# Depth Estimation from a Single Optical Encoded Image using a Learned Colored-Coded Aperture

arXiv: https://arxiv.org/abs/2309.08033 · HTML: https://mlsanity.com/paper/2309.08033/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [Deeper Depth Prediction with Fully Convolutional Residual Networks](https://mlsanity.com/paper/1606.00373/) (2016)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [Enforcing geometric constraints of virtual normal for depth prediction](https://mlsanity.com/paper/1907.12209/) (2019)
- [Cost-Effective Active Learning for Deep Image Classification](https://mlsanity.com/paper/1701.03551/) (2017)
- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](https://mlsanity.com/paper/2203.01502/) (2022)
- [Revisiting Single Image Depth Estimation: Toward Higher Resolution Maps with Accurate Object Boundaries](https://mlsanity.com/paper/1803.08673/) (2018)
- [DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation](https://mlsanity.com/paper/2203.14211/) (2022)
- [P3Depth: Monocular Depth Estimation with a Piecewise Planarity Prior](https://mlsanity.com/paper/2204.02091/) (2022)
- [Lite-Mono: A Lightweight CNN and Transformer Architecture for Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/2211.13202/) (2022)
- [Multi-Scale Continuous CRFs as Sequential Deep Networks for Monocular Depth Estimation](https://mlsanity.com/paper/1704.02157/) (2017)
- [Monocular Depth Estimation Based On Deep Learning: An Overview](https://mlsanity.com/paper/2003.06620/) (2020)
- [Deep Optics for Monocular Depth Estimation and 3D Object Detection](https://mlsanity.com/paper/1904.08601/) (2019)
- [Robust Monocular Depth Estimation under Challenging Conditions](https://mlsanity.com/paper/2308.09711/) (2023)
- [Single-shot Hyperspectral-Depth Imaging with Learned Diffractive Optics](https://mlsanity.com/paper/2009.00463/) (2020)
- [Hierarchical Regression Network for Spectral Reconstruction from RGB Images](https://mlsanity.com/paper/2005.04703/) (2020)
- [Deep Depth from Defocus: how can defocus blur improve 3D estimation using dense neural networks?](https://mlsanity.com/paper/1809.01567/) (2018)
- [Time-Multiplexed Coded Aperture Imaging: Learned Coded Aperture and Pixel Exposures for Compressive Imaging Systems](https://mlsanity.com/paper/2104.02820/) (2021)
- [Deep Coded Aperture Design: An End-to-End Approach for Computational Imaging Tasks](https://mlsanity.com/paper/2105.03390/) (2021)
- [Deep Optical Coding Design in Computational Imaging](https://mlsanity.com/paper/2207.00164/) (2022)
- [Data Driven Coded Aperture Design for Depth Recovery](https://mlsanity.com/paper/1705.10021/) (2017)

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

- [Integration of Programmable Diffraction with Digital Neural Networks](https://mlsanity.com/paper/2406.10688/) (2024)
- [Distilling Knowledge for Designing Computational Imaging Systems](https://mlsanity.com/paper/2501.17898/) (2025)
- [Aperture-aware Dispersion 5-D Light-field Imaging Spectrometer](https://mlsanity.com/paper/2607.04635/) (2026)

## Abstract (arXiv)

Depth estimation from a single image of a conventional camera is a challenging task since depth cues are lost during the acquisition process. State-of-the-art approaches improve the discrimination between different depths by introducing a binary-coded aperture (CA) in the lens aperture that generates different coded blur patterns at different depths. Color-coded apertures (CCA) can also produce color misalignment in the captured image which can be utilized to estimate disparity. Leveraging advances in deep learning, more recent works have explored the data-driven design of a diffractive optical element (DOE) for encoding depth information through chromatic aberrations. However, compared with binary CA or CCA, DOEs are more expensive to fabricate and require high-precision devices. Different from previous CCA-based approaches that employ few basic colors, in this work we propose a CCA with a greater number of color filters and richer spectral information to optically encode relevant depth information in a single snapshot. Furthermore, we propose to jointly learn the color-coded aperture (CCA) pattern and a convolutional neural network (CNN) to retrieve depth information by using an end-to-end optimization approach. We demonstrate through different experiments on three different data sets that the designed color-encoding has the potential to remove depth ambiguities and provides better depth estimates compared to state-of-the-art approaches. Additionally, we build a low-cost prototype of our CCA using a photographic film and validate the proposed approach in real scenarios.