Instance segmentation is one of the fundamental tasks in computer vision, which enables numerous downstream vision applications. It is challenging as it requires to predict both the location and the semantic mask of each instance in an image. Therefore intuitively instance segmentation can be solved by bounding box detection then semantic segmentation within each box, adopted by two-stage methods, such as Mask R-CNN. Recent trends in the vision community have spent more effort in designing simpler pipelines of bounding box detectors [14, 18, 25, 26, 28] and subsequent instance-wise recognition tasks including instance segmentation [2, 4, 29], which is also the main focus of our work here. Thus, our aim is to design a conceptually simple mask prediction module that can be easily plugged into many off-the-shelf detectors, enabling instance segmentation.
Instance segmentation is usually solved by binary classification in a spatial layout surrounded by bounding boxes, shown in Figure 1(b). Such pixel-to-pixel correspondence prediction is luxurious, especially in the single-shot methods. Instead, we point out that masks can be recovered successfully and effectively if the contour is obtained. An intuitive method to locate contours is shown in Figure 1(c), which predicts the Cartesian coordinates of the point composing the contour. Here we term it as Cartesian Representation. The second approach is Polar Representation, which applies the angle and the distance as the coordinate to locate points, shown in Figure 1(d).
In this work, we design instance segmentation methods based on the Polar Representation since its inherent advantages are as follows: (1) The origin point of the polar coordinate can be seen as the center of object. (2) Starting from the origin point, the point in contour is determined by the distance and angle. (3) The angle is naturally directional and makes it very convenient to connect the points into a whole contour. We claim that Cartesian Representation may exhibit first two properties similarly. However, it lacks the advantage of the third property.
We instantiate such an instance segmentation method by using the recent object detector FCOS , mainly for its simplicity. Note that, it is possible to use other detectors such as RetinaNet , YOLO  with minimal modification to our framework. Specifically, we propose PolarMask, formulating instance segmentation as instance center classification and dense distance regression in a polar coordinate, shown in Figure 2. The model takes an input image and predicts the distance from a sampled positive location (candidates of the instance center) to the instance contour at each angle, and after assembling, outputs the final mask. The overall pipeline of PolarMask is almost as simple and clean as FCOS. It introduces negligible computation overhead. Simplicity and efficiency are the two key factors to single shot instance segmentation, and PolarMask achieves them successfully.
Furthermore, PolarMask can be viewed as a generalization of FCOS, or FCOS is a special case of PolarMask since bounding boxes can be viewed as the simplest mask with only 4 direction. Thus, one is suggested to use PolarMask over FCOS for instance recognition wherever mask annotation is available [5, 19].
In order to maximize the advantages of Polar Representation, we propose Polar Centerness and Polar IoU Loss to deal with sampling high-quality center examples and optimization for dense distance regression, respectively. They improve mask accuracy by about 15% relatively, showing considerable gains under stricter localization metrics. Without bells and whistles, PolarMask achieves 32.9% in mask mAP with single-model and single-scale training/testing on the challenging COCO dataset .
The main contributions of this work are three-fold:
We introduce a new method for instance segmentation, termed PolarMask, to model instance masks in the polar coordinate, which converts instance segmentation to two parallel tasks: instance center classification and dense distance regression. The main desirable characteristics of PolarMask is being simple and effective.
We propose the Polar IoU Loss and Polar Centerness, tailored for our framework. We show that the proposed Polar IoU loss can largely ease the optimization and considerably improve the accuracy, compared with standard loss such as the smooth- loss. In parallel, Polar Centerness improves the original idea of ‘centreness’ in FCOS, leading to further performance boost.
For the first time, we demonstrate a much simpler and flexible instance segmentation framework achieving competitive performance compared with more complex one-stage methods, which typically involve multi-scale train and longer training time. We hope that PolarMask can serve as a fundamental and strong baseline for single shot instance segmentation.
2 Related Work
Two-Stage Instance Segmentation. Two-stage instance segmentation often formulates this task as the paradigm of ‘Detect then Segment’ [16, 12, 20, 15]. They often detect bounding boxes then perform segmentation in the area of each bounding box. The main idea of FCIS  is to predict a set of position-sensitive output channels fully convolutionally. These channels simultaneously address object classes, boxes, and masks, making the system fast. Mask R-CNN , built upon Faster R-CNN, simply adds an additional mask branch add use RoI-Align to replace RoI-Pooling  for improved accuracy. Following Mask R-CNN, PANet  introduces bottom-up path augmentation, adaptive feature pooling and fully-connected fusion to boost up the performance of instance segmentation. Mask Scoring R-CNN  re-scores the confidence of mask from classification score by adding a mask-IoU branch, which makes the network to predict the IoU of mask and ground-truth.
In summary, the above methods typically consist of two steps, first detecting bounding box and then segmenting in each bounding box. They can achieve state-of-the-art performance but are often slow.
One Stage Instance Segmentation. Deep Watershed Transform  uses fully convolutional networks to predict the energy map of the whole image and use the watershed algorithm to yield connected components corresponding to object instances. InstanceFCN  uses instance-sensitive score maps for generating proposals. It first produces a set of instance-sensitive score maps, then an assembling module is used to generate object instances in a sliding window. The recent YOLACT  first generates a set of prototype masks, the linear combination coefficients for each instance, and bounding boxes, then linearly combines the prototypes using the corresponding predicted coefficients and then crops with a predicted bounding box. TensorMask 
investigates the paradigm of dense sliding-window instance segmentation, using structured 4D tensors to represent masks over a spatial domain. ExtremeNet uses keypoint detection to predict 8 extreme points of one instance and generates an octagon mask, achieving relatively reasonable object mask prediction. The backbone of ExtremeNet is HourGlass , which is very heavy and often needs longer training time. It also needs several steps for post-processing including grouping. In contrast, our method is simpler than ExtremeNet while much achieving better results than ExtremeNet.
Note that these methods do not model instances directly and they can sometime be hard to optimize (e.g., longer training time, more data augmentation and extra labels). Our PolarMask directly models instance segmentation with a much simpler and flexible way of two paralleled branches: classifying each pixel of mass-center of instance and regressing the dense distance of rays between mass-center and contours. The most significant advantage of PolarMask is being simple and efficient compared with all above methods. In the experiments, we have not adopted many training tricks, such as data augmentation and longer training time, since our goal is to design a conceptually simple and flexible mask prediction module.
3 Our Method
In this section, we first briefly introduce the overallarchitecture of the proposed PolarMask. Then, we reformulate instance segmentation with the proposed Polar Representation. Next, we introduce a novel concept of Polar Centerness to ease the procedure of choosing high-quality center samples. Finally, we introduce a new Polar IoU Loss to optimize dense regression problem.
PolarMask is a simple, unified network composed of a backbone network , a feature pyramid network , and two or three task-specific heads, depending on whether predicting bounding boxes.111It is optional to have the box prediction branch or not. As we empirically show, the box prediction branch has little impact on mask prediction. The settings of the backbone and feature pyramid network are same as FCOS . While there exist many stronger candidates for those components, we align these setting with FCOS to show the simplicity and effectiveness of our instance modeling method.
3.2 Polar Mask Segmentation
In this section, we will describe how to model instances in the polar coordinate in detail.
Polar Representation Given an instance mask, we firstly sample a candidate center of the instance and the point located on the contour , , , , . Then, starting from the center, rays are emitted uniformly with the same angle interval (e.g., , ), whose length is determined from the center to the contour.
Thus we model the instance mask in the polar coordinate as center and rays. Since the angle interval is pre-defined, only the length of the ray needs to be predicted. In this way, we formulate the instance segmentation as instance center classification and dense distance regression in a polar coordinate.
Mass Center There are many choices for the center of the instance, such as box center or mass-center. How to choose a better center depends on its effect on the mask prediction performance. Here we verify the upper bound of box center and mass-center, and conclude that mass-center is more advantageous. Details are in Figure 7
. We explain that the mass-center has a greater probability of falling inside the instance, compared with the box center. Although for some extreme cases, such as a donut, neither mass-center nor box center lies inside the instance. We leave it for further research.
Center Samples Location is considered as a center sample if it falls into areas around the mass-center of any instance. Otherwise it is a negative sample. We define the region for sampling positive pixels to be 1.5strides  of the feature map from the mass-center to left, top, right and bottom. Thus each instance has about 916 pixels near the mass-center as center examples. It has two advantages: (1) Increasing the number of positive samples from 1 to 916 can largely avoid imbalance of positive and negative samples. Nevertheless, focal loss  is still needed when training the classification branch. (2) Mass-center may not be the best center sample of an instance. More candidate points make it possible to automatically find the best center of one instance. We will discuss it in details in Section 3.3.
Distance Regression Given a center point and the intersection points located on the contour , , , , , the angle and the distance between the center point and each contour point can be computed easily, from which the required rays can be picked up in most cases. However, there are some corner cases:
If one ray has multiple intersection points with the contour of instance, we directly choose the one with the maximum length.
If one ray, which starts from the center outside of the mask, does not have intersection points with the contour of an instance at some certain angles, we set its regression target as the minimum value (e.g., ).
We argue that these corner cases are the main obstacles of restricting the upper bound of Polar Representation from reaching 100% AP. However, it is not supposed to be seen as Polar Representation being inferior to the non-parametric Pixel-wise Representation. The evidence is two-folds. First, even the Pixel-wise Representation is far away from the upper bound of 100% AP in practice, since some operation, such as down-sampling, is indispensable. Second, current performance is far away from the upper bound regardless of the Pixel-wise Representation or Polar Representation. Therefore, the research effort is suggested to better spend on improving the practical performance of models, rather than the theoretical upper bound.
The training of regression branch is non-trivial. First, the mask branch in PolarMask is actually a dense distance regression task since every training example has rays (e.g., ). It may cause the imbalance between the regression loss and classification loss. Second, for one instance, its rays are relevant and should be trained as a whole, rather than being seen as a set of independent regression examples. Therefore, we put forward the Polar IoU Loss, discussed in details in Section 3.4.
Mask Assembling During inference, the network outputs the classification and centerness, we multiply centerness with classification and obtain final confidence scores. We only assemble masks from at most 1k top-scoring predictions per FPN level, after thresholding the confidence scores at 0.05. The top predictions from all levels are merged and non-maximum suppression (NMS) with a threshold of 0.5 is applied to yield the final results. Here we introduce the mask assembling process and a fast NMS process.
Given a center sample and the ray’s length , , , , , we can calculate the position of each corresponding contour point with the following formula:
Starting from , the contour points are connected one by one, shown in Figure 3 and finally assembles a whole contour as well as the mask.
We apply NMS to remove redundant masks. To fasten the process, We calculate the smallest bounding boxes of masks and then apply NMS based on the IoU of boxes. We verify that such a simplified post-processing do not negatively effect the final mask performance.
3.3 Polar Centerness
Centerness  is introduced to suppress these low-quality detected objects without introducing any hyper-parameters and it is proven to be effective in object bounding box detection. However, directly transferring it to our system can be sub-optimal since its centerness is designed for bounding boxes and we care about mask prediction.
Given a set for the length of rays of one instance, where and are the maximum and minimum of the set. We propose Polar Centerness:
Specifically, we add a single layer branch, in parallel with the classification branch to predict Polar Centerness of a location, as shown in Figure 2. It is a simple yet effective strategy to re-weight the points so that the closer and are, higher weight the point is assigned. Experiments show that Polar Centerness improves the accuracy especially under stricter localization metrics, such as AP.
3.4 Polar IoU Loss
As discussed above, the method of polar segmentation converts the task of instance segmentation into a set of regression problems. In most cases in the field of object detection and segmentation, smooth- loss  and IoU loss  are the two effective ways to supervise the regression problems. However, smooth-
loss overlooks the correlation between samples of the same objects, thus, resulting in less accurate localization. IoU loss, however, the training procedure considers the optimization as a whole, and directly optimizes the metric of interest. Nevertheless, computing the IoU of the predicted mask and its ground-truth is tricky and very difficult to implement parallel computations. In this work, we derive an easy and effective algorithm to compute mask IoU based on the polar vector representation and achieve competitive performance, as shown in Figure5.
We introduce Polar IoU Loss starting from the definition of IoU, which is the ratio of interaction area over union area between the predicted mask and ground-truth. In the polar coordinate system, for an instance, mask IoU is calculated as follows:
where regression target and predicted are length of the ray, angle is .
Then we transform it to the discrete form222For notation convenience, we define:
When approaches infinity, the discrete form is equal to continuous form. We assume that the rays are uniformly emitted, so , which further simplifies the expression. We empirically observe that the power form has little impact on the performance if it is discarded and simplified into the following form:
Polar IoU Loss is the binary cross entropy (BCE) loss of Polar IoU. Since the optimal IoU is always 1, the loss is actually is negative logarithm of Polar IoU:
Our proposed Polar IoU Loss exhibits two advantageous properties: (1) It is differentiable, enabling back propagation; and is very easy to implement parallel computations, thus facilitating a fast training process. (2) It predicts the regression targets as a whole. It improves the overall performance by a large margin compared with smooth- loss, shown in our experiments. (3) As a bonus, Polar IoU Loss is able to automatically keep the balance between classification loss and regression loss of dense distance prediction. We will discuss it in detail in our experiments.
We present results of instance segmentation on the challenging COCO benchmark . Following common practice [12, 4], we train using the union of 80K train images and a 35K subset of val images (), and report ablations on the remaining 5K val. images (). We also compare results on -. We adopt the 1 training strategy [10, 3], single scale training and testing of image short-edge as 800 unless otherwise noted.
are used. Specifically, our network is trained with stochastic gradient descent (SGD) for 90K iterations with the initial learning rate being 0.01 and a mini-batch of 16 images. The learning rate is reduced by a factor of 10 at iteration 60K and 80K, respectively. Weight decay and momentum are set as 0.0001 and 0.9, respectively. We initialize our backbone networks with the weights pre-trained on ImageNet. The input images are resized to have their shorter side being 800 and their longer side less or equal to 1333.
4.1 Ablation Study
Verification of Upper Bound The first concern about PolarMask is that it might not depict the mask precisely. In this section we prove that this concern may not be necessary. Here we verify the upper bound of PolarMask as the IoU of predicted mask and ground-truth when all of the rays regress to the distance equal to ground-truth. The verification results on different numbers of rays are shown in Figure 7. It can be seen that IoU is approaching to nearly perfect (above 90%) when the number of rays increases, which shows that Polar Segmentation is able to model the mask very well. Therefore, the concern about the upper bound of PolarMask is not necessary. Also, it is more reasonable to use mass-center than bounding box-center as the center of an instance because the bounding box center is more likely to fall out of the instance.
Number of Rays It plays the fundamental role in the whole system of PolarMask. From Table 0(a) and Figure 7, more rays show higher upper bound and better AP. For example, 36 rays improve by 1.5% AP compared to 18 rays. Also, too many rays, 72 rays, saturate the performance since it already depicts the mask contours well and the number of rays is no longer the main factor constraining the performance.
Polar IoU Loss vs. Smooth- Loss We test both Polar IoU Loss and Smooth- Loss in our architecture. We note that the regression loss of Smooth- Loss is significantly larger than the classification loss, since our architecture is a task of dense distance prediction. To cope with the imbalance, we select different factor to regression loss in Smooth- Loss. Experiments results are shown in Table 0(b). Our Polar IoU Loss achieves 27.7% AP without balancing regression loss and classification loss. In contrast, the best setting for Smooth- Loss achieves 25.1% AP, a gap of 2.6% AP, showing that Polar IoU Loss is more effective than Smooth- loss for training the regression task of distance between mass-center and contours.
We hypothesize that the gap may come from two folds. First, the Smooth- Loss may need more hyper-parameter search to achieve better performance, which can be time-consuming compared to the Polar IoU Loss. Second, Polar IoU Loss predicts all rays of one instance as a whole, which is superior to Smooth- Loss.
In Figure 6 we compare some results using the Smooth- Loss and Polar IoU Loss respectively. Smooth- Loss exhibits systematic artifacts, suggesting that it lacks supervision of the level of the whole object. PolarMask shows more smooth and precise contours.
Polar Centerness vs. Cartesian Centerness The comparison experiments are shown in Table 0(c). Polar Centerness improves by 1.4% AP overall. Particularly, AP and AP are raised considerably, 2.3% AP and 2.6% AP, respectively.
We explain as follows. On the one hand, low-quality masks make more negative effect on high-IoU. On the other hand, large instances have more possibility of large difference between maximum and minimum lengths of rays, which is exactly the problem which Polar Centerness is committed to solve.
Box Branch Most of previous methods of instance segmentation require the bounding box to locate area of object and then segment the pixels inside the object. In contrast, PolarMask is capable to directly output the mask without bounding box.
In this section, we test whether the additional bounding box can help improve the mask AP as follows. If the ray reaches outside of the bounding box, the ray is cut off at the boundary. From Table 0(d), we can see that bounding box makes little difference to performance of mask prediction. Thus, we do not have the bounding box prediction head in PolarMask for simplicity and faster speed.
Backbone Architecture Table 0(e)
shows the results of PolarMask on different backbones. It can be seen that better feature extracted by deeper and advanced design networks improve the performance as expected.
Speed vs. Accuracy Larger image sizes yield higher accuracy, in slower inference speeds. Table 0(f) shows the speed/accuracy trade-off for different input image scales, defined by the shorter image side. The FPS is reported on an outdated Titan-X GPU.
|Mask R-CNN ||ResNeXt-101-FPN||12||37.1||60.0||39.4||16.9||39.9||53.5|
4.2 Comparison to state-of-the-art
We evaluate PolarMask on the COCO dataset and compare - results to state-of-the-art methods including both one-stage and two-stage models, shown in Table 2. PolarMask outputs are visualized in Figure 8.
Without any bells and whistles, PolarMask is able to achieve competitive performance with more complex one-stage methods. Since our aim is to design a conceptually simple and flexible mask prediction module, many improvements methods [24, 22], such as multi-scale training and longer training time is beyond the scope of this work. We argue that the gap of YOLACT  and PolarMask comes from more training epochs and data augmentation. If these methods are applied to PolarMask, the performance can be readily improved. Besides, the gap of TensorMask  and PolarMask arises from tensor bipyramid and aligned representation. Considering these methods are time-costing and memory-costing, we do not plug them to PolarMask.
PolarMask is a single shot anchor-free instance segmentation method with two paralleled branches: classifying mass-center of instances and regressing the dense lengths of rays between sampled locations around the mass-center and contours. Different from previous works that typically solve mask prediction as binary classification in a spatial layout, PolarMask puts forward polar representation and transforms mask prediction to dense distance regression. PolarMask is designed almost as simple and clean as single shot object detectors, introducing negligible computing overhead. We hope that the proposed PolarMask framework can serve as a fundamental and strong baseline for single shot instance segmentation task.
Deep watershed transform for instance segmentation.
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5221–5229. Cited by: §2.
-  (2019) YOLACT: Real-time instance segmentation. arXiv. Cited by: §1, §2, §4.2, Table 2.
-  (2019) MMDetection: open mmlab detection toolbox and benchmark. External Links: Cited by: §4.
-  (2019) Tensormask: a foundation for dense object segmentation. arXiv preprint arXiv:1903.12174. Cited by: §1, §2, §4.2, Table 2, §4.
The cityscapes dataset for semantic urban scene understanding. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3213–3223. Cited by: §1.
-  (2016) Instance-sensitive fully convolutional networks. In European Conference on Computer Vision, pp. 534–549. Cited by: §2.
-  (2016) Instance-aware semantic segmentation via multi-task network cascades. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3150–3158. Cited by: Table 2.
-  (2009) Imagenet: a large-scale hierarchical image database. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 248–255. Cited by: §4.
-  (2014) Rich feature hierarchies for accurate object detection and semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 580–587. Cited by: §3.4.
-  (2018) Detectron. Note: https://github.com/facebookresearch/detectron Cited by: Table 2, §4.
-  (2015) Fast R-CNN. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1440–1448. Cited by: §2.
-  (2017) Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pp. 2961–2969. Cited by: §1, §2, Table 2, §4.
-  (2016-06) Deep residual learning for image recognition. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §3.1, §4.
-  (2015) Densebox: unifying landmark localization with end to end object detection. arXiv preprint arXiv:1509.04874. Cited by: §1.
-  (2019) Mask scoring r-cnn. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 6409–6418. Cited by: §2.
-  (2017) Fully convolutional instance-aware semantic segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2359–2367. Cited by: §2, Table 2.
-  (2017-07) Feature pyramid networks for object detection. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §3.1, §4.
-  (2017-10) Focal loss for dense object detection. In The IEEE International Conference on Computer Vision (ICCV), Cited by: §1, §1, §3.2.
-  (2014) Microsoft coco: common objects in context. In European conference on computer vision, pp. 740–755. Cited by: §1, §1, §4.
-  (2018) Path aggregation network for instance segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 8759–8768. Cited by: §2.
Stacked hourglass networks for human pose estimation. In European conference on computer vision, pp. 483–499. Cited by: §2.
-  (2018) Megdet: a large mini-batch object detector. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 6181–6189. Cited by: §4.2.
-  (2016) You only look once: unified, real-time object detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 779–788. Cited by: §1.
-  (2018) An analysis of scale invariance in object detection snip. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3578–3587. Cited by: §4.2.
-  (2019) FCOS: fully convolutional one-stage object detection. Proc. International Conf. Computer Vision (ICCV). Cited by: §1, §1, §3.1, §3.2, §3.3, §4.
-  (2019) RepPoints: point set representation for object detection. arXiv preprint arXiv:1904.11490. Cited by: §1.
-  (2016) Unitbox: an advanced object detection network. In Proceedings of the 24th ACM International Conference on Multimedia, pp. 516–520. Cited by: §3.4.
-  (2019) Objects as points. arXiv preprint arXiv:1904.07850. Cited by: §1.
-  (2019) Bottom-up object detection by grouping extreme and center points. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 850–859. Cited by: §1, §2, Table 2.