# Mapped Convolutions

arXiv: https://arxiv.org/abs/1906.11096 · HTML: https://mlsanity.com/paper/1906.11096/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

## Built on by (most cited first, 14 of 14)

- [OmniFusion: 360 Monocular Depth Estimation via Geometry-Aware Fusion](https://mlsanity.com/paper/2203.00838/) (2022)
- [ACDNet: Adaptively Combined Dilated Convolution for Monocular Panorama Depth Estimation](https://mlsanity.com/paper/2112.14440/) (2021)
- [Pano3D: A Holistic Benchmark and a Solid Baseline for 360o Depth Estimation](https://mlsanity.com/paper/2109.02749/) (2021)
- [HRDFuse: Monocular 360degDepth Estimation by Collaboratively Learning Holistic-with-Regional Depth Distributions](https://mlsanity.com/paper/2303.11616/) (2023)
- [PanelNet: Understanding 360 Indoor Environment via Panel Representation](https://mlsanity.com/paper/2305.09078/) (2023)
- [High-Resolution Depth Estimation for 360-degree Panoramas through Perspective and Panoramic Depth Images Registration](https://mlsanity.com/paper/2210.10414/) (2022)
- [PanoDepth: A Two-Stage Approach for Monocular Omnidirectional Depth Estimation](https://mlsanity.com/paper/2202.01323/) (2022)
- [OmniLayout: Room Layout Reconstruction from Indoor Spherical Panoramas](https://mlsanity.com/paper/2104.09403/) (2021)
- [Single-Shot Cuboids: Geodesics-based End-to-end Manhattan Aligned Layout Estimation from Spherical Panoramas](https://mlsanity.com/paper/2102.03939/) (2021)
- [Hybrid Skip: A Biologically Inspired Skip Connection for the UNet Architecture](https://mlsanity.com/paper/2207.04721/) (2022)
- [Neural Contourlet Network for Monocular 360 Depth Estimation](https://mlsanity.com/paper/2208.01817/) (2022)
- [Deformable Convolution Based Road Scene Semantic Segmentation of Fisheye Images in Autonomous Driving](https://mlsanity.com/paper/2407.16647/) (2024)
- [SphereFusion: Efficient Panorama Depth Estimation via Gated Fusion](https://mlsanity.com/paper/2502.05859/) (2025)
- [Cross-Domain Synthetic-to-Real In-the-Wild Depth and Normal Estimation for 3D Scene Understanding](https://mlsanity.com/paper/2212.05040/) (2022)

## Abstract (arXiv)

We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these two components, freeing the operation from the confines of the image grid and allowing the kernel to process any type of structured data. As a test case, we demonstrate its use by applying it to dense inference on spherical data. We perform an in-depth study of existing spherical image convolution methods and propose an improved sampling method for equirectangular images. Then, we discuss the impact of data discretization when deriving a sampling function, highlighting drawbacks of the cube map representation for spherical data. Finally, we illustrate how mapped convolutions enable us to convolve directly on a mesh by projecting the spherical image onto a geodesic grid and training on the textured mesh. This method exceeds the state of the art for spherical depth estimation by nearly 17%. Our findings suggest that mapped convolutions can be instrumental in expanding the application scope of convolutional neural networks.