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Title: A measure of directional outlyingness with applications to image data and video Authors:  Jakob Raymaekers - KU Leuven (Belgium) [presenting]
Peter Rousseeuw - KU Leuven (Belgium)
Mia Hubert - KU Leuven (Belgium)
Abstract: Images and video can be considered as functional data with a bivariate domain, where the data per grid point can be univariate (e.g. grayscale values) or multivariate (e.g. red, green, and blue intensities). This often yields large datasets, in which outliers may occur that can distort the analysis. At each grid point we propose to compute a fast measure of outlyingness which accounts for skewness in the data. It can be used for univariate data and, by means of projection pursuit, for multivariate data. The influence function of this outlyingness measure is computed as well as its implosion and explosion bias. We also construct a cutoff value for the outlyingness. Heatmaps of the outlyingness indicate the regions in which an image deviates most from the majority of images. To illustrate the performance of the method it is applied to real multivariate functional data. One example consists of MRI images which are augmented with their gradients. We also show an example of video surveillance data, where we compare the exact method with faster approximations.