetics 10:e1004724, 2014.

• Density Estimators of Gaussian Type on Closed Riemannian Manifolds

J. Bates and W. Mio
Journal of Mathematical Imaging and Vision 50 (2014), 53-59.

• Identification of Grass Pollen Through the Quantitative Analysis of Surface Ornamentation and Texture

L. Mander, M. Li, W. Mio, C. Fowlkes, S. Punyasena
Proc. Royal Soc. B: Biological Sciences 280 (2013), 20131905.

• Multiscale Covariance Fields, Local Scales, and Shape Transforms

D. H. Diaz Martinez, F. Mémoli, W. Mio
Proc. Geometric Science of Information (Paris, France, 2013), LNCS 8085, 794-801, Springer, 2013.

• Genetics and Evolution of Function-Valued Traits: Understanding Environmentally Responsive Phenotypes

J. Stinchcombe, Function-Valued Traits Working Group, M. Kirkpatrick
Trends in Ecology and Evolution (TREE) 27(11) (2012), 637-647

• Spatial Sampling for Image Segmentation

M. Rivera, O. Dalmau, W. Mio, A. Ramirez-Manzanares
The Computer Journal 55(3) (2012), 313-324.

• Bioinspiration from Biodiversity in Sensor Design

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.

• A Computational Model of Multidimensional Shape

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.

• Models of Normal Variation and Local Contrasts in Hippocampal Anatomy

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.

• Shape of Elastic Strings in Euclidean Space

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.

• On Shape of Plane Elastic Curves

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.