\thanks{This work was supported in part by the National Nature Science Foundation of China (Grant Nos. 62276208, 12326607) and in part by the Natural Science Basic Research Program of Shaanxi Province (Grant No. 2024JC-JCQN-02).}%
\thanks{S. Wang, J. Liu, Z. Song and K. Sun are with the School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China.}
\thanks{X. Cao is with the School of Computer Science and Technology and the Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an 710049, China.}
Lane detection is a critical and challenging task in autonomous driving, particularly in real-world scenarios where traffic lanes can be slender, lengthy, and often obscured by other vehicles, complicating detection efforts. Existing anchor-based methods typically rely on prior lane anchors to extract features and refine location and shape of lanes. While these methods achieve high performance, manually setting prior anchors is cumbersome, and ensuring sufficient coverage across diverse datasets often requires a large number of dense anchors. Furthermore,
the use of \textit{Non-Maximum Suppression} (NMS) to eliminate redundant predictions complicates real-world deployment and may underperform in complex scenarios. In this paper, we propose \textit{Polar R-CNN}, a NMS-free anchor-based method for lane detection. By incorporating both local and global polar coordinate systems, Polar R-CNN facilitates flexible anchor proposals and significantly reduces the number of anchors required without compromising performance. Additionally, we introduce a heuristic \textit{Graph Neural Network} (GNN)-based NMS-free head that supports an end-to-end paradigm, enhancing deployment efficiency and performance in scenarios with dense lanes. Our method achieves competitive results on five popular lane detection benchmarks—\textit{Tusimple}, \textit{CULane}, \textit{LLAMAS}, \textit{CurveLanes}, and \textit{DL-Rail}—while maintaining a lightweight design and straightforward structure. Our source code is available at \href{https://github.com/ShqWW/PolarRCNN}{\textit{https://github.com/ShqWW/PolarRCNN}}.
\IEEEPARstart{L}{ane} detection is a critical task in computer vision and autonomous driving, aimed at identifying and tracking lane markings on the road \cite{adas}. While extensive research has been conducted in ideal environments, it is still challenging in adverse scenarios such as night driving, glare, crowd, and rainy conditions, where lanes may be occluded or damaged \cite{scnn}. Moreover, the slender shapes and complex topologies of lanes further complicate detection efforts \cite{polylanenet}. %Therefore, an effective lane detection method should take into account both global high-level semantic features and local low-level features to address these varied conditions and ensure robust performances in a real-time application. along with their global properties,
In the past few decades, a lot of methods primarily focus on handcrafted local feature extraction and lane shape modeling. Techniques such as the \textit{Canny edge detector}\cite{cannyedge},\textit{ Hough transform}\cite{houghtransform}, and \textit{deformable templates}\cite{kluge1995deformable} have been widely employed for lane fitting. However, these approaches often face limitations in real-world scenarios, especially when low-level and local features lack clarity and distinctiveness.
In recent years, advancements in deep learning and the availability of large datasets have led to significant progress in lane detection, especially deep models such as \textit{Convolutional Neural Networks} (CNNs)\cite{scnn} and \textit{transformer-based} architectures \cite{lstr}. Based on this, earlier approaches typically framed lane detection as a \textit{segmentation task}\cite{lanenet}, which, despite its straightforward, required time-consuming computations. There are still some methods that rely on \textit{parameter-based} models, which directly output lane curve parameters rather than pixel locations \cite{polylanenet}\cite{lstr}\cite{bezierlanenet}. Although these segmentation-based and parameter-based methods provide end-to-end solutions, their sensitivity to lane shape compromises their robustness.
\caption{Anchor (\textit{i.e.}, the yellow lines) settings of different methods and the ground truth lanes. (a) The initial anchor settings of CLRNet. (b) The learned anchor settings of CLRNet trained on CULane. (c) The learned anchors of our method. (d) The ground truth.}
\caption{Comparison of anchor thresholds in \textit{sparse} and \textit{dense} scenarios. (a) and (b) Ground truths in a dense and sparse scenarios, respectively. (c) Predictions with large NMS thresholds in a dense scenario, resulting in a lane prediction being mistakenly suppressed. (d) Predictions with a small NMS threshold in a sparse scenario, where redundant prediction results are not effectively removed.}
%, where some lane instances are close with each others; , where the lane instance are far apart
\par
Drawing inspiration from object detection methods such as \textit{YOLO}\cite{yolov10} and \textit{Faster R-CNN}\cite{fasterrcnn}, several anchor-based approaches have been introduced for lane detection, with representative works including \textit{LaneATT}\cite{laneatt} and \textit{CLRNet}\cite{clrnet}. These methods have shown superior performance by leveraging anchor \textit{priors} (as shown in Fig. \ref{anchor setting}) and enabling larger receptive fields for feature extraction. However, anchor-based methods encounter similar drawbacks to those in general object detection, including the following:
\item As shown in Fig. \ref{anchor setting}(a), a large number of lane anchors are predefined in the image, even in \textbf{\textit{sparse scenarios}}---the situations where lanes are distributed widely and located far apart from each other, as illustrated in the Fig. \ref{anchor setting}(d).
\item A \textit{Non-Maximum Suppression} (NMS) \cite{nms} post-processing step is required to eliminate redundant predictions but may struggle in \textbf{\textit{dense scenarios}} where lanes are close to each other, such as forked lanes and double lanes, as illustrated in the Fig. \ref{NMS setting}(a).
Regrading the first issue, \cite{clrnet} introduced learned anchors that optimize the anchor parameters during training to better adapt to lane distributions, as shown in Fig. \ref{anchor setting}(b). However, the number of anchors remains excessive to adequately cover the diverse potential distributions of lanes. Furthermore, \cite{adnet} proposes flexible anchors for each image by generating start points, rather than using a fixed set of anchors. Nevertheless, these start points of lanes are subjective and lack clear visual evidence due to the global nature of lanes. In contrast, \cite{srlane} uses a local angle map to propose sketch anchors according to the direction of ground truth. While this approach considers directional alignment, it neglects precise anchor positioning, resulting in suboptimal performance. Overall, the abundance of anchors is unnecessary in sparse scenarios.% where lane ground truths are sparse. The trend in new methodologies is to reduce the number of anchors while offering more flexible anchor configurations.%, which negatively impacts its performance. They also employ cascade cross-layer anchor refinement to bring the anchors closer to the ground truth. in the absence of cascade anchor refinement
\par
Regarding the second issue, nearly all anchor-based methods \cite{laneatt}\cite{clrnet}\cite{adnet}\cite{srlane} rely on direct or indirect NMS post-processing to eliminate redundant predictions. Although it is necessary to eliminate redundant predictions, NMS remains a suboptimal solution. On one hand, NMS is not deployment-friendly because it requires defining and calculating distances between lane pairs using metrics such as \textit{Intersection over Union} (IoU). This task is more challenging than in general object detection due to the intricate geometry of lanes. On the other hand, NMS can struggle in dense scenarios. Typically, a large distance threshold may lead to false negatives, as some true positive predictions could be mistakenly eliminated, as illustrated in Fig. \ref{NMS setting}(a)(c). Conversely, a small distance threshold may fail to eliminate redundant predictions effectively, resulting in false positives, as shown in Fig. \ref{NMS setting}(b)(d). Therefore, achieving an optimal trade-off across all scenarios by manually setting the distance threshold is challenging. %The root of this problem lies in the fact that the distance definition in NMS considers only geometric parameters while ignoring the semantic context in the image. As a result, when two predictions are ``close'' to each other, it is nearly impossible to determine whether one of them is redundant.% where lane ground truths are closer together than in sparse scenarios;including those mentioned above,
To address the above two issues, we propose Polar R-CNN, a novel anchor-based method for lane detection. For the first issue, we introduce local and global heads based on the polar coordinate system to create anchors with more accurate locations, thereby reducing the number of proposed anchors in sparse scenarios, as illustrated in Fig. \ref{anchor setting}(c). In contrast to \textit{State-Of-The-Art} (SOTA) methods \cite{clrnet}\cite{clrernet}, which utilize 192 anchors, Polar R-CNN employs only 20 anchors to effectively cover potential lane ground truths. For the second issue, we have revised Fast NMS \cite{yolact} to Graph-based Fast NMS, incorporating a new heuristic \textit{Graph Neural Network} (GNN) \cite{gnn} block (Polar GNN block) into the NMS head. The Polar GNN block offers an interpretable structure, achieving nearly equivalent performance in sparse scenarios and superior performance in dense scenarios. We conducted experiments on five major benchmarks: \textit{TuSimple}\cite{tusimple}, \textit{CULane}\cite{scnn}, \textit{LLAMAS}\cite{llamas}, \textit{CurveLanes}\cite{curvelanes}, and \textit{DL-Rail}\cite{dalnet}. Our proposed method demonstrates competitive performance compared to SOTA approaches. Our main contributions are summarized as follows:
\item We design a strategy to simplify the anchor parameters by using local and global polar coordinate systems and applied these to two-stage lane detection frameworks. Compared to other anchor-based methods, this strategy significantly reduces the number of proposed anchors while achieving better performance.
\item We propose a novel Polar GNN block to implement a NMS-free paradigm. The block is inspired by Graph-based Fast NMS, providing enhanced interpretability. Our Polar GNN block supports end-to-end training and testing while still allowing for traditional NMS post-processing as an option for a NMS version of our model.
\item By integrating the polar coordinate systems and Polar GNN block, we present a Polar R-CNN model for fast and efficient lane detection. And we conduct extensive experiments on five benchmark datasets to demonstrate the effectiveness of our model in high performance with fewer anchors and a NMS-free paradigm. %Additionally, our model features a straightforward structure—lacking cascade refinement or attention strategies—making it simpler to deploy.
\caption{An illustration of the Polar R-CNN architecture. It has a similar pipelines with the Faster R-CNN for the task of object detection, and consists of a backbone, a \textit{Feature Pyramid Network} with three levels of feature maps, respectively denote by $P_0, P_1, P_2$, followed by a \textit{Local Polar Module}, and a RoI pooling module to extract features fed to a \textit{Global Polar Module} for lane detection. Based on the designed lane representation and lane anchor representation in polar coordinate system, the local polar module can propose sparse line anchors and the global polar module can produce the robust and accurate lane predictions. The global polar module includes a triplet head, which comprises a \textit{one-to-one (O2O)} classification head, a \textit{one-to-many} (O2M) classification head , and a \textit{one-to-many} (O2M) regression head.}
%As mentioned above, our model is based on deep learning.
Generally, deep learning-based lane detection methods can be categorized into three groups: segmentation-based, parameter-based, and anchor-based methods. Additionally, NMS-free is an important technique for anchor-based methods, and it will also be described in this section.
\par
\textbf{Segmentation-based Methods.} These methods focus on pixel-wise prediction. They predefined each pixel into different categories according to different lane instances and background\cite{lanenet} and predicted information pixel by pixel. However, they often overly emphasize low-level and local features, neglecting global semantic information and real-time detection. To address this issue, \textit{SCNN}\cite{scnn} uses a larger receptive field. There are some methods such as \textit{UFLDv1-v2}\cite{ufld}\cite{ufldv2} and \textit{CondLaneNet}\cite{CondLaneNet} by utilizing row-wise or column-wise classification instead of pixel classification to improve detection speed. Another issue with these methods is that the lane instance prior is learned by the model itself, leading to a lack of prior knowledge. For example, \textit{LaneNet}\cite{lanenet} uses post-clustering to distinguish each lane instance, while \textit{UFLDv1-v2}
categorizes lane instances by angles and locations, allowing it to detect only a fixed number of lanes. In contrast, \textit{CondLaneNet} employs different conditional dynamic kernels to predict different lane instances. Additionally, some methods such as \textit{FOLOLane}\cite{fololane} and \textit{GANet}\cite{ganet} adopt bottom-up strategies to detect a few key points and model their global relations to form lane instances.
\par
\textbf{Parameter-based Methods.} Instead of predicting a series of points locations or pixel classifications, the parameter-based methods directly generate the curve parameters of lane instances. For example, \textit{PolyLanenet}\cite{polylanenet} and \textit{LSTR}\cite{lstr} consider the lane instance as a polynomial curve, outputting the polynomial coefficients directly. \textit{BézierLaneNet}\cite{bezierlanenet} treats the lane instance as a Bézier curve, generating the locations of their control points, while \textit{BSLane}\cite{bsnet} uses B-Spline to describe the lane, with curve parameters that emphasize local lane shapes. These parameter-based methods are mostly end-to-end and do not require post-processing, resulting in faster inference speed. However, since the final visual lane shapes are sensitive to their shapes, the robustness and generalization of these methods may not be optimal.
\textbf{Anchor-Based Methods.} These methods are inspired by general object detection models, such as YOLO \cite{yolov10} and Faster R-CNN \cite{fasterrcnn}, for lane detection. The earliest work is Line-CNN, which utilizes line anchors designed as rays emitted from the three edges (left, bottom, and right) of an image. However, the model’s receptive field is limited to the edges, rendering it suboptimal for capturing the entirety of the lane. LaneATT \cite{laneatt} improves upon this by employing anchor-based feature pooling to aggregate features along the entire line anchor, achieving faster speeds and better performance. Nevertheless, its grid sampling strategy and label assignment still pose limitations. A key advantage of the anchor-based methods is their flexibility, allowing the integration of strategies from anchor-based object detection. For example, \textit{CLRNet}\cite{clrnet} enhances the performance with \textit{cross-layer refinement strategies}, \textit{SimOTA label assignment}\cite{yolox}, and \textit{LIOU loss}, outperforming many previous methods. They also have some essential drawbacks, \textit{e.g.}, lane anchors are often handcrafted and numerous. Some approaches, such as \textit{ADNet}\cite{adnet}, \textit{SRLane}\cite{srlane}, and \textit{Sparse Laneformer}\cite{sparse}, attempt to reduce the number of anchors and provide more flexible proposals; however, this can slightly impact performance. Additionally, methods such as \cite{adnet}\cite{clrernet} still rely on NMS post-processing, complicating NMS threshold settings and model deployment. Although one-to-one label assignment during training, without NMS \cite{detr}\cite{o2o} during evaluation, alleviates this issue, its performance is still less satisfactory compared to NMS-based models.
\textbf{NMS-free Methods.} Due to the threshold sensitivity and computational overhead of NMS, many studies attempt to NMF-free methods or models that do not use NMS during the detection process. For example, \textit{DETR}\cite{detr} employs one-to-one label assignment to avoid redundant predictions without using NMS. Other NMS-free methods \cite{yolov10}\cite{learnNMS}\cite{date} have also been proposed to addressing this issue from two aspects: \textit{model architecture} and \textit{label assignment}. For example, studies in \cite{yolov10}\cite{date} suggest that one-to-one assignments are crucial for NMS-free predictions, but maintaining one-to-many assignments is still necessary to ensure effective feature learning of the model. While some works in \cite{o3d}\cite{relationnet} consider the model’s expressive capacity to provide non-redundant predictions. However, compared to the extensive studies conducted in general object detection, there has been limited research analyzing the NMS-free paradigm.
In this work, we aim to address the above two issues in the framework of anchor-based detection to achieve NMF-free and non-redundant lane predictions.
\caption{Different descriptions for anchor parameters: (a) Ray: defined by its start point (\textit{e.g.} the green point $\left( x_{1}^{s},y_{1}^{s}\right)$ or the yellow point $\left( x_{2}^{s},y_{2}^{s}\right)$) and direction $\theta$. (b) Polar: defined by its radius $r$ and angle $\theta$.}%rectangular coordinates
The overall architecture of our Polar R-CNN is illustrated in Fig. \ref{overall_architecture}. As shown in this figure, our Polar R-CNN for lane detection has a similar pipeline with Faster R-CNN \cite{fasterrcnn}, which consists of a backbone\cite{resnet}, a \textit{Feature Pyramid Network} (FPN) \cite{fpn}, a \textit{Region Proposal Network} (RPN) \cite{fasterrcnn} followed by a \textit{Local Polar Module} (LPM), and \textit{Region of Interest} (RoI) \cite{fasterrcnn} pooling module followed by a \textit{Global Polar Module} (GPM). In the following, we first introduce the polar coordinate representation of lane and lane anchors, and then present the designed LPM and GPM in our Polar R-CNN. %To investigate the fundamental factors affecting model performance, such as anchor settings and NMS post-processing, and also to enhance ease of deployment, our Polar R-CNN utilizes a simple and straightforward network structure. just relying on basic components, including convolutional or pooling operations, \textit{Multi-Layer Perceptrons} (MLPs), while deliberately excluding advanced elements like \textit{attention mechanisms}, \textit{dynamic kernels}, and \textit{cross-layer refinement} used in previous works \cite{clrnet}\cite{clrernet}.
\subsection{Representation of Lane and Lane Anchor}
%
Lanes are characterized by their thin, elongated, and curved shapes. A well-defined lane prior aids the model in feature extraction and location prediction.
\textbf{Lane and Anchor Representation as Ray.} Given an input image with dimensions of length $W$ and height $H$, a lane is represented by a set of 2D points $X=\{(x_1,y_1),(x_2,y_2),\cdots,(x_N,y_N)\}$ with equally spaced y-coordinates, i.e., $y_i=i\times\frac{H}{N}$, where $N$ is the number of data points. Since the y-coordinate is fixed, a lane can be uniquely defined by its x-coordinates. Previous studies \cite{linecnn}\cite{laneatt} have introduced \textit{lane priors}, also known as \textit{lane anchors}, which are represented as straight lines in the image plane and served as references. From a geometric perspective, a lane anchor can be viewed as a ray defined by a start point $(x_{0},y_{0})$ located at the edge of an image (left/bottom/right boundaries), along with a direction $\theta$. The primary task of a lane detection model is to estimate the x-coordinate offset from the lane anchor to the ground truth of the lane instance.
However, the representation of lane anchors as rays presents certain limitations. Notably, a lane anchor can have an infinite number of potential start points, which makes the definition of its start point ambiguous and subjective. As illustrated in Fig. \ref{coord}(a), the studies in \cite{dalnet}\cite{laneatt}\cite{linecnn} define the start points as being located at the boundaries of an image, such as the green point in Fig. \ref{coord}(a). In contrast, the research presented in \cite{adnet} defines the start points, exemplified by the purple point in Fig. \ref{coord}(a), based on their actual visual locations within the image. Moreover, occlusion and damage to the lane significantly affect the detection of these start points, highlighting the need for the model to have a large receptive field \cite{adnet}. Essentially, a straight lane has two degrees of freedom: the slope and the intercept, under a Cartesian coordinate system, implying that the lane anchor could be described using just two parameters instead of the three redundant parameters (\textit{i.e.}, two for the start point and one for orientation) employed in ray representation.
\caption{The local polar coordinate system. The ground truth of the radius $\hat{r}_{i}^{l}$ of the $i$-th local pole is defines as the minimum distance from the pole to the lane curve instance. A positive pole has a radius $\hat{r}_{i}^{l}$ that is below a threshold $\tau^{l}$, and vice versa. Additionally, the ground truth angle $\hat{\theta}^l_i$ is determined by the angle formed between the radius vector (connecting the pole to the closest point on the lanes) and the local polar axis.}
\textbf{Representation in Polar Coordinate.} As stated above, lane anchors represented by rays have some drawbacks. To address these issues, we introduce a polar coordinate representation of lane anchors. In mathematics, the polar coordinate is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point (also called the pole) and an angle $\theta$ from a reference direction (called polar axis). As shown in Fig. \ref{coord}(b), given a polar corresponding to the yellow point, a lane anchor for a straight line can be uniquely defined by two parameters: the radial distance from the pole (called radius), $r$, and the counterclockwise angle from the polar axis to the perpendicular line of the lane anchor, $\theta$, with $r \in\mathbb{R}$ and $\theta\in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right]$.
To better leverage the local inductive bias properties of CNNs, we define two types of polar coordinate systems: the local and global coordinate systems. The local polar coordinate system is to generate lane anchors, while the global coordinate system expresses these anchors in a form within the entire image and regresses them to the ground truth lane instances. Given the distinct roles of the local and global systems, we adopt a two-stage framewrok for our Polar R-CNN, similar to Faster R-CNN\cite{fasterrcnn}.
The local polar system is designed to predict lane anchors adaptable to both sparse and dense scenarios. In this system, there are many poles with each as the lattice point of the feature map, referred to as local poles. As illustrated on the left side of Fig. \ref{lpmlabel}, there are two types of local poles: positive and negative. Positive local poles (\textit{e.g.}, the blue points) have a radius $r_{i}^{l}$ below a threshold $\tau^l$, otherwise, they are classified as negative local poles (\textit{e.g.}, the red points). Each local pole is responsible for predicting a single lane anchor. While a lane ground truth may generate multiple lane anchors, as shown in Fig. \ref{lpmlabel}, there are three positive poles around the lane instance (green lane), which are expected to generate three lane anchors. This one-to-many approach is essential for ensuring comprehensive anchor proposals, especially since some local features around certain poles may be lost due to damage or occlusion of the lane curve.
In the local polar coordinate system, the parameters of each lane anchor are determined based on the location of its corresponding local pole. However, in practical terms, once a lane anchor is generated, its position becomes fixed and independent from its original local pole. To simplify the representation of lane anchors in the second stage of Polar-RCNN, a global polar system has been designed, featuring a single pole that serves as a reference point for the entire image. The location of this global pole is manually set, and in this case, it is positioned near the static vanishing point observed across the entire lane image dataset. This approach ensures a consistent and unified framework for expressing lane anchors within the global context of the image, facilitating accurate regression to the ground truth lane instances.
As shown in Fig. \ref{overall_architecture}, three levels of feature maps, denoted as $P_1, P_2, P_3$, are extracted using a \textit{Feature Pyramid Network} (FPN). To generate high-quality anchors around the lane ground truths within an image, we introduce the \textit{Local Polar Module} (LPM), which takes the highest feature map $P_3\in\mathbb{R}^{C_{f}\times H_{f}\times W_{f}}$ as input and outputs a set of lane anchors along with their confidence scores. As demonstrated in Fig. \ref{lpm}, it undergoes a \textit{downsampling} operation $DS(\cdot)$ to produce a lower-dimensional feature map of a size $H^l\times W^l$:
The downsampled feature map $F_d$ is then fed into two branches: a \textit{regression} branch $\phi_{reg}^{lpm}\left(\cdot\right)$ and a \textit{classification} branch $\phi_{cls}^{lpm}\left(\cdot\right)$, \textit{i.e.},
The regression branch consists of a single $1\times1$ convolutional layer and with the goal of generating lane anchors by outputting their angles $\theta_j$ and the radius $r^{l}_{j}$, \textit{i.e.}, $F_{reg\,\,}\equiv\left\{\theta_{j}, r^{l}_{j}\right\}_{j=1}^{H^{l}\times W^{l}}$, in the defined local polar coordinate system previously introduced. Similarly, the classification branch $\phi_{cls}^{lpm}\left(\cdot\right)$ only consists of two $1\times1$ convolutional layers for simplicity. This branch is to predict the confidence heat map $F_{cls\,\,}\equiv\left\{ s_j^l \right\}_{j=1}^{H^l\times W^l}$ for local poles, each associated with a feature point. By discarding local poles with lower confidence, the module increases the likelihood of selecting potential positive foreground lane anchors while effectively removing background lane anchors.
\textbf{Loss Function for Training the LPM.} To train the local polar module, we define the ground truth labels for each local pole as follows: the ground truth radius, $\hat{r}^l_i$, is set to be the minimum distance from a local pole to the corresponding lane curve, while the ground truth angle, $\hat{\theta}_i$, is set to be the orientation of the vector extending from the local pole to the nearest point on the curve. A positive pole is labeled as one; otherwise, it is labeled as zero. Consequently, we have a label set of local poles $F_{gt}=\{\hat{s}_j^l\}_{j=1}^{H^l\times W^l}$, where $\hat{s}_j^l=1$ if the $j$-th local pole is positive and $\hat{s}_j^l=0$ if it is negative. Once the regression and classification labels are established, as shown in Fig. \ref{lpmlabel}, the LPM can be trained using the \textit{smooth-L}1 loss $S_{L1}\left(\cdot\right)$ for regression branch and the \textit{binary cross-entropy} loss $BCE\left(\cdot , \cdot\right)$ for classification branch. The loss functions for the LPM are given as follows:
\textbf{Top-$K$ Anchor Selection.} As discussed above, all $H^{l}\times W^{l}$ anchors, each associated with a point in the feature map, are considered as candidate anchor during the training stage. It is helpful to our Polar R-CNN (the second stage) to learn from a sufficient variety of features, including negative anchor samples. However, only the top-$K$ anchors with the highest confidence scores $\{c_j^l\}$ are selected and fed into the next stage during the evaluation stage. This strategy effectively filters out potential negative anchors and reduces the computational complexity of the second stage. By doing this, it maintains the adaptability and flexibility of anchor distribution while decreasing the total number of anchors. The following experiments will demonstrate the effectiveness of our top-$K$ anchor selection strategy.
\caption{The main architecture of GPM. It consists of the RoI Pooling Layer and triplet heads (\textit{i.e.} the O2O classification head, O2M classification head and O2M regression head). The predictions from the O2M classification head $\left\{s_i^g\right\}$ are redundant and require NMS postprocessing. The O2O classification head serves as a replacement for NMS, directly outputting the non-redundant predictions (also denoted as $\left\{\tilde{s}_i^g\right\}$) based on the output scores from the O2M classification head.}
Similar to the pipeline of Faster R-CNN, the LPM serves as the first stage for generating lane anchor proposals. As illustrated in Fig. \ref{overall_architecture}, we introduce a novel \textit{Global Polar Module} (GPM) as the second stage to achieve accurate lane prediction. The GPM takes features samples from anchors and outputs the precise location and confidence scores of final lane detection results. The overall architecture of GPM is illustrated in the Fig. \ref{gpm}.
\textbf{RoI Pooling Layer.} It is designed to extract sampled features from lane anchors. For ease of the sampling operation, we first convert the radius of the positive lane anchors in a local polar coordinate, $r_j^l$, to the one in a global polar coordinate system, $r_j^g$, by the following equation
where $\boldsymbol{c}^{l}_{j}\in\mathbb{R}^{2}$ and $\boldsymbol{c}^{g}\in\mathbb{R}^{2}$ represent the Cartesian coordinates of $j$-th local pole and the global pole, respectively. Note that we keep the angle $\theta_j$ unchanged, since the local and global polar coordinate system have the same polar axis, as shown in Fig. \ref{lpmlabel}. And next, the feature points are sampled on each lane anchors by
where the y-coordinates $\{y_{1,j}, y_{2,j},\cdots,y_{N,j}\}$ of the $j$-th lane anchor are uniformly sampled vertically from the image, as previously mentioned.
Given the feature maps $P_1, P_2, P_3$ from FPN, we can extract feature vectors corresponding to the positions of feature points $\{(x_{1,j},y_{1,j}),(x_{2,j},y_{2,j}),\cdots,(x_{N,j},y_{N,j})\}_{j=1}^{N^{lpm}_{pos}}$, respectively denoted as $\boldsymbol{F}_{1}, \boldsymbol{F}_{2}, \boldsymbol{F}_{3}\in\mathbb{R}^{N^{lpm}_{pos}\times C_f}$. To enhance representation, similar to \cite{detr}, we employ a weighted sum strategy to combine features from different levels as
where $\boldsymbol{w}_{k}\in\mathbb{R}^{N^{lpm}_{pos}}$ represents the learnable aggregate weight, serving as a learned model weight. Instead of concatenating the three sampling features into $\boldsymbol{F}^s\in\mathbb{R}^{N_p\times d_f\times3}$ directly, the adaptive summation significantly reduces the feature dimensions to $\boldsymbol{F}^s\in\mathbb{R}^{N_p\times d_f}$, which is one-third of the original dimension. The weighted sum tensors are then fed into fully connected layers to obtain the pooled RoI features of an anchor:
\textbf{Triplet Head.} The triplet head comprises three distinct heads: the one-to-one classification (O2O cls) head, the one-to-many classification (O2M cls) head, and the one-to-many regression (O2M reg) head. In various studies \cite{laneatt}\cite{clrnet}\cite{adnet}\cite{srlane}, the detection head predominantly follows the one-to-many paradigm. During the training phase, multiple positive samples are assigned to a single ground truth. Consequently, during the evaluation stage, redundant detection results are often predicted for each instance. These redundancies are typically addressed using NMS, which eliminates duplicate results and retains the highest confidence detection for each groung truth. However, NMS relies on the definition of distance between detection results, and this calculation can be complex for curved lanes and other irregular geometric shapes. To achieve non-redundant detection results with a NMS-free paradigm, the one-to-one paradigm becomes crucial during training, as highlighted in \cite{o2o}. Nevertheless, merely adopting the one-to-one paradigm is insufficient; the structure of the detection head also plays a pivotal role in achieving NMS-free detection. This aspect will be further analyzed in the following sections.
\textbf{NMS vs NMS-free.} Let $\boldsymbol{F}^{roi}_{i}$ denotes the ROI features extracted from $i$-th anchors and the three subheads using $\boldsymbol{F}^{roi}_{i}$ as input. For now, let us focus on the O2M classification (O2M cls) head and the O2M regression (O2M reg) head, which follow the old paradigm used in previous work and can serve as a baseline for the new one-to-one paradigm. To maintain simplicity and rigor, both the O2M classification head and the O2M regression head consist of two layers with activation functions, featuring a plain structure without any complex mechanisms such as attention or deformable convolution. as previously mentioned, merely replacing the one-to-many label assignment with one-to-one label assignment is insufficient for eliminating NMS post-processing. This is because anchors often exhibit significant overlap or are positioned very close to each other, as shown in Fig. \ref{anchor setting}(b)\&(c). Let the $\boldsymbol{F}^{roi}_{i}$ and $\boldsymbol{F}^{roi}_{j}$ represent the features from two overlapping (or very close) anchors, implying that $\boldsymbol{F}^{roi}_{i}$ and $\boldsymbol{F}^{roi}_{j}$ will be almost identical. Let $f_{plain}^{cls}$ denotes the neural structure used in O2M classification head and suppose it's trained with one-to-one label assignment. If $\boldsymbol{F}^{roi}_{i}$ is a positive sample and the $\boldsymbol{F}^{roi}_{j}$ is a negative sample, the ideal output should be as follows:
The Eq. (\ref{sharp fun}) suggests that the property of $f_{cls}^{plain}$ need to be ``sharp'' enough to differentiate between two similar features. That is to say, the output of $f_{cls}^{plain}$ changes rapidly over short periods or distances, it implies that $f_{cls}^{plain}$ need to captures information with higher frequency. This issue is also discussed in \cite{o3d}. Capturing the high frequency with a plain structure is difficult because a naive MLP tends to capture information with lower frequency \cite{xu2022overview}. In the most extreme case, where $\boldsymbol{F}_{i}^{roi}=\boldsymbol{F}_{j}^{roi}$, it becomes impossible to distinguish the two anchors to positive and negative samples completely; in practice, both confidences converge to around 0.5. This problem arises from the limitations of the input format and the structure of the naive MLP, which restrict its expressive capability for information with higher frequency. Therefore, it is crucial to establish relationships between anchors and design a new model structure to effectively represent ``sharp'' information.
It is easy to see that the ``ideal'' one-to-one branch is equivalence to O2M cls branch with O2M regression and NMS post-processing. If the NMS could be replaced by some equivalent but learnable functions (\textit{e.g.} a neural network with specific structure), the O2O head could be trained to handle the one-to-one assignment. However, the NMS involves sequential iteration and confidence sorting, which are challenging to reproduce with a neural network. Although previous works, such as RNN-based approaches \cite{stewart2016end}, utilize an iterative format, they are time-consuming and introduce additional complexity into the model training process due to their iterative nature. To eliminate the iteration process, we proposed a equivalent format of Fast NMS\cite{yolact}.
The positive confidence get from o2m classification head, $s_i$;\\
The positive regressions get from o2m regression head, the horizontal offset $\varDelta\boldsymbol{x}_{i}^{roi}$ and end point location $\boldsymbol{e}_{i}$.\\
\STATE Calculate the confidential adjacent matrix $\boldsymbol{C}\in\mathbb{R}^{N_{pos}\times N_{pos}}$, where the element $C_{ij}$ in $\boldsymbol{C}$ is caculate as follows:
\STATE Calculate the geometric prior adjacent matrix $\boldsymbol{M}\in\mathbb{R}^{N_{pos}\times N_{pos}}$, where the element $M_{ij}$ in $\boldsymbol{M}$ is caculate as follows:
\STATE Calculate the inverse distance matrix $\boldsymbol{D}\in\mathbb{R}^{N_{pos}\times N_{pos}}$, where the element $D_{ij}$ in $\boldsymbol{D}$ is defined as follows:
where $d\left(\cdot, \cdot, \cdot, \cdot\right)$ is some predefined function to quantify the distance between two lane predictions.
\STATE Define the adjacent matrix $\boldsymbol{T}=\,\,\boldsymbol{C}\land\boldsymbol{M}$ and the final confidence $\tilde{s}_i$ is calculate as following:
For simplicity, Fast NMS only satisfies the condition (1) and (2), which may lead to an increase in false negative predictions but offers faster processing without sequential iteration. Leveraging the “iteration-free” property, we propose a further refinement called “sort-free” Fast NMS. This new approach, named Graph-based Fast NMS, is detailed in Algorithm \ref{Graph Fast NMS}.
It is straightforward to demonstrate that, when all elements in $\boldsymbol{M}$ are all set to 1 (regardless of geometric priors), Graph-based Fast NMS is equivalent to Fast NMS. Building upon our newly proposed Graph-based Fast NMS, we can design the structure of the one-to-one classification head in a manner that mirrors the principles of following Graph-based Fast NMS.
According to the analysis of the shortcomings of traditional NMS post-processing shown in Fig. \ref{NMS setting}, the fundamental issue arises from the definition of the distance between predictions. Traditional NMS relies on geometric properties to define distances between predictions, which often neglects the contextual semantics. For example, in some scenarios, two predicted lanes with a small geometric distance should not be suppressed, such as the case of double lines or fork lines. Although setting a threshold $d_{\tau}$ can mitigate this problem, it is challenging to strike a balance between precision and recall.
To address this, we replace the explicit definition of the inverse distance function with an implicit graph neural network. Additionally, the coordinates of anchors is also replace with the anchor features ${F}_{i}^{roi}$. According to information bottleneck theory \cite{alemi2016deep}, ${F}_{i}^{roi}$ , which contains the location and classification information, is sufficient for modelling the explicit geometric distance by neural network. Besides the geometric information, features ${F}_{i}^{roi}$ containes the implicit contextual information of an anchor, which provides additional clues for establishing implicit contextual distances between two anchors. The implicit contextual distance is calculated as follows:
Eq. (\ref{edge_layer}) represents the implicit expression of Eq. (\ref{al_1-3}), where the inverse distance $\boldsymbol{D}_{ij}^{edge}$ is no longer a scalar but a semantic tensor with dimension $d_{dis}$. $\boldsymbol{D}_{ij}^{edge}$ containes more complex information compared to traditional geometric distance. The confidence caculation is expressed as follows:
The Eq. (\ref{node_layer}) serves as the implicit replacement for Eq. (\ref{al_1-4}). In this approach, we use elementwise max pooling of tensors instead of scalar-based max operations. The pooled tensor is then fed into a neural network with a sigmoid activation function to directly obtain the confidence. By eliminating the need for a predefined distance threshold, all confidence calculation patterns are derived from the training data.
It should be noted that the O2O classification head depends on the predictons of O2M classification head as outlined in Eq. (\ref{al_1-1}). From a probablity percpective, the confidence output by O2M classification head, $s_{j}$, represents the probability that the $j$-th detection is a positive sample. The confidence output by O2O classification head, $\tilde{s}_i$, denotes the conditional probablity that $i$-th sample shouldn't be suppressed given the condition that the $i$-th sample identified as a positive sample:
where $N_a$ equals $H^{l}\times W^{l}$ during the training stage and $K_{a}$ during the testing stage. The overall architecture of O2O classification head is illustrated in Fig. \ref{o2o_cls_head}.
\textbf{Label assignment and Cost function.} We use the label assignment (SimOTA) similar to previous works \cite{clrnet}\cite{clrernet}. However, to make the function more compact and consistent with general object detection works \cite{iouloss}\cite{giouloss}, we have redefined the lane IoU. As illustrated in Fig. \ref{glaneiou}, the newly-defined lane IoU, which we refer to as GLaneIoU, is redefined as follows:
where $w_{b}$ is the base semi-width of the lane instance. The definations of $d_{i}^{\mathcal{O}}$ and $d_{i}^{\mathcal{\xi}}$ is similar but slightly different from those in \cite{clrnet} and \cite{adnet}, with adjustments made to ensure the values are non-negative. This format is intended to maintain consistency with the IoU definitions used for bounding boxes. Therefore, the overall GLaneIoU is given as follows:
where j and k are the indices of the valid points (the start point and the end point). It's straightforward to observed that when $g=0$, the GLaneIoU is correspond to GIoU\cite{giouloss} for bounding box, with a value range of $\left[0, 1\right]$. When $g=1$, the GLaneIoU is correspond to GIoU for bounding box, with a value range of $\left(-1, 1\right]$. In general, when $g>0$, the value range of GLaneIoU is $\left(-g, 1\right]$.
This cost function is more compact than those in previous works\cite{clrnet}\cite{adnet} and takes both location and confidence into account. For label assignment, SimOTA (with k=4) \cite{yolox} is used for the two O2M heads with one-to-many assignment, while the Hungarian \cite{detr} algorithm is employed for the O2O classification head for one-to-one assignment.
where the set of the one-to-one sample, $\varOmega_{pos}^{o2o}$ and $\varOmega_{neg}^{o2o}$, is restricted to the positive sample set of O2M classification head:
Only one sample with confidence larger than $C_{o2m}$ is chosed as the canditate sample of O2O classification head. According to \cite{pss}, to maintain feature quality during training stage, the gradient of O2O classification head are stopped from propagating back to the rest of the network (stop from the roi feature of the anchor $\boldsymbol{F}_{i}^{roi}$). Additionally, we use the rank loss to increase the gap between positive and negative confidences of O2O classification head:
We directly use the GLaneIoU loss, $\mathcal{L}_{GLaneIoU}$, to regression the offset of xs (with g=1) and Smooth-L1 loss for the regression of end points (namely the y axis of the start point and the end point), denoted as $\mathcal{L}_{end}$. In order to make model learn the global features, we proposed the auxiliary loss illustrated in Fig. \ref{auxloss}:
The anchors and ground truth are divided into several segments. Each anchor segment is regressed to the main components of the corresponding segment of the assigned ground truth. This trick assists the anchors in learning more about the global geometric shape.
The first line in the loss function represents the loss for LPH, which includes both classification and regression components. The second line pertains to the losses associated with the two classification heads (O2M and O2O), while the third line represents the loss for the regression head within the triplet head. Each term in the equation is weighted by a factor to balance the contributions of each component to the gradient. The entire training process is end-to-end.
\caption{Infos and hyperparameters for five datasets. For CULane, $*$ denotes the actual number of training samples used to train our model. Please note that labels for some validation/test sets are missing; therefore, we have selected different splits (test or validation set) for different datasets.}
We conducted experiments on four widely used lane detection benchmarks and one rail detection dataset: CULane\cite{scnn}, TuSimple\cite{tusimple}, LLAMAS\cite{llamas}, CurveLanes\cite{curvelanes}, and DL-Rail\cite{dalnet}. Among these datasets, CULane and CurveLanes are particularly challenging. The CULane dataset consists various scenarios but has sparse lane distributions, whereas CurveLanes includes a large number of curved and dense lane types, such as forked and double lanes. The DL-Rail dataset, focused on rail detection across different scenarios, is chosen to evaluate our model’s performance beyond traditional lane detection. The details for five dataset are shown in Table. \ref{dataset_info}
We use the F1-score to evaluate our model on the CULane, LLAMAS, DL-Rail, and Curvelanes datasets, maintaining consistency with previous works. The F1-score is defined as follows:
In our experiment, we use different IoU thresholds to calculate the F1-score for different datasets: F1@50 and F1@75 for CULane \cite{clrnet}, F1@50 for LLAMAS \cite{clrnet} and Curvelanes \cite{CondLaneNet}, and F1@50, F1@75, and mF1 for DL-Rail \cite{dalnet}. The mF1 is defined as:
where $C_{clip}$ and $S_{clip}$ represent the number of correct points (predicted points within 20 pixels of the ground truth) and the ground truth points, respectively. If the accuracy exceeds 85\%, the prediction is considered correct. TuSimples also report the False Positive Rate (FPR=1-Precision) and False Negative Rate (FNR=1-Recall) formular.
All input images are cropped and resized to $800\times320$. Similar to \cite{clrnet}, we apply random affine transformations and random horizontal flips. For the optimization process, we use the AdamW \cite{adam} optimizer with a learning rate warm-up and a cosine decay strategy. The initial learning rate is set to 0.006. The number of sampled points and regression points for each lane anchor are set to 36 and 72, respectively. The power coefficients of cost function, $\beta_{c}$ and $\beta_{r}$, are set to 1 and 6 respectively. We set different base semi-widths, denoted as $w_{b}^{assign}$, $w_{b}^{cost}$ and $w_{b}^{loss}$ for label assignment, cost function and loss function, respectively, as demonstrated in previous work\cite{clrernet}. Other parameters, such as batch size and loss weights for each dataset, are detailed in Table \ref{dataset_info}. Since some test/validation sets for the five datasets are not accessible, the test/validation sets used are also listed in Table \ref{dataset_info}. All the expoeriments are conducted on a single NVIDIA A100-40G GPU. To make our model simple, we only use CNN-based backbone, namely ResNet\cite{resnet} and DLA34\cite{dla}.
The comparison results of our proposed model with other methods are shown in Tables \ref{culane result}, \ref{tusimple result}, \ref{llamas result}, \ref{dlrail result}, and \ref{curvelanes result}. We present results for two versions of our model: the NMS-based version, denoted as Polar R-CNN-NMS, and the NMS-free version, denoted as Polar R-CNN. The NMS-based version utilizes predictions obtained from the O2M head followed by NMS post-processing, while the NMS-free version derives predictions directly from the O2O classification head without NMS.
To ensure a fair comparison, we also include results for CLRerNet \cite{clrernet} on the CULane and CurveLanes datasets, as we use a similar training strategy and data split. As illustrated in the comparison results, our model demonstrates competitive performance across five datasets. Specifically, on the CULane, TuSimple, LLAMAS, and DL-Rail datasets (sparse scenarios), our model outperforms other anchor-based methods. Additionally, the performance of the NMS-free version is nearly identical to that of the NMS-based version, highlighting the effectiveness of the O2O head in eliminating redundant predictions. On the CurveLanes dataset, the NMS-free version achieves superior F1-measure and Recall compared to both NMS-based and segment\&grid-based methods.
We also compare the number of anchors and processing speed with other methods. Fig. \ref{anchor_num_method} illustrates the number of anchors used by several anchor-based methods on CULane. Our proposed model utilizes the fewest proposal anchors (20 anchors) while achieving the highest F1-score on CULane. It remains competitive with state-of-the-art methods like CLRerNet, which uses 192 anchors and a cross-layer refinement strategy. Conversely, the sparse Laneformer, which also uses 20 anchors, does not achieve optimal performance. It is important to note that our model is designed with a simpler structure without additional refinement, indicating that the design of flexible anchors is crucial for performance in sparse scenarios. Furthermore, due to its simple structure and fewer anchors, our model exhibits lower latency compared to most methods, as shown in Fig. \ref{speed_method}. The combination of fast processing speed and a straightforward architecture makes our model highly deployable.
To validate and analyze the effectiveness and influence of different component of Polar R-CNN, we conduct serveral ablation expeoriments on CULane and CurveLanes dataset to show the performance.
\textbf{Ablation study on polar coordinate system and anchor number.} To assess the importance of local polar coordinates of anchors, we examine the contribution of each component (i.e., angle and radius) to model performance. As shown in Table \ref{aba_lph}, both angle and radius contribute to performance to varying degrees. Additionally, we conduct experiments with auxiliary loss using fixed anchors and Polar R-CNN. Fixed anchors refer to using anchor settings trained by CLRNet, as illustrated in Fig. \ref{anchor setting}(b). Model performance improves by 0.48% and 0.3% under the fixed anchor paradigm and proposal anchor paradigm, respectively.
We also explore the effect of different local polar map sizes on our model, as illustrated in Fig. \ref{anchor_num_testing}. The overall F1 measure improves with increasing the local polar map size and tends to stabilize when the size is sufficiently large. Specifically, precision improves, while recall decreases. A larger polar map size includes more background anchors in the second stage (since we choose k=4 for SimOTA, with no more than four positive samples for each ground truth). Consequently, the model learns more negative samples, enhancing precision but reducing recall. Regarding the number of anchors chosen during the evaluation stage, recall and F1 measure show a significant increase in the early stages of anchor number expansion but stabilize in later stages. This suggests that eliminating some anchors does not significantly affect performance. Fig. \ref{cam} displays the heat map and top-$K_{a}$ selected anchors’ distribution in sparse scenarios. Brighter colors indicate a higher likelihood of anchors being foreground anchors. It is evident that most of the proposed anchors are clustered around the lane ground truth.
\textbf{Ablation study on NMS-free block in sparse scenarios.} We conduct several experiments on the CULane dataset to evaluate the performance of the NMS-free head in sparse scenarios. As shown in Table \ref{aba_NMSfree_block}, without using the GNN to establish relationships between anchors, Polar R-CNN fails to achieve a NMS-free paradigm, even with one-to-one assignment. Furthermore, the classification matrix (cls matrix) proves crucial, indicating that conditional probability is effective. Other components, such as the neighbor matrix (provided as a geometric prior) and rank loss, also contribute to the performance of the NMS-free block.
To compare the NMS-free paradigm with the traditional NMS paradigm, we perform experiments with the NMS-free block under both proposal and fixed anchor strategies. Table \ref{NMS vs NMS-free} presents the results of these experiments. Here, O2M-B refers to the O2M classification head, O2O-B refers to the O2O classification head with a plain structure, and O2O-G refers to the O2O classification head with Polar GNN block. To assess the ability to eliminate redundant predictions, NMS post-processing is applied to each head. The results show that NMS is necessary for the traditional O2M classification head. In the fixed anchor paradigm, although the O2O classification head with a plain structure effectively eliminates redundant predictions, it is less effective than the proposed Polar GNN block. In the proposal anchor paradigm, the O2O classification head with a plain structure fails to eliminate redundant predictions due to high anchor overlap and similar RoI features. Thus, the GNN structure is essential for Polar R-CNN in the NMS-free paradigm. Both in the fixed and proposal anchor paradigms, the O2O classification head with the GNN structure successfully eliminates redundant predictions, indicating that our GNN-based O2O classification head can replace NMS post-processing in sparse scenarios without a decrease in performance. This confirms our earlier theory that both structure and label assignment are crucial for a NMS-free paradigm.
We also explore the stop-gradient strategy for the O2O classification head. As shown in Table \ref{stop}, the gradient of the O2O classification head negatively impacts both the O2M classification head (with NMS post-processing) and the O2O classification head. This suggests that one-to-one assignment introduces critical bias into feature learning.
\textbf{Ablation study on NMS-free block in dense scenarios.} Despite demonstrating the feasibility of replacing NMS with the O2O classification head in sparse scenarios, the shortcomings of NMS in dense scenarios remain. To investigate the performance of the NMS-free block in dense scenarios, we conduct experiments on the CurveLanes dataset, as detailed in Table \ref{aba_NMS_dense}.
In the traditional NMS post-processing \cite{clrernet}, the default IoU threshold is set to 50 pixels. However, this default setting may not always be optimal, especially in dense scenarios where some lane predictions might be erroneously eliminated. Lowering the IoU threshold increases recall but decreases precision. To find the most effective IoU threshold, we experimented with various values and found that a threshold of 15 pixels achieves the best trade-off, resulting in an F1-score of 86.81\%. In contrast, the NMS-free paradigm with the GNN-based O2O classification head achieves an overall F1-score of 87.29\%, which is 0.48\% higher than the optimal threshold setting in the NMS paradigm. Additionally, both precision and recall are improved under the NMS-free approach. This indicates that the GNN-based O2O classification head is capable of learning both explicit geometric distance and implicit semantic distances between anchors in addition to geometric distances, thus providing a more effective solution for dense scenarios compared to the traditional NMS post-processing.
\textbf{Visualization.} We present the Polar R-CNN predictions for both sparse and dense scenarios. Fig. \ref{vis_sparse} displays the predictions for sparse scenarios across four datasets. LPH effectively proposes anchors that are clustered around the ground truth, providing a robust prior for the RoI stage to achieve the final lane predictions. Moreover, the number of anchors has significantly decreased compared to previous works, making our method faster than other anchor-based methods in theory. Fig. \ref{vis_dense} shows the predictions for dense scenarios. We observe that NMS@50 mistakenly removes some predictions, leading to false negatives, while NMS@15 fails to eliminate redundant predictions, resulting in false positives. This highlights the trade-off between using a large IoU threshold and a small IoU threshold. The visualization clearly demonstrates that geometric distance becomes less effective in dense scenarios. Only the O2O classification head, driven by data, can address this issue by capturing semantic distance beyond geometric distance. As shown in Fig. \ref{vis_dense}, the O2O classification head successfully eliminates redundant true predictions while retaining dense predictions with small geometric distances.
In this paper, we propose Polar R-CNN to address two key issues in anchor-based lane detection methods. By incorporating a local and global polar coordinate system, our Polar R-CNN achieves improved performance with fewer anchors. Additionally, the introduction of the O2O classification head with Polar GNN block allows us to replace the traditional NMS post-processing, and the NMS-free paradigm demonstrates superior performance in dense scenarios. Our model is highly flexible and the number of anchors can be adjusted based on the specific scenario. Users have the option to use either the O2M classification head with NMS post-processing or the O2O classification head for a NMS-free approach. Polar R-CNN is also deployment-friendly due to its simple structure, making it a potential new baseline for lane detection. Future work could explore incorporating new structures, such as large kernels or attention mechanisms, and experimenting with new label assignment, training, and anchor sampling strategies. We also plan to extend Polar R-CNN to video instance lane detection and 3D lane detection, utilizing advanced geometric modeling for these new tasks.
received the Master degree from Xi'an Jiaotong University, Xi'an, China, in 2022. He is now pursuing for the Ph.D. degree in statistics at Xi'an Jiaotong University. His research interests include low-level computer vision, deep learning, and so on.
was born in 1982. He received the Ph.D. degree in Mathematics from Xi'an Jiaotong University, Xi'an, China, in 2013. From 2011 to 2012, he served as a Research Assistant with the Department of Geography and Resource Management at the Chinese University of Hong Kong, Hong Kong, China. From 2014 to 2017, he worked as a Visiting Scholar at the University of Maryland, College Park, USA. He is currently a full Professor at the School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China. His research interests are mainly focused on the theory and application of machine learning and image processing. He has published over 60+ research papers in international conferences and journals.
\end{IEEEbiography}
\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{thesis_figure/xiangyongcao.jpg}}]{Xiangyong Cao (Member, IEEE)}
received the B.Sc. and Ph.D. degrees from Xi’an Jiaotong University, Xi’an, China, in 2012 and 2018, respectively. From 2016 to 2017, he was a Visiting Scholar with Columbia University, New York, NY, USA. He is an Associate Professor with the School of Computer Science and Technology, Xi’an Jiaotong University. His research interests include statistical modeling
