# Visual Deprojection: Probabilistic Recovery of Collapsed Dimensions

arXiv: https://arxiv.org/abs/1909.00475 · HTML: https://mlsanity.com/paper/1909.00475/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Uncertainty Inspired Underwater Image Enhancement](https://mlsanity.com/paper/2207.09689/) (2022)
- [Adaptive deep learning framework for robust unsupervised underwater image enhancement](https://mlsanity.com/paper/2212.08983/) (2022)
- [Affine-modeled video extraction from a single motion blurred image](https://mlsanity.com/paper/2104.03777/) (2021)
- [Deep Demixing: Reconstructing the Evolution of Network Epidemics](https://mlsanity.com/paper/2306.07938/) (2023)

## Abstract (arXiv)

We introduce visual deprojection: the task of recovering an image or video that has been collapsed along a dimension. Projections arise in various contexts, such as long-exposure photography, where a dynamic scene is collapsed in time to produce a motion-blurred image, and corner cameras, where reflected light from a scene is collapsed along a spatial dimension because of an edge occluder to yield a 1D video. Deprojection is ill-posed-- often there are many plausible solutions for a given input. We first propose a probabilistic model capturing the ambiguity of the task. We then present a variational inference strategy using convolutional neural networks as functional approximators. Sampling from the inference network at test time yields plausible candidates from the distribution of original signals that are consistent with a given input projection. We evaluate the method on several datasets for both spatial and temporal deprojection tasks. We first demonstrate the method can recover human gait videos and face images from spatial projections, and then show that it can recover videos of moving digits from dramatically motion-blurred images obtained via temporal projection.