# Learning Graphical Models of Images, Videos and Their Spatial Transformations

arXiv: https://arxiv.org/abs/1301.3854 · HTML: https://mlsanity.com/paper/1301.3854/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

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

- [World Modeling with Probabilistic Structure Integration](https://mlsanity.com/paper/2509.09737/) (2025)
- [Physical Object Understanding with a Physically Controllable World Model](https://mlsanity.com/paper/2606.00439/) (2026)
- [Perceptual 3D Simulation With Physical World Modeling](https://mlsanity.com/paper/2606.27575/) (2026)

## Abstract (arXiv)

Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by including a discrete transformation variable. The resulting models perform clustering, dimensionality reduction and time-series analysis in a way that is invariant to transformations in the input. Using the EM algorithm, these transformation-invariant models can be fit to static data and time series. We give results on filtering microscopy images, face and facial pose clustering, handwritten digit modeling and recognition, video clustering, object tracking, and removal of distractions from video sequences.