# Beyond the Pixel-Wise Loss for Topology-Aware Delineation

arXiv: https://arxiv.org/abs/1712.02190 · HTML: https://mlsanity.com/paper/1712.02190/

## Key facts

- Cited by 83 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2017.

## Built on by (most cited first, 30 of 83)

- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [FANet: A Feedback Attention Network for Improved Biomedical Image Segmentation](https://mlsanity.com/paper/2103.17235/) (2021)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Structure-Aware Image Segmentation with Homotopy Warping](https://mlsanity.com/paper/2112.07812/) (2021)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [SPIN Road Mapper: Extracting Roads from Aerial Images via Spatial and Interaction Space Graph Reasoning for Autonomous Driving](https://mlsanity.com/paper/2109.07701/) (2021)
- [FocusNetv2: Imbalanced Large and Small Organ Segmentation with Adversarial Shape Constraint for Head and Neck CT Images](https://mlsanity.com/paper/2104.01771/) (2021)
- [TA-Net: Topology-Aware Network for Gland Segmentation](https://mlsanity.com/paper/2110.14593/) (2021)
- [Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation](https://mlsanity.com/paper/2411.03228/) (2024)
- [Sequential vessel segmentation via deep channel attention network](https://mlsanity.com/paper/2102.05229/) (2021)
- [DeepMesh: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2106.11795/) (2021)
- [High-Definition Map Generation Technologies For Autonomous Driving](https://mlsanity.com/paper/2206.05400/) (2022)
- [Local Intensity Order Transformation for Robust Curvilinear Object Segmentation](https://mlsanity.com/paper/2202.12587/) (2022)
- [DTU-Net: Learning Topological Similarity for Curvilinear Structure Segmentation](https://mlsanity.com/paper/2205.11115/) (2022)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [Topologically Faithful Multi-class Segmentation in Medical Images](https://mlsanity.com/paper/2403.11001/) (2024)
- [A Systematic Performance Analysis of Deep Perceptual Loss Networks: Breaking Transfer Learning Conventions](https://mlsanity.com/paper/2302.04032/) (2023)
- [Enabling Uncertainty Estimation in Iterative Neural Networks](https://mlsanity.com/paper/2403.16732/) (2024)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods](https://mlsanity.com/paper/2404.18539/) (2024)
- [PointScatter: Point Set Representation for Tubular Structure Extraction](https://mlsanity.com/paper/2209.05774/) (2022)
- [Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matching](https://mlsanity.com/paper/2412.02076/) (2024)
- [TEDS-Net: Enforcing Diffeomorphisms in Spatial Transformers to Guarantee Topology Preservation in Segmentations](https://mlsanity.com/paper/2107.13542/) (2021)
- [PLGAN: Generative Adversarial Networks for Power-Line Segmentation in Aerial Images](https://mlsanity.com/paper/2204.07243/) (2022)
- [SemiCurv: Semi-Supervised Curvilinear Structure Segmentation](https://mlsanity.com/paper/2205.08706/) (2022)
- [Self Pre-training with Topology- and Spatiality-aware Masked Autoencoders for 3D Medical Image Segmentation](https://mlsanity.com/paper/2406.10519/) (2024)
- [What's Cracking? A Review and Analysis of Deep Learning Methods for Structural Crack Segmentation, Detection and Quantification](https://mlsanity.com/paper/2202.03714/) (2022)

## Abstract (arXiv)

Delineation of curvilinear structures is an important problem in Computer Vision with multiple practical applications. With the advent of Deep Learning, many current approaches on automatic delineation have focused on finding more powerful deep architectures, but have continued using the habitual pixel-wise losses such as binary cross-entropy. In this paper we claim that pixel-wise losses alone are unsuitable for this problem because of their inability to reflect the topological impact of mistakes in the final prediction. We propose a new loss term that is aware of the higher-order topological features of linear structures. We also introduce a refinement pipeline that iteratively applies the same model over the previous delineation to refine the predictions at each step while keeping the number of parameters and the complexity of the model constant. When combined with the standard pixel-wise loss, both our new loss term and our iterative refinement boost the quality of the predicted delineations, in some cases almost doubling the accuracy as compared to the same classifier trained with the binary cross-entropy alone. We show that our approach outperforms state-of-the-art methods on a wide range of data, from microscopy to aerial images.