Biomedical Applications of Geometric Functional Data Analysis

Matuk, James; Mohammed, Shariq; Kurtek, Sebastian; Bharath, Karthik

doi:10.1007/978-3-030-31351-7_24

Cited by 9 publications

(3 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Geometric Morphometric methods have been used in fields such as evolutionary biology (8,28), medical image analysis (29,30), and archaeology (16,31,32) for many years. Diffeomorphic methods, by contrast, have been applied only recently (e.g., (33)(34)(35)(36)(37)(38)(39)(40)(41)). As far as we know these two, very different, approaches to shape analysis have not been tested against each other on real objects.…”

Section: Geometricmentioning

confidence: 99%

Classifying Organisms and Artefacts By Their Shapes

Salili-James¹,

MacKay²,

Rodríguez-Álvarez³

et al. 2021

Preprint

View full text Add to dashboard Cite

Section: Geometricmentioning

confidence: 99%

Classifying Organisms and Artefacts By Their Shapes

Salili-James¹,

MacKay²,

Rodríguez-Álvarez³

et al. 2021

Preprint

View full text Add to dashboard Cite

“…Diffeomorphic methods, by contrast, have been applied only recently (e.g. [ 33 – 41 ]). As far as we know, these two, rather different, approaches to shape analysis have not been tested against each other on real objects.…”

Section: Introductionmentioning

confidence: 99%

Classifying organisms and artefacts by their outline shapes

Salili-James

Mackay

Rodríguez-Álvarez

et al. 2022

J. R. Soc. Interface.

View full text Add to dashboard Cite

We often wish to classify objects by their shapes. Indeed, the study of shapes is an important part of many scientific fields, such as evolutionary biology, structural biology, image processing and archaeology. However, mathematical shape spaces are rather complicated and nonlinear. The most widely used methods of shape analysis, geometric morphometrics, treat the shapes as sets of points. Diffeomorphic methods consider the underlying curve rather than points, but have rarely been applied to real-world problems. Using a machine classifier, we tested the ability of several of these methods to describe and classify the shapes of a variety of organic and man-made objects. We find that one method, based on square-root velocity functions (SRVFs), outperforms all others, including a standard geometric morphometric method (eigenshapes), and that it is also superior to human experts using shape alone. When the SRVF approach is constrained to take account of homologous landmarks it can accurately classify objects of very different shapes. The SRVF method identifies a shortest path between shapes, and we show that this can be used to estimate the shapes of intermediate steps in evolutionary series. Diffeomorphic shape analysis methods, we conclude, now provide practical and effective solutions to many shape description and classification problems in the natural and human sciences.

show abstract

“…This framework of permutation tests and classification models has also been successfully used for the analysis of imaging data in the context of diabetic retinopathy. 17,18…”

mentioning

confidence: 99%