Multidim Syst Sign Process https://doi.org/10.1007/s11045-018-0550-z Extended histogram: probabilistic modelling of video content temporal evolutions Elham Shabaninia 1 · Ahmad Reza Naghsh-Nilchi 1 · Shohreh Kasaei 2 Received: 13 March 2017 / Revised: 9 December 2017 / Accepted: 6 January 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract A probabilistic video content analysis method called extended histogram (EH) is proposed for modelling temporal evolutions of a set of histograms extracted from video frames. In EH, the number of counts for each histogram bin is considered as a random variable (instead of a single value) to account for bin variations. This representation is especially suit- able for modelling the dynamic behaviour of a tracked video content of interest in a general manner. The pitfall of such a modelling is its negligence of the temporal order of observa- tions in the collection. To overcome that problem, a hierarchical approach called hierarchical extended histogram (HEH) is proposed for extracting EHs in different levels of the temporal pyramid. Once these generative models are identified for each video, an information-based metric is proposed to be used for defining the similarity of the two EHs. Having this metric, EHs can be used in many different tasks including video retrieval, classification, summa- rization, and so forth. Especially in the case of discriminant learning, probabilistic kernels based on this metric are also defined to be able to use EHs/HEHs alongside machine learning models such as the SVM. Person re-identification and human action recognition are used as pilot applications to show the capabilities of proposed representations. Experimental results show the significant effectiveness of proposed models. Keywords Extended histogram (EH) · Hierarchical extended histogram (HEH) · Probabilistic modelling · Temporal evolutions · Human action recognition · Person re-identification B Ahmad Reza Naghsh-Nilchi nilchi@eng.ui.ac.ir 1 Department of Artificial Intelligence, Faculty of Computer Engineering, University of Isfahan, Isfahan, Iran 2 Department of Computer Engineering, Sharif University of Technology, Tehran, Iran 123