# InverseForm: A Loss Function for Structured Boundary-Aware Segmentation

arXiv: https://arxiv.org/abs/2104.02745 · HTML: https://mlsanity.com/paper/2104.02745/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 54 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation](https://mlsanity.com/paper/1909.11065/) (2019)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [PointRend: Image Segmentation as Rendering](https://mlsanity.com/paper/1912.08193/) (2019)
- [PAD-Net: Multi-Tasks Guided Prediction-and-Distillation Network for Simultaneous Depth Estimation and Scene Parsing](https://mlsanity.com/paper/1805.04409/) (2018)
- [High-Resolution Representations for Labeling Pixels and Regions](https://mlsanity.com/paper/1904.04514/) (2019)
- [Large Kernel Matters -- Improve Semantic Segmentation by Global Convolutional Network](https://mlsanity.com/paper/1703.02719/) (2017)
- [UberNet: Training a `Universal' Convolutional Neural Network for Low-, Mid-, and High-Level Vision using Diverse Datasets and Limited Memory](https://mlsanity.com/paper/1609.02132/) (2016)
- [Hierarchical Multi-Scale Attention for Semantic Segmentation](https://mlsanity.com/paper/2005.10821/) (2020)
- [Gated-SCNN: Gated Shape CNNs for Semantic Segmentation](https://mlsanity.com/paper/1907.05740/) (2019)
- [MTI-Net: Multi-Scale Task Interaction Networks for Multi-Task Learning](https://mlsanity.com/paper/2001.06902/) (2020)
- [Attentive Single-Tasking of Multiple Tasks](https://mlsanity.com/paper/1904.08918/) (2019)
- [Pattern-Affinitive Propagation across Depth, Surface Normal and Semantic Segmentation](https://mlsanity.com/paper/1906.03525/) (2019)
- [Bi-directional Cross-Modality Feature Propagation with Separation-and-Aggregation Gate for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2007.09183/) (2020)
- [CascadePSP: Toward Class-Agnostic and Very High-Resolution Segmentation via Global and Local Refinement](https://mlsanity.com/paper/2005.02551/) (2020)
- [ACNet: Attention Based Network to Exploit Complementary Features for RGBD Semantic Segmentation](https://mlsanity.com/paper/1905.10089/) (2019)
- [Boundary-Aware Feature Propagation for Scene Segmentation](https://mlsanity.com/paper/1909.00179/) (2019)
- [SegFix: Model-Agnostic Boundary Refinement for Segmentation](https://mlsanity.com/paper/2007.04269/) (2020)
- [Learning Affinity via Spatial Propagation Networks](https://mlsanity.com/paper/1710.01020/) (2017)
- [AET vs. AED: Unsupervised Representation Learning by Auto-Encoding Transformations rather than Data](https://mlsanity.com/paper/1901.04596/) (2019)
- [Temporally Distributed Networks for Fast Video Semantic Segmentation](https://mlsanity.com/paper/2004.01800/) (2020)

## Built on by (most cited first, 30 of 65)

- [HUGS: Holistic Urban 3D Scene Understanding via Gaussian Splatting](https://mlsanity.com/paper/2403.12722/) (2024)
- [Delivering Arbitrary-Modal Semantic Segmentation](https://mlsanity.com/paper/2303.01480/) (2023)
- [HUGSIM: A Real-Time, Photo-Realistic and Closed-Loop Simulator for Autonomous Driving](https://mlsanity.com/paper/2412.01718/) (2024)
- [Vivim: a Video Vision Mamba for Medical Video Segmentation](https://mlsanity.com/paper/2401.14168/) (2024)
- [X-Align: Cross-Modal Cross-View Alignment for Bird's-Eye-View Segmentation](https://mlsanity.com/paper/2210.06778/) (2022)
- [Loss Functions in the Era of Semantic Segmentation: A Survey and Outlook](https://mlsanity.com/paper/2312.05391/) (2023)
- [Semantic Diffusion Network for Semantic Segmentation](https://mlsanity.com/paper/2302.02057/) (2023)
- [X3KD: Knowledge Distillation Across Modalities, Tasks and Stages for Multi-Camera 3D Object Detection](https://mlsanity.com/paper/2303.02203/) (2023)
- [Semantic Image Segmentation: Two Decades of Research](https://mlsanity.com/paper/2302.06378/) (2023)
- [Fully Transformer Networks for Semantic Image Segmentation](https://mlsanity.com/paper/2106.04108/) (2021)
- [Open-World Semantic Segmentation Including Class Similarity](https://mlsanity.com/paper/2403.07532/) (2024)
- [Semi-supervised Multi-task Learning for Semantics and Depth](https://mlsanity.com/paper/2110.07197/) (2021)
- [Centering the Value of Every Modality: Towards Efficient and Resilient Modality-agnostic Semantic Segmentation](https://mlsanity.com/paper/2407.11344/) (2024)
- [Strong but simple: A Baseline for Domain Generalized Dense Perception by CLIP-based Transfer Learning](https://mlsanity.com/paper/2312.02021/) (2023)
- [4D Panoptic Segmentation as Invariant and Equivariant Field Prediction](https://mlsanity.com/paper/2303.15651/) (2023)
- [Delving into Shape-aware Zero-shot Semantic Segmentation](https://mlsanity.com/paper/2304.08491/) (2023)
- [DistractFlow: Improving Optical Flow Estimation via Realistic Distractions and Pseudo-Labeling](https://mlsanity.com/paper/2303.14078/) (2023)
- [Pixel Difference Convolutional Network for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2302.11951/) (2023)
- [U3M: Unbiased Multiscale Modal Fusion Model for Multimodal Semantic Segmentation](https://mlsanity.com/paper/2405.15365/) (2024)
- [X-Distill: Improving Self-Supervised Monocular Depth via Cross-Task Distillation](https://mlsanity.com/paper/2110.12516/) (2021)
- [HS3: Learning with Proper Task Complexity in Hierarchically Supervised Semantic Segmentation](https://mlsanity.com/paper/2111.02333/) (2021)
- [MAGIC++: Efficient and Resilient Modality-Agnostic Semantic Segmentation via Hierarchical Modality Selection](https://mlsanity.com/paper/2412.16876/) (2024)
- [RealEngine: Simulating Autonomous Driving in Realistic Context](https://mlsanity.com/paper/2505.16902/) (2025)
- [Panoptic, Instance and Semantic Relations: A Relational Context Encoder to Enhance Panoptic Segmentation](https://mlsanity.com/paper/2204.05370/) (2022)
- [Boosting Night-time Scene Parsing with Learnable Frequency](https://mlsanity.com/paper/2208.14241/) (2022)
- [DCANet: Differential Convolution Attention Network for RGB-D Semantic Segmentation](https://mlsanity.com/paper/2210.06747/) (2022)
- [DejaVu: Conditional Regenerative Learning to Enhance Dense Prediction](https://mlsanity.com/paper/2303.01573/) (2023)
- [SemARFlow: Injecting Semantics into Unsupervised Optical Flow Estimation for Autonomous Driving](https://mlsanity.com/paper/2303.06209/) (2023)
- [Milestones in Autonomous Driving and Intelligent Vehicles Part II: Perception and Planning](https://mlsanity.com/paper/2306.01980/) (2023)
- [PosSAM: Panoptic Open-vocabulary Segment Anything](https://mlsanity.com/paper/2403.09620/) (2024)

## Abstract (arXiv)

We present a novel boundary-aware loss term for semantic segmentation using an inverse-transformation network, which efficiently learns the degree of parametric transformations between estimated and target boundaries. This plug-in loss term complements the cross-entropy loss in capturing boundary transformations and allows consistent and significant performance improvement on segmentation backbone models without increasing their size and computational complexity. We analyze the quantitative and qualitative effects of our loss function on three indoor and outdoor segmentation benchmarks, including Cityscapes, NYU-Depth-v2, and PASCAL, integrating it into the training phase of several backbone networks in both single-task and multi-task settings. Our extensive experiments show that the proposed method consistently outperforms baselines, and even sets the new state-of-the-art on two datasets.