# A Measure of Directional Outlyingness with Applications to Image Data and Video

arXiv: https://arxiv.org/abs/1608.05012 · HTML: https://mlsanity.com/paper/1608.05012/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2016.

## Built on by (most cited first, 3 of 3)

- [Functional Anomaly Detection: a Benchmark Study](https://mlsanity.com/paper/2201.05115/) (2022)
- [A geometric perspective on functional outlier detection](https://mlsanity.com/paper/2109.06849/) (2021)
- [Kernel Outlier Detection](https://mlsanity.com/paper/2506.22994/) (2025)

## Abstract (arXiv)

Functional data covers a wide range of data types. They all have in common that the observed objects are functions of of a univariate argument (e.g. time or wavelength) or a multivariate argument (say, a spatial position). These functions take on values which can in turn be univariate (such as the absorbance level) or multivariate (such as the red/green/blue color levels of an image). In practice it is important to be able to detect outliers in such data. For this purpose we introduce a new measure of outlyingness that we compute at each gridpoint of the functions' domain. The proposed Directional Outlyingness} (DO) measure accounts for skewness in the data and only requires O(n) computation time per direction. We derive the influence function of the DO and compute a cutoff for outlier detection. The resulting heatmap and functional outlier map reflect local and global outlyingness of a function. To illustrate the performance of the method on real data it is applied to spectra, MRI images, and video surveillance data.