# DOGE: Differentiable Bezier Graph Optimization for Road Network Extraction

arXiv: https://arxiv.org/abs/2511.19850 · HTML: https://mlsanity.com/paper/2511.19850/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 30 of 32)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [MapTR: Structured Modeling and Learning for Online Vectorized HD Map Construction](https://mlsanity.com/paper/2208.14437/) (2022)
- [HDMapNet: An Online HD Map Construction and Evaluation Framework](https://mlsanity.com/paper/2107.06307/) (2021)
- [DeepGlobe 2018: A Challenge to Parse the Earth through Satellite Images](https://mlsanity.com/paper/1805.06561/) (2018)
- [VectorMapNet: End-to-end Vectorized HD Map Learning](https://mlsanity.com/paper/2206.08920/) (2022)
- [iSAID: A Large-scale Dataset for Instance Segmentation in Aerial Images](https://mlsanity.com/paper/1905.12886/) (2019)
- [SpaceNet: A Remote Sensing Dataset and Challenge Series](https://mlsanity.com/paper/1807.01232/) (2018)
- [CityFlow: A City-Scale Benchmark for Multi-Target Multi-Camera Vehicle Tracking and Re-Identification](https://mlsanity.com/paper/1903.09254/) (2019)
- [Im2Vec: Synthesizing Vector Graphics without Vector Supervision](https://mlsanity.com/paper/2102.02798/) (2021)
- [RoadTracer: Automatic Extraction of Road Networks from Aerial Images](https://mlsanity.com/paper/1802.03680/) (2018)
- [Rethinking Efficient Lane Detection via Curve Modeling](https://mlsanity.com/paper/2203.02431/) (2022)
- [End-to-End Vectorized HD-map Construction with Piecewise Bezier Curve](https://mlsanity.com/paper/2306.09700/) (2023)
- [Towards Layer-wise Image Vectorization](https://mlsanity.com/paper/2206.04655/) (2022)
- [SVGDreamer: Text Guided SVG Generation with Diffusion Model](https://mlsanity.com/paper/2312.16476/) (2023)
- [Relationformer: A Unified Framework for Image-to-Graph Generation](https://mlsanity.com/paper/2203.10202/) (2022)
- [CLIPascene: Scene Sketching with Different Types and Levels of Abstraction](https://mlsanity.com/paper/2211.17256/) (2022)
- [Sat2Graph: Road Graph Extraction through Graph-Tensor Encoding](https://mlsanity.com/paper/2007.09547/) (2020)
- [DiffSketcher: Text Guided Vector Sketch Synthesis through Latent Diffusion Models](https://mlsanity.com/paper/2306.14685/) (2023)
- [Lane Graph as Path: Continuity-preserving Path-wise Modeling for Online Lane Graph Construction](https://mlsanity.com/paper/2303.08815/) (2023)
- [Neural Turtle Graphics for Modeling City Road Layouts](https://mlsanity.com/paper/1910.02055/) (2019)
- [Segment Anything Model for Road Network Graph Extraction](https://mlsanity.com/paper/2403.16051/) (2024)
- [DeepVecFont-v2: Exploiting Transformers to Synthesize Vector Fonts with Higher Quality](https://mlsanity.com/paper/2303.14585/) (2023)
- [RNGDet: Road Network Graph Detection by Transformer in Aerial Images](https://mlsanity.com/paper/2202.07824/) (2022)
- [TorontoCity: Seeing the World with a Million Eyes](https://mlsanity.com/paper/1612.00423/) (2016)
- [RNGDet++: Road Network Graph Detection by Transformer with Instance Segmentation and Multi-scale Features Enhancement](https://mlsanity.com/paper/2209.10150/) (2022)
- [Compositional Generative Model of Unbounded 4D Cities](https://mlsanity.com/paper/2501.08983/) (2025)
- [Vectorization of Line Drawings via PolyVector Fields](https://mlsanity.com/paper/1801.01922/) (2018)
- [Towards Satellite Image Road Graph Extraction: A Global-Scale Dataset and A Novel Method](https://mlsanity.com/paper/2411.16733/) (2024)

## Abstract (arXiv)

Automatic extraction of road networks from aerial imagery is a fundamental task, yet prevailing methods rely on polylines that struggle to model curvilinear geometry. We maintain that road geometry is inherently curve-based and introduce the B'ezier Graph, a differentiable parametric curve-based representation. The primary obstacle to this representation is to obtain the difficult-to-construct vector ground-truth (GT). We sidestep this bottleneck by reframing the task as a global optimization problem over the B'ezier Graph. Our framework, DOGE, operationalizes this paradigm by learning a parametric B'ezier Graph directly from segmentation masks, eliminating the need for curve GT. DOGE holistically optimizes the graph by alternating between two complementary modules: DiffAlign continuously optimizes geometry via differentiable rendering, while TopoAdapt uses discrete operators to refine its topology. Our method sets a new state-of-the-art on the large-scale SpaceNet and CityScale benchmarks, presenting a new paradigm for generating high-fidelity vector maps of road networks. We will release our code and related data.