# LiftFormer: Lifting and Frame Theory Based Monocular Depth Estimation Using Depth and Edge Oriented Subspace Representation

arXiv: https://arxiv.org/abs/2604.06576 · HTML: https://mlsanity.com/paper/2604.06576/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 80 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [AdaBins: Depth Estimation using Adaptive Bins](https://mlsanity.com/paper/2011.14141/) (2020)
- [BEVDepth: Acquisition of Reliable Depth for Multi-view 3D Object Detection](https://mlsanity.com/paper/2206.10092/) (2022)
- [ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases](https://mlsanity.com/paper/2103.10697/) (2021)
- [3D Packing for Self-Supervised Monocular Depth Estimation](https://mlsanity.com/paper/1905.02693/) (2019)
- [From Big to Small: Multi-Scale Local Planar Guidance for Monocular Depth Estimation](https://mlsanity.com/paper/1907.10326/) (2019)
- [Unsupervised CNN for Single View Depth Estimation: Geometry to the Rescue](https://mlsanity.com/paper/1603.04992/) (2016)
- [CMT: Convolutional Neural Networks Meet Vision Transformers](https://mlsanity.com/paper/2107.06263/) (2021)
- [BinsFormer: Revisiting Adaptive Bins for Monocular Depth Estimation](https://mlsanity.com/paper/2204.00987/) (2022)
- [Learning Depth from Monocular Videos using Direct Methods](https://mlsanity.com/paper/1712.00175/) (2017)
- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](https://mlsanity.com/paper/2203.01502/) (2022)
- [DDP: Diffusion Model for Dense Visual Prediction](https://mlsanity.com/paper/2303.17559/) (2023)
- [Rethinking BiSeNet For Real-time Semantic Segmentation](https://mlsanity.com/paper/2104.13188/) (2021)
- [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)
- [Deep Convolutional Neural Fields for Depth Estimation from a Single Image](https://mlsanity.com/paper/1411.6387/) (2014)
- [PanoFormer: Panorama Transformer for Indoor 360 Depth Estimation](https://mlsanity.com/paper/2203.09283/) (2022)
- [FastDepth: Fast Monocular Depth Estimation on Embedded Systems](https://mlsanity.com/paper/1903.03273/) (2019)

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

- [Monocular Depth Estimation From the Perspective of Feature Restoration: A Diffusion Enhanced Depth Restoration Approach](https://mlsanity.com/paper/2604.07664/) (2026)
- [Adaptive Depth-converted-Scale Convolution for Self-supervised Monocular Depth Estimation](https://mlsanity.com/paper/2604.07665/) (2026)
- [GeoBridge: Evolving Transferable Decoder Topologies for Geometric Vision](https://mlsanity.com/paper/2610.15280/) (2026)

## Abstract (arXiv)

Monocular depth estimation (MDE) has attracted increasing interest in the past few years, owing to its important role in 3D vision. MDE is the estimation of a depth map from a monocular image/video to represent the 3D structure of a scene, which is a highly ill-posed problem. To solve this problem, in this paper, we propose a LiftFormer based on lifting theory topology, for constructing an intermediate subspace that bridges the image color features and depth values, and a subspace that enhances the depth prediction around edges. MDE is formulated by transforming the depth value prediction problem into depth-oriented geometric representation (DGR) subspace feature representation, thus bridging the learning from color values to geometric depth values. A DGR subspace is constructed based on frame theory by using linearly dependent vectors in accordance with depth bins to provide a redundant and robust representation. The image spatial features are transformed into the DGR subspace, where these features correspond directly to the depth values. Moreover, considering that edges usually present sharp changes in a depth map and tend to be erroneously predicted, an edge-aware representation (ER) subspace is constructed, where depth features are transformed and further used to enhance the local features around edges. The experimental results demonstrate that our LiftFormer achieves state-of-the-art performance on widely used datasets, and an ablation study validates the effectiveness of both proposed lifting modules in our LiftFormer.