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PolyLaneNet: Lane Estimation via Deep Polynomial Regression
Lucas Tabelini, Rodrigo Berriel, Thiago M. Paixão, Claudine Badue, Alberto F. De Souza, Thiago Oliveira-Santos
TL;DR
Lane detection must be accurate and efficient for real-time autonomous driving, yet remains difficult in varied road scenes. PolyLaneNet uses end-to-end deep polynomial regression to map forward-facing vehicle-camera images to lane representations. It is reported as competitive on TuSimple at 115 FPS, while the paper also examines evaluation metrics and supports replication with released code and models.
Problem
Lane detection remains an incomplete autonomous-driving problem because real-time systems must combine high accuracy with processing speed across challenging driving conditions.
Method
PolyLaneNet is a convolutional neural network that predicts polynomial lane markings, polynomial domains, confidence scores, and the horizon position directly from forward-looking vehicle-camera images.
Results
115 FPS was reported for PolyLaneNet, which was competitive with existing state-of-the-art methods on the TuSimple dataset.
Takeaways & Limitations
The paper provides a computationally efficient, publicly released baseline with source code and trained models for replicating its lane-detection results.
Takeaways & Limitations
The paper reports that TuSimple’s evaluation metric can hide errors concentrated near the horizon and insufficiently distinguish polynomial-model differences.
Abstract
from arXiv · showhide
One of the main factors that contributed to the large advances in autonomous driving is the advent of deep learning. For safer self-driving vehicles, one of the problems that has yet to be solved completely is lane detection. Since methods for this task have to work in real-time (+30 FPS), they not only have to be effective (i.e., have high accuracy) but they also have to be efficient (i.e., fast). In this work, we present a novel method for lane detection that uses as input an image from a forward-looking camera mounted in the vehicle and outputs polynomials representing each lane marking in the image, via deep polynomial regression. The proposed method is shown to be competitive with existing state-of-the-art methods in the TuSimple dataset while maintaining its efficiency (115 FPS). Additionally, extensive qualitative results on two additional public datasets are presented, alongside with limitations in the evaluation metrics used by recent works for lane detection. Finally, we provide source code and trained models that allow others to replicate all the results shown in this paper, which is surprisingly rare in state-of-the-art lane detection methods. The full source code and pretrained models are available at https://github.com/lucastabelini/PolyLaneNet.
I. INTRODUCTION
Lane estimation is important for autonomous driving but remains difficult across varied markings, traffic, weather, and illumination. PolyLaneNet addresses these challenges with end-to-end polynomial regression designed for efficient, reproducible lane-marking estimation.
- Lane markings define the ego-lane boundaries and provide visual cues that constrain driving actions, including whether lane changes are allowed.
- Dashed or occluded markers require semantic scene understanding, while traffic, weather, and changing illumination increase lane-estimation difficulty.
- Traditional hand-crafted features followed by curve fitting work mainly in normal, limited conditions and are less robust in adverse environments.
- ADAS can benefit from methods that remove two-step processing, reduce computational cost, support low-energy hardware, and use less permissive evaluation metrics.
- PolyLaneNet directly maps forward-facing vehicle-camera images to polynomial lane markings, domains, and confidence scores without post-processing.
II. RELATED WORKS
Earlier lane-detection methods relied on specialized features or deep models with post-processing, private data, or unavailable code. The paper emphasizes publicly evaluated and reproducible lane-detection research.
- Pre-deep-learning lane detectors commonly used hand-crafted shape and color features with straight or curved lane representations.
- Deep-learning approaches introduced learned representations but often produced intermediate maps requiring post-processing, such as DBSCAN clustering or lane drawing.
- The TuSimple challenge established a public benchmark, with SCNN using spatial-information propagation and IoU-based evaluation.
- Related work was difficult to reproduce because some methods used private datasets, proprietary code, or undocumented engineering techniques.
- PolyLaneNet reports competitive results on public datasets and provides source code while including a dataset from outside the United States.
III. POLYLANENET
PolyLaneNet is an end-to-end CNN that predicts polynomial lane candidates, their vertical domains and confidence scores, and the horizon position. Training combines polynomial-fitting, confidence, and auxiliary regression objectives, while inference filters candidates by confidence.
- PolyLaneNet predicts Mmax polynomial lane candidates and the horizon position h from a forward-looking vehicle-camera image.
- Each lane marking is represented by polynomial coefficients, a restricted image-height domain, a vertical offset, and a confidence score cj ∈[0, 1].
- At inference, only lane candidates whose confidence score meets the threshold are considered detected.
- The model associates annotated lane markings with output units and disregards surplus outputs beyond the image’s annotated lane count during training.
- The multi-task loss balances polynomial regression, confidence classification, and horizon-related terms using constant weights, with MSE and BCE regressions.
- The polynomial-fitting loss measures how well each predicted polynomial matches annotated points and reduces emphasis on already well-aligned points.
IV. EXPERIMENTAL METHODOLOGY
The experimental methodology section introduces the public datasets used for evaluation and then describes implementation details, metrics, and experiments.
- PolyLaneNet was evaluated on publicly available datasets, followed by descriptions of implementation details, evaluation metrics, and experiments.
A. Datasets
PolyLaneNet is evaluated on TuSimple for quantitative results and on LLAMAS and ELAS for qualitative results, including data from Brazil.
- Three datasets—TuSimple, LLAMAS, and ELAS—were used to evaluate PolyLaneNet.
- TuSimple contains 6,408 annotated 1280×720 images split into training, validation, and testing sets.The split is 3,268 training, 358 validation, and 2,782 testing images.
- LLAMAS contains 100,042 1280×717 images, but only qualitative results are presented because benchmark and test annotations are unavailable.Its split is 58,269 training, 20,844 validation, and 20,929 test images.
- ELAS contains 16,993 640×480 images from Brazilian cities and uses author-created training and testing splits.The splits contain 11,036 training and 5,957 testing images.
- Unlike TuSimple and LLAMAS, ELAS annotates only the ego-lane.
B. Implementation details
Experiments use a consistent training setup centered on EfficientNet-b0, image augmentation, resizing, normalization, and Adam optimization with cosine annealing.
- EfficientNet-b0 was used as the backbone network for every experiment.The hyperparameters were kept the same except during the ablation study.
- Training used rotation, horizontal flipping, and random cropping for data augmentation.The rotation angle was sampled from U(−10, 10), flipping had probability 0.5, and crops measured 1152×648 pixels.
- Augmented images were resized to 640×360 pixels and normalized with ImageNet’s mean and standard deviation.
- The Adam optimizer was combined with a Cosine Annealing learning-rate scheduler.The initial learning rate was 3e-4 and the schedule period was 770 epochs.
C. Evaluation Metrics
Evaluation combines TuSimple prediction-quality metrics with Lane Position Deviation and computational-efficiency measures to assess accuracy, local errors, and speed.
- TuSimple evaluation reports accuracy, false-positive, and false-negative rates.A predicted lane is counted as a true positive when its accuracy reaches the threshold ϵ.
- The benchmark uses τacc = 20 pixels and ϵ = 0.85, with metrics averaged across images.
- TuSimple’s metric can be too permissive toward local errors, motivating the additional LPD evaluation.
- Lane Position Deviation measures ego-lane prediction error across near and far depths of view.The ego-lane is defined as the two markings closest to the bottom-center of the image.
- Frames-per-second and MACs assess implementation speed and computational cost.FPS reflects runtime on a modern GPU, while MACs support comparisons across frameworks and setups.
D. Quantitative Evaluation
Quantitative evaluation compares PolyLaneNet with state-of-the-art methods and studies polynomial degree, backbone, input size, and other design choices under TuSimple-based protocols.
- State-of-the-art Comparison: The main comparison trains on TuSimple’s training and validation union and evaluates on its test set against four state-of-the-art methods.The compared methods are SCNN, Line-CNN, ENet-SAD, and FastDraw, with FPS also reported.
- State-of-the-art Comparison: MACs are reported for PolyLaneNet alongside speed and prediction-quality metrics.One MAC is approximately equivalent to 2 FLOPS.
- Polynomial Degree: Polynomial-degree experiments compare first- and second-order models with the default third-order representation.The study also computes upper bounds to examine the permissiveness of TuSimple’s metric.
- Ablation Study: The ablation study evaluates ResNet-34, ResNet-50, and EfficientNet-b1 as alternative backbones.
- Ablation Study: Additional ablations vary input resolution, horizon sharing, ImageNet pretraining, and data augmentation.The tested smaller input sizes are 480×270 and 320×180 pixels.
E. Qualitative Evaluation
The qualitative evaluation extends PolyLaneNet to ELAS and LLAMAS, including an optional lane marking type classification task.
- PolyLaneNet was evaluated qualitatively on ELAS and LLAMAS using models initialized with TuSimple pretraining.Two models were trained on ELAS, with and without lane marking type classification, and another was trained on LLAMAS.
- The ELAS models received 385 additional training epochs after TuSimple pretraining.This corresponds to half a period of the selected learning-rate scheduler, when the learning rate reaches a minimum.
- The LLAMAS model received 75 additional training epochs because its training set is approximately five times larger than ELAS.The epoch count approximated the number of iterations used for ELAS.
- Lane marking type classification was added by predicting a category for each lane, demonstrating a straightforward model extension.
V. RESULTS
PolyLaneNet is competitive on TuSimple and provides qualitative results on additional datasets, while experiments examine polynomial degree, architecture, input size, and training choices. The results also expose limitations in benchmark metrics and reduced accuracy during lane changes.
- State-of-the-art Comparison: PolyLaneNet predictions are accurate near the camera but less accurate near the horizon, especially for lane markings with strong curvature.The authors conjecture that dataset imbalance biases the network toward predicting first-order polynomials.
- Polynomial Degree: 0.35 p.p. accuracy was lost when lane markings were represented with first-order instead of higher-order polynomials.The small difference is attributed partly to dataset imbalance and partly to the benchmark metric’s permissiveness.
- Polynomial Degree: LPD distinguishes polynomial upper bounds more clearly than TuSimple’s metric, including differences between fourth- and fifth-degree representations.TuSimple’s thresholds can hide errors concentrated near the horizon, where lane markings appear nearly straight.
- Ablation Study: EfficientNet-b1 achieved the highest accuracy, but its gains were not significant or consistent and it was more computationally expensive.The comparison considers FPS, MACs, and training time in addition to accuracy.
- Ablation Study: ImageNet pretraining and data augmentation substantially improved accuracy, while transfer learning produced reasonable qualitative results with fewer additional training epochs.Qualitative evaluation covered ELAS and LLAMAS using models initialized from TuSimple training.
VI. CONCLUSION
PolyLaneNet is presented as a simple, efficient lane-detection method with competitive accuracy and publicly available resources for reproducibility. The paper also identifies shortcomings in current lane-detection evaluation metrics.
- PolyLaneNet uses deep polynomial regression to provide computationally efficient lane detection with competitive accuracy against state-of-the-art methods.
- Publicly releasing the source code establishes a reproducible baseline for future lane-marking detection research and comparison.
- The paper highlights problems in existing lane-detection metrics and calls for metrics that better expose method flaws across different approaches.