# Defocus Aberration Theory Confirms Gaussian Model in Most Imaging Devices

arXiv: https://arxiv.org/abs/2601.04779 · HTML: https://mlsanity.com/paper/2601.04779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 7 of 7)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Learning Depth from Single Monocular Images Using Deep Convolutional Neural Fields](https://mlsanity.com/paper/1502.07411/) (2015)
- [Deep Convolutional Neural Fields for Depth Estimation from a Single Image](https://mlsanity.com/paper/1411.6387/) (2014)
- [DepthTransfer: Depth Extraction from Video Using Non-parametric Sampling](https://mlsanity.com/paper/2001.00987/) (2019)
- [GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimation](https://mlsanity.com/paper/2012.06980/) (2020)
- [Exact Blur Measure Outperforms Conventional Learned Features for Depth Finding](https://mlsanity.com/paper/1709.00072/) (2017)

## Abstract (arXiv)

Over the past three decades, defocus has consistently provided groundbreaking depth information in scene images. However, accurately estimating depth from 2D images continues to be a persistent and fundamental challenge in the field of 3D recovery. Heuristic approaches involve with the ill-posed problem for inferring the spatial variant defocusing blur, as the desired blur cannot be distinguished from the inherent blur. Given a prior knowledge of the defocus model, the problem become well-posed with an analytic solution for the relative blur between two images, taken at the same viewpoint with different camera settings for the focus. The Gaussian model stands out as an optimal choice for real-time applications, due to its mathematical simplicity and computational efficiency. And theoretically, it is the only model can be applied at the same time to both the absolute blur caused by depth in a single image and the relative blur resulting from depth differences between two images. This paper introduces the settings, for conventional imaging devices, to ensure that the defocusing operator adheres to the Gaussian model. Defocus analysis begins within the framework of geometric optics and is conducted by defocus aberration theory in diffraction-limited optics to obtain the accuracy of fitting the actual model to its Gaussian approximation. The results for a typical set of focused depths between 1 and 100 meters, with a maximum depth variation of 10% at the focused depth, confirm the Gaussian model's applicability for defocus operators in most imaging devices. The findings demonstrate a maximum Mean Absolute Error (!M!A!E) of less than 1%, underscoring the model's accuracy and reliability.