1 Introduction
Layout of road networks is essential for diverse applications in geographic information systems. Efficient reconstruction from images and timely updates of road networks are important both for map designs and handling events such as natural disasters. The availability of highresolution satellite images has enabled such technology in recent years though the process is not fully automatic. Currently the road extraction from satellite images is mainly completed manually [20]. Doing so automatically or even semiautomatically in a reliable manner is challenging as there are a variety of different types of roads whose images are cluttered with noise and occlusions (by cars/trees etc).
Extracting lanerelated information from high resolution satellite images has been addressed in recent years [11, 19, 24]
. Specifically for road extraction, a range of methods that combine machine learning and computer vision methods have been proposed to reconstruct roads using labelled data. These are semiautomatic in the sense that they use manually curated samples to train the classifier. These methods often consist of two main stages. The first stage consists of the background segmentation and the second stage consists of the centerline extraction. The background segmentation is usually done via machine learning methods such as performing feature extraction and pixelwise label predictions with SVM
[4, 16] or CNN [3]. More recently, a CNN framework called UNet [15] is proposed that outputs the segmentations directly, improving the predictions and the running time significantly. The baseline algorithms for SpaceNet Challenge [20] use the architecture such as UNet and PSPNet [25]. For the second stage, methods like skeleton or medial axis extraction with pre and postprocessing are often used to obtain the final road networks. However, recovering the correct connections and junctions of roads still remain challenging. This problem is critical since the road network is often used in routing and false breaks in the extraction lead to unacceptable results. This twostage approach can potentially be fully automatized if training samples can be produced algorithmically.To achieve the full automatization, one needs to have a direct reconstruction from images that may not be completely faithful but reliable enough to serve as the generator of good training samples. Then, one can iteratively use the technique to improve upon the training samples. This is what we achieve in this work for automatic road reconstruction. It turns out that our direct reconstruction method even improves over the stateoftheart techniques for semiautomatic reconstructions by providing a more robust algorithm for the second stage. Our direct reconstruction method is a topologybased graph reconstruction algorithm. It uses the recent techniques of topological persistence [8] and discrete Morse theory [10] in topological data analysis. This topologybased approach for recovering hidden structures has been proposed and studied recently [5, 12, 14, 22]. It has been applied to extracting graphlike structures from simulated dark matter density fields [18] and reconstructing road networks from GPS traces [21, 6]. This discreteMorse based graph reconstruction framework is clean both conceptually and implementationwise. Most importantly, as it uses a global topological structure to make decisions (instead of using purely local information to decide whether a point is on or off the road), the algorithm is robust to noise, nonuniform sampling of the data, and reliable at recovering junctions. Very recently, this graph reconstruction algorithm has been further simplified, and theoretical guarantees of this graph reconstruction algorithm for the case when the signal prevails noise have been provided [7].
Specific contributions:
Our contribution is twofold.
(1) First, in a semiautomatic framework, we apply the discreteMorse based graph reconstruction algorithm on the segmented satellite images obtained by a CNN. This, of course, requires user provided training samples to train the CNN. We show that this leads to reconstructions with better network connectivity and less noise compared to some existing stateoftheart technique.
(2) More importantly, next, in a fully automatic framework, we develop a novel method to leverage the power of the discreteMorse based graph reconstruction algorithm to train a CNN from a collection of images without labelled data so that it can produce segmentation for new images. To elaborate, we start with running the graph reconstruction algorithm on the raw satellite images to obtain some initial reconstructions. We then put the pixels from reliable branches of the output graph as positive and others as negative to create the labels for the training, and produce an intermediate CNN classifier. We predict the segmented images for the training set using this intermediate CNN and then repeat the same process on the output to gradually improve the CNN. Our experiment shows that after several iterations of training, the labels computed from the graph reconstruction algorithm become less noisy and the performance of the classifier improves significantly. If we relax the condition slightly and assume that we know the labels for only 10% of the train set, we can incorporate this partially labelled data into our framework, and the performance of the classifier becomes even better.
We experiment on datasets from SpaceNet Challenge [20] which consists of high resolution images for four cities. For the semiautomatic framework, we compare our results with the results of the winner’s algorithm, using the APLS score (defined in [20]) as well as another metric which we call Average Hausdorff distance, to evaluate the quality of the reconstructed networks compared to the groundtruth (provided by SpaceNet Challenge). Overall, our reconstructions tend to have better connectivity and are less noisy. For the fully automatic framework, we show that the reconstruction quality is significantly improved through our iterative training process. Furthermore, our framework can be modified to include a small set of labelled data and the accuracy improves as we use more and more labelled data.
This paper is organized as follows, Section 2 briefly describes the idea of the discreteMorse based graph reconstruction algorithm. Section 3 introduces our semiautomatic framework and fully automatic framework. Section 4 provides various experiment results for both frameworks and discusses limitations and future works.
2 DiscreteMorse based graph reconstruction
On the high level, the road network reconstruction from satellite images framework has two stages; see Figure 1. In Stage 1, we use some machine learning techniques to convert a given satellite image into a segmented image where roughly speaking, the value at each pixel represents the likelihood of this pixel being on / around roads. In Stage 2, we extract the hidden roadnetwork (graph) from this segmented image.
We apply the simplified version of our discreteMorse based graph reconstruction algorithm [7] to extract road networks from the segmented images (sometimes called “road masking” in the literature). Given that our approach mostly uses this reconstruction algorithm as a black box, we only provide a highlevel description of the main ideas here. Interested readers should see [7] for more details.
Given a segmented image, we view it as a density field defined on a 2D grid, where the function value at each vertex reflects the likelihood of the corresponding pixel belonging to the road class. The goal is to extract a graph that represents the hidden road network.
In particular, for simplicity, assume we have a triangulation of the grid (image), and thus the segmented image can be viewed as a “density function” with reflecting how likely is in the road class. The graph of this density function can be viewed as a terrain with the height of a point being its function value ; see Figure 1(a). Algorithm MorseGraphRecon() of [7] (developed based on earlier work, e.g, [5, 12, 18, 21]) proposes to use the “mountain ridge” of this terrain to describe the hidden graph. Intuitively, the mountain ridge structures are formed by those flow lines (following the steepest descending direction) that connect maxima and saddles of this terrain. Curves in the mountain ridges connect mountain peaks and saddles, and separate different “valleys”. A point on such a curve has a higher function value than points off the curve in a direction orthogonal to the curve locally. This is consistent with what a “road” should be: points in a road have higher “density” than points off the road in the orthogonal direction though this point may not have the highest density value along the road itself. See Figure 1(b).
Algorithm MorseGraphRecon() extracts the “mountain ridges” from the input density function (terrain) via the socalled 1stable manifolds from Morse theory. For the sake of efficient and numerically stable computation, it uses the discrete Morse theory [10] to implement it. Very importantly, the algorithm also uses the concept of persistent homology [9] to capture “importance” of different pieces of 1stable manifolds (more precisely, important maxsaddle pairs) in a meaningful manner. This allows the algorithm to remove noise and simplify the output graph (road network) systematically.
Notice that, since this algorithm uses the global “mountain ridges” to infer the hidden networks, it does not need to identify the junction nodes separately, and it can also bridge through small gaps in the density field. The algorithm is clean (uses only one parameter) and efficient. It takes time for a planar triangulation with vertices.
3 Approaches
3.1 Semiautomatic framework
The semiautomatic framework follows the highlevel twostage approach as outlined in Figure 1. In the first stage, we train a CNN using training images consisting of groundtruth roads labeled. Given a raw satellite image, we feed it to this trained CNN to obtain a segmented image. In the second stage, we apply the discreteMorse based graph reconstruction algorithm to extract the roadnetwork from the segmented image. For the second stage to work more accurately, we need to detect road ends called “tips” in the segmented images obtained in the first stage. We take advantage of the CNN to add a simple “tipdetection” stage that enhances the segmented images. The overall pipeline for Stage1 of the semiautomatic framework is shown in Figure 3. The inputs for the framework are high resolution satellite images, which are split into a test set and a train set. The train set has ground truth graphs (obtained manually) that represent the centerlines of the road networks. The roadlabels for training are created by thickening the ground truth graph and labeling pixels inside the thickened graph as positive and others as negative.
CNN architecture
Reconstructing tips.
The graph reconstruction algorithm MorseGraphRecon() sometimes may miss hanging branches. To remedy this, we propose a novel way to enhance the segmented images. In particular, following the edit strategy of [6], we modify the density values (i.e, the pixel values of the segmented images) of the tips to high values thus causing them to become local maxima which in turn forces reconstructed roads connecting to them. We develop two techniques to detect the tips: (1) Learn the locations of the tips with the same CNN architectures. (2) Detect the tips from the segmented images by checking the windows around points with high densities. As shown in Figure 3, we add up the segmented image and the two tip enhancements to obtain the final segmented image to feed to Stage 2. Figure 4 shows the comparison between reconstructions without and with tip enhancements.
3.2 Fully Automatic Framework
The ground truth labeling used in the semiautomatic framework is itself a graph like structure. In this section, we propose to create the labels using the discreteMorse based graph reconstruction algorithm without the knowledge of the ground truth. These labels are used to train a CNN for image segmentation. The segmented images are again labeled by the output of the graph reconstruction algorithm and fed to the CNN for training purpose. A few iterations of training and labeling improves the quality of the image segmentation significantly as our experiments show. This framework is particularly useful when there is no or very few labelled data to begin with.
Our framework can deal with the following two scenarios. We perform labelfree learning when we do not have ground truth roads for any input satellite images to begin with. We perform partiallylabeled learning when we have a small fraction of images (say of training set) with road labels.
Labelfree case.
We describe the framework for the labelfree case, and the partiallylabeled case can be handled by a slight modification of it. The highlevel pipeline of Stage 1 (training a CNN for segmenting an input image) is in Figure 5. Given an input set of raw satellite images (with no labels), we split it into the training and testing sets, denoted by and , respectively. We run algorithm MorseGraphRecon() on each image from , and let be its corresponding output. We use a large threshold for simplification in algorithm MorseGraphRecon() so as to generate a reconstruction of the more reliable part of the input. Then we label pixels on as positive and pixels on the complement of as negative. Next we train the CNN classifier with those labeled pixels, and this is our first classifier (shown in Algorithm 1).
Now feeding each original training image from to returns a collection of segmented images , where in each image, every pixel has a value reflecting the likelihood of it being positive (on the road). We repeat the steps with images in and obtain a new CNN classifier . In a generic th iteration of this process, feeding the training images to returns segmented images , which we use to train a new CNN classifier . The process terminates when the segmented images undergo little changes over iterations.
Partiallylabelled case.
For this scenario, we start training the CNN classifier using only the labelled training images to obtain . In each of the subsequent iteration , we use both the labels computed from the segmented images at this iteration, as well as the original labels from the ground truth.
4 Experiments
Datasets
We consider data from the SpaceNet Challenge 3 [20]. It includes four cities: Las Vegas, Paris, Shanghai and Khartoum and consists of the original panchromatic band, the 1.24m resolution 8band multispectral 11bit geotiff, and a 30 cm resolution PanSharpened 3band and 8band 16bit geotiff. We only use the 30 cm resolution PanSharpened 3band (RGB) 16bit geotiff in our experiments. Each image from the dataset covers 400m by 400m with a size of 1300px by 1300px. The ground truth for each image is a graph representing the centerline of the roads. The width of the roads in the masks is 4 meters. To evaluate the results, we need to compare the proposed graphs with the ground truth. So we only take the train set from this challenge (since ground truth is only known for this set).
Metrics.
The first metric we use to evaluate the results is the Average Path Length Similarity (APLS) [20]. This is the metric used for evaluation in SpaceNet Challenge 3.
Definition 4.1
Let and be two input graphs. For where exists in , let (resp. ) denote the closet node to (resp. to ) in . denote the length of the shortest path. First we define the cost of :
We next define
Where = # unique paths in , and we take the sum over all unique paths. Finally, the APLS score of and
is defined to be the harmonic mean of
and :This metric sums the differences in optimal paths existing between nodes in the ground truth graph and the reconstructed graph . It consists of two parts: part 1 considers optimal paths from the ground truth graph, finds paths from the reconstructed graph which correspond to them and measure differences; and part 2, in opposite direction, considers paths from the reconstructed graph, finds their correspondences in the groundtruth and compare them. The final score is the harmonic mean of these two parts. It cares about the connections between the nodes and punishes breaks in the roads. However, this metric may not be accurate when the size of the graph and the total amount of paths are small since the metric evaluates the portion (ratio) of paths that match well. In this case, a small difference in the graphs could result in a relatively large difference in the score (see Figure 6). To obtain a more comprehensive picture, we also use the following Average Hausdorff distance:
Definition 4.2
Suppose and are two graphs; is the point set sampled from ; is the point set sampled from , and denotes the Euclidean distance. Then, the onedirectional Hausdorff distance is:
Here, MAX is a specific maximum value. We set as final Average Hausdorff distance between and .
Note that for APLS score, the higher the score is, the more similar the two graphs are. But for Average Hausdorff distance, the lower the distance is, the more similar the two graphs are.
Parameters.
There are several parameters in the entire pipeline, among which the persistence threshold (for the discreteMorse based reconstruction algorithm) and the arcintensity threshold
(used to further remove noisy arcs during the postprocessing) affect the results most. To tune these two hyperparameters, we experiment on the validation set with a range of parameters that are chosen empirically, then take the set of parameters that give the highest score. We take APLS scores as the reference to tune the parameters.
Furthermore, for datasets AOI_3 (Shanghai) and AOI_4 (Paris), there are many images with extremely sparse signal, while many of them have much denser signal. We thus use a twothreshold system for the arcintensity threshold: For those images we need a low arcintensity threshold : We sort the images by the sum of their intensities, and apply a lower to those images with low totalintensity. We use a higher for the remaining images.
For example, see the right figure for dataset AOI_4, where axis is the percentage of images (sorted in increasing totalintensity), and axis is their totalintensity. Given that there is a sharp transition around , we apply a lower threshold to the of images with the lowest total intensity. We use the same strategy for AOI_3, and choose as the threshold to have two values.
4.1 Semiautomatic reconstruction results
train  validation  test  total  

AOI_2_Vegas  659  165  165  989 
AOI_3_Paris  206  52  52  310 
AOI_4_Shanghai  798  200  200  1198 
AOI_5_Khartoum  189  47  47  283 
APLS  

Buslaev[2]  ours  Buslaev[2]  ours  
AOI_2  0.8211  0.8278  18.3539  17.7841 
AOI_3  0.5848  0.6324  291.0188  289.9532 
AOI_4  0.6630  0.6632  69.5775  68.9596 
AOI_5  0.6069  0.6477  44.4201  41.6037 
AOI_2  0.12  0.4 
AOI_3  0.1  0.3(30%)/0.4 
AOI_4  0.1  0.3(40%)/0.4 
AOI_5  0.07  0.3 
Compared method: Buslaev’s method [2]
We compare our framework with the method of the winner of SpaceNet Challenge 3 [2]. It uses the same CNN architecture to train and then predict the segmented images. In Stage 2, Buslaev’s method first extracts the skeleton from the thresholded segmented images. Then, it transforms the skeleton to a multigraph using library “sknw” [17]. Finally, it translates the multigraph to a graph with straight edges. Buslaev’s method outperforms other methods in SpaceNet Challenge 3, so we only compare ours with this one.
Results.
As mentioned before, we tested on four datasets. The split of trainvalidationtest is 4:1:1 for each data set, and the precise numbers are listed in Table 1.
Tables 2 shows the scores under the two metrics for Buslaev’s framework and ours over test datasets (on validation datasets our scores are consistently better). Each score is an average of scores for all test images (recall the split of trainvalidationtest is shown in Table 1). For APLS score, the larger value the better it is. For Average Hausdorff distance, the smaller value the better it is. Note that AOI_4 and AOI_5 are rather noisy images (especially AOI_5) and most challenging among all datasets. Our method significantly outperforms Buslaev’s method on AOI_5. We also observe that, in general, our output tends to have better connectivity. Figure 7 shows a few examples. Buslaev’s algorithm tends to have more extra branches, and worse connectivity. We note that the final average APLS score reported here for Buslaev’s method is different from the posted one 0.6663 in [23]. This is because the posted score is computed for the original test set from SpaceNet challenge, while we our test set is a subset of the original train set – we cannot compare on the original test set from SpaceNet challenge as the ground truth for them are not publicly available. Tables 3 shows the finally chosen parameters for the reproducibility of the experiment.
Running time.
For each of the two larger datasets (AOI_2_Vegas and AOI_3_Shanghai): Training takes around 500 minutes to learn both the lanes and the tipmarks. Testing (to obtain the segmentation on all images from the testset) takes around 18 minutes. The final road network extraction stage takes 20 mins for each choice of two hyperparameters (persistence threshold and intensity threshold), and total 20 * 9 = 180 minutes to tune the two hyper parameters on validation sets and then run on the final testing sets. We note that the graph reconstruction code is not optimized and we believe can be improved for the 2D setting, which would improve the time for the last final road network extraction stage.
For each of the two smaller datasets (AOI_3_Paris and AOI_5_Khartoum): Training takes around 140 minutes to learn both the lanes and tipmarks. Testing (to obtain the segmentation on all images from the testset) takes around 6 minutes. The final road network extraction stage takes 6 mins for each choice of parameter set, and total 54 minutes to tune the two hyper parameters on validation sets and then run on the final testing sets.
Train  Test  Road extraction  

AOI_2  
AOI_3  
AOI_4  
AOI_5 
4.2 Fully automatic reconstruction results
In the following experiments, we randomly select 200 images as the training set , and 50 images as the test set for each dataset. We evaluate the method by computing the APLS scores on the original test set after each iteration. We initialize our fully automatic approach by converting each RGB image to grayscale and then applying a Gaussian filter. One could potentially use other image processing methods to further preprocess it. When applying the graph reconstruction algorithm, we use the same parameters used in Section 4.1 Table 3.
Alternative method for centerline detection.
To show that the discreteMorse based graph reconstruction algorithm is important for our fullyautomatic training framework, we develop the following alternative scheme SkeletonLabelTrain() as a baseline to compare: the graph reconstruction algorithm is replaced with the Buslaev’s [2] skeleton extraction algorithm (as described in Section 4.1).
Note that this skeleton extraction used in [2] is not designed to work directly on the raw satellite images; see Figure 8, where in (a) we show an output by this skeleton extraction algorithm directly applied to a raw satellite image (yellow curves are ground truth), while (b) shows the output of the discrete Morsebased algorithm on the same input, which is much better. Hence to improve the performance of this the baseline method SkeletonLabelTrain(), we will still first use the discreteMorse graph reconstruction algorithm (or if there are partiallylabelled data, using those first) at the beginning of the training process, and switch to the skeleton extraction algorithm only after a few iterations.
AOI_2  

MorseLabelTrain()  0.2523  0.3340  0.3886  0.4173  0.4332  0.4655  0.4829  0.5252  0.5497  0.5813  0.5922 
SkeletonLabelTrain()  0.2677  0.2643  0.2763  0.2753 
Results for labelfree case.
We show results here for dataset AOI_2_Vegas, which is a cleaner dataset from SpaceNet Challenge. Our new fullyautomatic framework is less effective on AOI_5_Khartoum, which is much more noisy; however, we will show later that, with 10% labelled images, it can obtain reasonable results on the challenging AOI_5_Khartoum dataset as well.
For test images, we always apply tip detection and arc removal when running the graph reconstruction algorithm. These two procedures are not applied to the segmented images during the first three iterations of the training process of the pipeline in Figure 5, as removing arcs results in loss of signals and tip detection tends to introduce noise when the segmented images are not yet reliable. From onward, we start to apply tip detection since the segmented images are now less noisy. We also decrease the threshold for persistence simplification for the discreteMorse based graph reconstruction for , as the quality of segmented images becomes better and better.
In Table 5, we show the APLSscore for test images using the CNN learned at the th iterations, as increases (the Average Hausdorff distance shows a similar trend). In particular, represents the output reconstructed from the segmented images of the set using the trained CNN . We compare the output of our framework for labelfree case, denoted by MorseLabelTrain(), with the output of the baseline method SkeletonLabelTrain(). Note that, as explained earlier, the first two iterations for SkeletonLabelTrain() are done by MorseLabelTrain() (using discrete Morse graph reconstruction), and thus no APLSscores are given for those two iterations for SkeletonLabelTrain(). Also no APLSscores is shown for SkeletonLabelTrain() after the 6th iterations as the score does not improve further. In contrast, the APLSscore continues to improve (for test images) during the iterative process. In Figure 9, we show an example of the reconstructed graph using the CNN from different iterations of our fully automatic training process: observe that at the beginning, only part of signals are captured. Subsequently, the classifier becomes better and more and more signals are captured.
For this set of (200 + 50) images sampled from AOI_2 dataset, the APLSscore for our semiautomatic framework is about . In this fully automatic framework, in the end we obtain a score of , which is worse. However, keep in mind that no labels are used at all.
APLS  
AOI_2 ours  0.6521  0.6918  0.7305  0.7210 
AOI_2 Skel.  0.4860  0.5137  0.5214  0.5252 
AOI_5 ours  0.5351  0.5787  0.5893  0.6077 
AOI_5 Skel.  0.5247  0.5091  0.4884  0.4543 
With 10% ground truth
Now we use a small set of labelled data: Specifically, we assume that only 10% images (i.e, 20 images) have labels (i.e, groundtruth roads given). Table 6 shows the APLSscore for test images after different iterations by MorseLabelTrain() and SkeletonLabelTrain(). For MorseLabelTrain, all scores improve. It is important to note that with only 10% labeledimages, we can now also handle the challenging AOI_5 dataset, and achieve an APLSscore of . (For the case of AOI_2, compared to the labelfree case, the score of our new MorseLabelTrain() improves to from ).
It is interesting to note that this iterative procedure does not seem to help SkeletonLabelTrain() much, with scores even getting worse for the noisy dataset AOI_5. We show some examples of reconstructed graphs at different iterations for our algorithm (Figure 10) and for the alternative SkeletonLabelTrain() method (Figure 11).
4.3 Limitations and future work
First, currently we choose the parameter globally. Figure 12 shows the effect of the persistence threshold . The example demonstrates that there is no single parameter value that works for all cases. As for the parameter arcintensity threshold , we choose it adaptively for AOI_3_Shanghai and AOI_4_Paris by the intensity of the images to deal with the extreme sparse images. For general cases, it is hard to make this choice simply based on the intensities of the images, see Figure 13. An interesting future research direction would be to investigate how to choose these parameters adaptively, yet (semi)automatically. Second, we recover the tips by locating their positions and modifying the density values. It will be interesting to see if we can recover the tips from the graph reconstruction algorithm directly. Third, we observe that the fully automatic framework sometimes is not efficient for a noisy dataset such as AOI_5_Khartoum. It would be good to improve the performance of this approach for noisy datasets.
Acknowledgment: We acknowledge the NSF grants CCF1740761, RI1815697, CCF1733798 and CCF1618247 for partially supporting this research.
References

[1]
(2018)
Fully convolutional network for automatic road extraction from satellite imagery.
In
The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops
, Cited by: §3.1.  [2] (2018) Spacenet round 3 winner.. Note: https://github.com/SpaceNetChallenge/RoadDetector/tree/master/albusolution Cited by: Figure 8, §4.1, §4.1, §4.2, §4.2, Table 2.

[3]
(2012)
Deep neural networks segment neuronal membranes in electron microscopy images
. In Advances in neural information processing systems, pp. 2843–2851. Cited by: §1.  [4] (2011) Use of salient features for the design of a multistage framework to extract roads from highresolution multispectral satellite images. IEEE transactions on Geoscience and Remote sensing 49 (10), pp. 3906–3931. Cited by: §1.
 [5] (201503) Skeletonization and partitioning of digital images using discrete morse theory. IEEE Trans. Pattern Anal. Machine Intelligence 37 (3), pp. 654–666. External Links: ISSN 01628828 Cited by: §1, §2.
 [6] (2017) Improved road network reconstruction using discrete morse theory. In Proc. 25th ACM SIGSPATIAL, pp. 58. Cited by: §1, §3.1.
 [7] (2018) Graph Reconstruction by Discrete Morse Theory. In Proc. 34th Sympos. Comput. Geom., pp. 31:1–31:15. Cited by: §1, §2, §2.
 [8] (2010) Computational topology : an introduction. American Mathematical Society. Cited by: §1.
 [9] (2002) Topological persistence and simplification. Discr. Comput. Geom. 28, pp. 511–533. Cited by: §2.
 [10] (1998) Morse theory for cell complexes. Advances in mathematics 134 (1), pp. 90–145. Cited by: §1, §2.
 [11] (2015) Fusion of color images and lidar data for lane classification. In Proc. 23rd ACM SIGSPATIAL, pp. 69. Cited by: §1.
 [12] (200711) Topologically clean distance fields. IEEE Trans. Visualization Computer Graphics 13 (6), pp. 1432–1439. External Links: ISSN 10772626 Cited by: §1, §2.
 [13] (2016) Deep residual learning for image recognition. In Proc. of the IEEE conference on computer vision and pattern recognition, pp. 770–778. Cited by: §3.1.
 [14] (201108) Theory and algorithms for constructing discrete morse complexes from grayscale digital images. IEEE Trans. Pattern Anal. Machine Intelligence 33 (8), pp. 1646–1658. External Links: ISSN 01628828 Cited by: §1.
 [15] (2015) Unet: convolutional networks for biomedical image segmentation. In International Conference on Medical image computing and computerassisted intervention, pp. 234–241. Cited by: §1, §3.1.
 [16] (2014) An integrated method for urban mainroad centerline extraction from optical remotely sensed imagery. IEEE Transactions on Geoscience and Remote Sensing 52 (6), pp. 3359–3372. Cited by: §1.
 [17] (2017) Note: https://github.com/yxdragon/sknw Cited by: §4.1.
 [18] (201106) The persistent cosmic web and its filamentary structure  I. Theory and implementation. 414, pp. 350–383. External Links: 1009.4015 Cited by: §1, §2.
 [19] (2018) Combining satellite imagery and gps data for road extraction. In Proc. of the 2nd ACM SIGSPATIAL International Workshop on AI for Geographic Knowledge Discovery, pp. 29–32. Cited by: §1.
 [20] (2018) SpaceNet: a remote sensing dataset and challenge series. arXiv preprint arXiv:1807.01232. Cited by: §1, §1, §1, §4, §4.
 [21] (2015) Efficient map reconstruction and augmentation via topological methods. In Proc. 23rd ACM SIGSPATIAL, pp. 25. Cited by: §1, §2.
 [22] (2013) A primal/dual representation for discrete morse complexes on tetrahedral meshes. In Computer Graphics Forum, Vol. 32, pp. 361–370. Cited by: §1.
 [23] (2018) Winning solutions from spacenet road detection and routing challenge. Note: https://github.com/SpaceNetChallenge/RoadDetector Cited by: §4.1.
 [24] (2017) Lane boundary extraction from satellite imagery. In Proc. of the 1st ACM SIGSPATIAL Workshop on HighPrecision Maps and Intelligent Applications for Autonomous Vehicles, pp. 1. Cited by: §1.
 [25] (2017) Pyramid scene parsing network. In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 2881–2890. Cited by: §1.
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