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Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields
Abstract
The maximum of a Gaussian random field was used by Worsley et al. (1992) to test for activation at an unknown point in positron emission tomography images of blood flow in the human brain. The Euler characteristic of excursion sets was used as an estimator of the number of regions of activation. The expected Euler characteristic of excursion sets of stationary Gaussian random fields has been derived by Adler and Hasofer (1976) and Adler (1981). In this paper we extend the results of Adler (1981) toχ2,Fandtfields. The theory is applied to some three-dimensional images of cerebral blood flow from a study on pain perception.
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Cited by
Statistical parametric maps in functional imaging: A general linear approach
Friston, K. J., Holmes, A. P., Worsley, K. J., Poline, J. ‐., Frith, C. D., & Frackowiak, R. S. J. (1994) · Human Brain Mapping · doi:10.1002/hbm.460020402 · Cited by 9,688
Self-citationNonparametric permutation tests for functional neuroimaging: A primer with examples
Nichols, T. E., & Holmes, A. P. (2002) · Human Brain Mapping · doi:10.1002/hbm.1058 · Cited by 6,256
Subcortical and cortical brain activity during the feeling of self-generated emotions
Damasio, A. R., Grabowski, T. J., Bechara, A., Damasio, H., Ponto, L. L. B., Parvizi, J., & Hichwa, R. D. (2000) · Nature Neuroscience · doi:10.1038/79871 · Cited by 2,117
Detecting activations in PET and fMRI: levels of inference and power
Friston, K. J., Holmes, A., Poline, J.-B., Price, C. J., & Frith, C. D. (1996) · NeuroImage · doi:10.1006/nimg.1996.0074 · Cited by 1,148
Generalized N-Dimensional Biomechanical Field Analysis Using Statistical Parametric Mapping
Pataky, T. C. (2010) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2010.03.008 · Cited by 907
Metadata
- Authors
- Worsley, K. J.
- Venue
- Advances in Applied Probability
- Publisher
- Cambridge University Press
- Published
- 1994-03-01
- Volume
- 26
- Issue
- 01
- Pages
- 13-42
- ISSN
- 0001-8678 (ISSN-L)
- OpenAlex
- W4238054270
- Cited by
- 309
- References
- 0
- FWCI
- 17.54
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields. https://app.cochat.ai/papers/10.1017/s0001867800025970
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- Worsley, K. J. (1994). Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields. Advances in Applied Probability. https://doi.org/10.1017/s0001867800025970
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
