# Perspective Transformation Layer

arXiv: https://arxiv.org/abs/2201.05706 · HTML: https://mlsanity.com/paper/2201.05706/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 14 Jan 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Perspective Transformer Nets: Learning Single-View 3D Object Reconstruction without 3D Supervision](https://mlsanity.com/paper/1612.00814/) (2016)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Deep attention-based classification network for robust depth prediction](https://mlsanity.com/paper/1807.03959/) (2018)
- [Equivariant Transformer Networks](https://mlsanity.com/paper/1901.11399/) (2019)
- [Inverse Compositional Spatial Transformer Networks](https://mlsanity.com/paper/1612.03897/) (2016)
- [On Classification of Distorted Images with Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.01924/) (2017)
- [DECA: Deep viewpoint-Equivariant human pose estimation using Capsule Autoencoders](https://mlsanity.com/paper/2108.08557/) (2021)
- [gvnn: Neural Network Library for Geometric Computer Vision](https://mlsanity.com/paper/1607.07405/) (2016)
- [Detecting Lane and Road Markings at A Distance with Perspective Transformer Layers](https://mlsanity.com/paper/2003.08550/) (2020)

## Built on by (most cited first, 1 of 1)

- [TIACam: Text-Anchored Invariant Feature Learning with Auto-Augmentation for Camera-Robust Zero-Watermarking](https://mlsanity.com/paper/2602.18863/) (2026)

## Abstract (arXiv)

Incorporating geometric transformations that reflect the relative position changes between an observer and an object into computer vision and deep learning models has attracted much attention in recent years. However, the existing proposals mainly focus on the affine transformation that is insufficient to reflect such geometric position changes. Furthermore, current solutions often apply a neural network module to learn a single transformation matrix, which not only ignores the importance of multi-view analysis but also includes extra training parameters from the module apart from the transformation matrix parameters that increase the model complexity. In this paper, a perspective transformation layer is proposed in the context of deep learning. The proposed layer can learn homography, therefore reflecting the geometric positions between observers and objects. In addition, by directly training its transformation matrices, a single proposed layer can learn an adjustable number of multiple viewpoints without considering module parameters. The experiments and evaluations confirm the superiority of the proposed layer.