ArticleJournal of vision2021
A method to integrate and classify normal distributions.
Article in Journal of vision, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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Who cites it
4 citing papers in PubMed.
- Proximity as a Ground-Truth Proxy for Training Texture Discrimination and Segmentation.bioRxiv : the preprint server for biology · 2026Article
- Principles of Local and Global Grouping that Underlie Segmentation of Natural Texture Images.bioRxiv : the preprint server for biology · 2026Article
- Article
- Brain Infraslow Activity Correlates With Arousal Levels.Frontiers in neuroscience · 2022Article
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Authors and funding
2 authors.
Funding
Abstract
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases where these integrals are easy to calculate, there exist no general analytical expressions, standard numerical methods, or software for these integrals. Here we present mathematical results and open-source software that provide (a) the probability in any domain of a normal in any dimensions with any parameters; (b) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector; (c) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index, and relation to the receiver operating characteristic (ROC); (d) dimension reduction and visualizations for such problems; and (e) tests for how reliably these methods may be used on given data. We demonstrate these tools with vision research applications of detecting occluding objects in natural scenes and detecting camouflage.
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