clDice - a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation
Open accessAbstract
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the inter-section of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we pro-pose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
We compared our nerve segmentation model with other advanced 3D image segmentation networks, training each on the same training dataset until full convergence.
“We compared our nerve segmentation model with other advanced 3D image segmentation networks50 (Supplementary Table 1): VNet51, Attention U-Net52, nnFormer53, UNETR54, SwinUNETR55, nnU-Net56 and nnUNetRes56. Each network was trained on the same training dataset until full convergence, defined as no decrease in the training loss for ten consecutive epochs.”
From A deep-learning framework reveals whole-body perturbations at cell level (2026) · cites this paper as [50]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
U-Net: Convolutional Networks for Biomedical Image Segmentation
Ronneberger, O., Fischer, P., & Brox, T. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-24574-4_28 · Cited by 99,404 · see citing works
V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation
Milletari, F., Navab, N., & Ahmadi, S.-A. (2016) · 2016 Fourth International Conference on 3D Vision (3DV) · doi:10.1109/3dv.2016.79 · Cited by 11,931 · cited 1× · see citing works
“As baselines, we use the same architectures trained using soft-Dice [27, 45].”
Method3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation
Çiçek, Ö., Abdulkadir, A., Lienkamp, S. S., Brox, T., & Ronneberger, O. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-46723-8_49 · Cited by 7,945 · cited 2× · see citing works
“We trained two segmentation architectures, a U-Net and an FCN, for the various loss functions in our experimental setup.”
MethodRidge-based vessel segmentation in color images of the retina
Staal, J., Abramoff, M. D., Niemeijer, M., Viergever, M. A., & van Ginneken, B. (2004) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2004.825627 · Cited by 4,202 · cited 1× · see citing works
“In 2D, we evaluate on the DRIVE retina dataset [43], the Massachusetts Roads dataset [28] and the CREMI neuron dataset [12].”
MethodMetrics for evaluating 3D medical image segmentation: analysis, selection, and tool
Taha, A. A., & Hanbury, A. (2015) · BMC Medical Imaging · doi:10.1186/s12880-015-0068-x · Cited by 3,022 · cited 1× · see citing works
“For example, Dice and Jaccard rely on the average voxel-wise hit or miss prediction [46].”
MethodGeneralised Dice Overlap as a Deep Learning Loss Function for Highly Unbalanced Segmentations
Sudre, C. H., Li, W., Vercauteren, T., Ourselin, S., & Jorge Cardoso, M. (2017) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-67558-9_28 · Cited by 2,829 · see citing works
Computational topology an introduction
Edelsbrunner, H., & Harer, J. (2010) · Cited by 1,718 · see citing works
Building Skeleton Models via 3-D Medial Surface Axis Thinning Algorithms
Lee, T. C., Kashyap, R. L., & Chu, C.-N. (1994) · CVGIP Graphical Models and Image Processing · doi:10.1006/cgip.1994.1042 · Cited by 1,587 · cited 1× · see citing works
“For binary geometries, various algorithms based on thinning and medial surfaces have been proven to be topologypreserving according to varying definitions of topology [23, 25, 26, 35].”
Digital topology: Introduction and survey
Kong, T. Y., & Rosenfeld, A. (1989) · Computer Vision Graphics and Image Processing · doi:10.1016/0734-189x(89)90147-3 · Cited by 1,013 · cited 2× · see citing works
“Additionally, we provide an elaborate explanation of clDice topological properties, using concepts of applied digital topology in the theory section of the Supplementary material [24, 23].”
MethodA review of vessel extraction techniques and algorithms
Kirbas, C., & Quek, F. K. H. (2004) · ACM Computing Surveys · doi:10.1145/1031120.1031121 · Cited by 896 · see citing works
Whitehead, J. H. C. (1949) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1949-09175-9 · Cited by 846 · see citing works
Machine learning for aerial image labeling
Hinton, G. E., & Mnih, V. (2013) · TSpace (University of Toronto) · Cited by 722 · see citing works
Topological persistence and simplification
Edelsbrunner, H., Letscher, D., & Zomorodian, A. J. (2002) · Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2000.892133 · Cited by 716 · cited 1× · see citing works
“However, analyzing preservation of topology while simplifying geometries is a difficult analytical and computational problem [11, 10].”
BackgroundTopology preserving level set method for geometric deformable models
Han, X., Xu, C., & Prince, J. L. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1201824 · Cited by 487 · cited 2× · see citing works
“As a comparison, [17] needs O(c2mlog(m)) (see [15]) complexity to compute the 1d persistent homology where d is the number of points with zero gradients in the prediction and m is the number of simplices.”
Graph cut based image segmentation with connectivity priors
Vicente, S., Kolmogorov, V., & Rother, C. (2008) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2008.4587440 · Cited by 391 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodJoutel, A., Monet-Leprêtre, M., Gosele, C., Baron-Menguy, C., Hammes, A., Schmidt, S., Lemaire-Carrette, B., Domenga, V., Schedl, A., Lacombe, P., et al. (2010) · Journal of Clinical Investigation · doi:10.1172/jci39733 · Cited by 379 · cited 1× · see citing works
“In the aforementioned domains, a topologically accurate segmentation is necessary to guarantee error-free downstream tasks, such as computational hemodynamics, route planning, Alzheimer’s disease prediction [18], or stroke modeling [20].”
BackgroundMachine Learning for Aerial Image Labeling
Mnih, V. (2013) · TSpace (University of Toronto) · Cited by 376 · see citing works
Hu, K., Zhang, Z., Niu, X., Zhang, Y., Cao, C., Xiao, F., & Gao, X. (2018) · Neurocomputing · doi:10.1016/j.neucom.2018.05.011 · Cited by 349 · cited 1× · see citing works
“tures, are 1) overlap based measures such as Dice, precision, recall, and Jaccard index; and 2) volumetric distance measures such as the Hausdorff and Mahalanobis distance [21, 40, 36, 16].”
MethodMachine learning analysis of whole mouse brain vasculature
Todorov, M. I., Paetzold, J. C., Schoppe, O., Tetteh, G., Shit, S., Efremov, V., Todorov-Völgyi, K., Düring, M., Dichgans, M., Piraud, M., et al. (2020) · Nature Methods · doi:10.1038/s41592-020-0792-1 · Cited by 338 · see citing works
Self-citationCellular and Molecular Probing of Intact Human Organs
Zhao, S., Todorov, M. I., Cai, R., -Maskari, R. A., Steinke, H., Kemter, E., Mai, H., Rong, Z., Warmer, M., Stanic, K., et al. (2020) · Cell · doi:10.1016/j.cell.2020.01.030 · Cited by 292 · cited 1× · see citing works
“Both scenarios are pronounced in imaging modalities, such as fluorescence microscopy [48, 58] and optoacoustics, which focus on mapping small capillary structures.”
BackgroundSelf-citationA Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology
Clough, J. R., Byrne, N., Öksüz, İ., Zimmer, V. A., Schnabel, J. A., & King, A. P. (2020) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.3013679 · Cited by 281 · cited 1× · see citing works
“Another approach enables the predefinition of Betti numbers and enforces them on the training[8].”
BackgroundBeyond the Pixel-Wise Loss for Topology-Aware Delineation
Mosinska, A., Márquez-Neila, P., Koziński, M., & Fua, P. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00331 · Cited by 280 · see citing works
Tetteh, G., Efremov, V., Forkert, N. D., Schneider, M., Kirschke, J. S., Weber, B., Zimmer, C., Piraud, M., & Menze, B. H. (2020) · Frontiers in Neuroscience · doi:10.3389/fnins.2020.592352 · Cited by 274 · cited 3× · see citing works
“In stark contrast to previous works, where segmentation and centerline prediction has been learned jointly as multi-task learning [50, 47], we are not interested in learning the centerline.”
MethodResultSelf-citationFunke, J., Tschopp, F., Grisaitis, W., Sheridan, A., Singh, C., Saalfeld, S., & Turaga, S. C. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2835450 · Cited by 219 · see citing works
A Higher-Order CRF Model for Road Network Extraction
Wegner, J. D., Zegarra, J. A. M., & Schindler, K. (2013) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2013.222 · Cited by 201 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodHunter, J. M., Kwan, J., Malek‐Ahmadi, M. H., Maarouf, C. L., Kokjohn, T. A., Belden, C. M., Sabbagh, M. N., Beach, T. G., & Roher, A. E. (2012) · PLoS ONE · doi:10.1371/journal.pone.0036893 · Cited by 175 · cited 1× · see citing works
“In the aforementioned domains, a topologically accurate segmentation is necessary to guarantee error-free downstream tasks, such as computational hemodynamics, route planning, Alzheimer’s disease prediction [18], or stroke modeling [20].”
BackgroundTopology-Preserving Deep Image SegmentationPreprint
Hu, X., Li, F., Samaras, D., & Chen, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.05404 · Cited by 164 · cited 5× · see citing works
“proposed the first continuous-valued loss function based on the Betti number and persistent homology [17].”
BackgroundMethodInfluentialTopology Aware Fully Convolutional Networks for Histology Gland Segmentation
BenTaieb, A., & Hamarneh, G. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-46723-8_53 · Cited by 163 · cited 1× · see citing works
“Further, topological priors of containment were applied to histology scans [5], a 3D CNN with graph refinement was used to improve airway connectivity [19], and recently, Mosinska et al.”
MethodON TOPOLOGY PRESERVATION IN 2-D AND 3-D THINNING
Kong, T. Y. (1995) · International Journal of Pattern Recognition and Artificial Intelligence · doi:10.1142/s0218001495000341 · Cited by 151 · cited 3× · see citing works
“Additionally, we provide an elaborate explanation of clDice topological properties, using concepts of applied digital topology in the theory section of the Supplementary material [24, 23].”
MethodWhole-Brain Vasculature Reconstruction at the Single Capillary Level
Giovanna, A. P. D., Tibo, A., Silvestri, L., Müllenbroich, M. C., Costantini, I., Mascaro, A. L. A., Sacconi, L., Frasconi, P., & Pavone, F. S. (2018) · Scientific Reports · doi:10.1038/s41598-018-30533-3 · Cited by 129 · cited 1× · see citing works
“30 μm for arterioles and 5 μm for capillaries [48, 9], training on a globally averaged loss induces a strong bias towards the volumetric segmentation of large vessels.”
BackgroundOn Topology Preservation in 3D Thinning
Ma, C. M. (1994) · CVGIP Image Understanding · doi:10.1006/ciun.1994.1023 · Cited by 122 · cited 1× · see citing works
“For binary geometries, various algorithms based on thinning and medial surfaces have been proven to be topologypreserving according to varying definitions of topology [23, 25, 26, 35].”
Probabilistic image segmentation with closedness constraints
Andres, B., Kappes, J. H., Beier, T., Köthe, U., & Hamprecht, F. A. (2011) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2011.6126550 · Cited by 105 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodA skeletonization algorithm by maxima tracking on Euclidean distance transform
Shih, F. Y., & Pu, C. C. (1995) · Pattern Recognition · doi:10.1016/0031-3203(94)00104-t · Cited by 105 · cited 1× · see citing works
“Euclidean distance transform has been used on multiple occasions [42, 55], but remains a discrete operation and, to the best of our knowledge, an end-to-end differentiable approximation remains to be developed, preventing the use in a loss function for training neural networks.”
MethodLearning tree-structured representation for 3D coronary artery segmentation
Kong, B., Wang, X., Bai, J., Lu, Y., Gao, F., Cao, K., Xia, J., Song, Q., & Yin, Y. (2019) · Computerized Medical Imaging and Graphics · doi:10.1016/j.compmedimag.2019.101688 · Cited by 102 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodTopology cuts: A novel min-cut/max-flow algorithm for topology preserving segmentation in N–D images
Zeng, Y., Samaras, D., Chen, W., & Peng, Q. (2008) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2008.07.008 · Cited by 84 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodDeep vessel tracking: A generalized probabilistic approach via deep learning
Wu, A., Xu, Z., Gao, M., Buty, M., & Mollura, D. J. (2016) · IEEE International Symposium on Biomedical Imaging (ISBI) · doi:10.1109/isbi.2016.7493520 · Cited by 83 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodSchneider, M., Hirsch, S., Weber, B., Székely, G. J., & Menze, B. H. (2014) · Medical Image Analysis · doi:10.1016/j.media.2014.09.007 · Cited by 77 · cited 1× · see citing works
“tures, are 1) overlap based measures such as Dice, precision, recall, and Jaccard index; and 2) volumetric distance measures such as the Hausdorff and Mahalanobis distance [21, 40, 36, 16].”
MethodSelf-citationGlobal connectivity potentials for random field models
Nowozin, S., & Lampert, C. H. (2009) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvprw.2009.5206567 · Cited by 73 · see citing works
Tissue metabolism driven arterial tree generation
Schneider, M., Reichold, J., Weber, B., Székely, G. J., & Hirsch, S. (2012) · Medical Image Analysis · doi:10.1016/j.media.2012.04.009 · Cited by 72 · cited 1× · see citing works
“In 3D, a synthetic vessel dataset with an added Gaussian noise term [39] and the Vessap dataset of multi-channel volumetric scans of brain vessels is used [48, 34].”
MethodJin, D., Xu, Z., Harrison, A. P., George, K., & Mollura, D. J. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-67389-9_17 · Cited by 66 · cited 1× · see citing works
“Further, topological priors of containment were applied to histology scans [5], a 3D CNN with graph refinement was used to improve airway connectivity [19], and recently, Mosinska et al.”
MethodVascular Segmentation in TOF MRA Images of the Brain Using a Deep Convolutional Neural Network
Phellan, R., Peixinho, A. Z., Falcão, A. X., & Forkert, N. D. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-67534-3_5 · Cited by 66 · cited 1× · see citing works
“tures, are 1) overlap based measures such as Dice, precision, recall, and Jaccard index; and 2) volumetric distance measures such as the Hausdorff and Mahalanobis distance [21, 40, 36, 16].”
MethodShape-Aware Complementary-Task Learning for Multi-organ Segmentation
Navarro, F., Shit, S., Ezhov, I., Paetzold, J. C., Gafita, A., Peeken, J. C., Combs, S. E., & Menze, B. H. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-32692-0_71 · Cited by 66 · see citing works
Self-citationUnsupervised Microvascular Image Segmentation Using an Active Contours Mimicking Neural Network
Gur, S., Wolf, L., Golgher, L., & Blinder, P. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.01082 · Cited by 61 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodA 3-subiteration 3D thinning algorithm for extracting medial surfaces
Palágyi, K. (2002) · Pattern Recognition Letters · doi:10.1016/s0167-8655(01)00142-8 · Cited by 54 · cited 2× · see citing works
“Importantly, thinning using morphological operations (skeletonization) on curvilinear structures can be topologypreserving [35].”
BackgroundReconstructing Curvilinear Networks Using Path Classifiers and Integer Programming
Türetken, E., Benmansour, F., Andres, B., Głowacki, P., Pfister, H., & Fua, P. (2016) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2016.2519025 · Cited by 54 · see citing works
Active Contours Under Topology Control—Genus Preserving Level Sets
Ségonne, F. (2007) · International Journal of Computer Vision · doi:10.1007/s11263-007-0102-8 · Cited by 53 · see citing works
Global connectivity potentials for random field models
Nowozin, S., & Lampert, C. H. (2009) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2009.5206567 · Cited by 53 · see citing works
A Deep Learning Design for Improving Topology Coherence in Blood Vessel Segmentation
Araújo, R. J., Cardoso, J. S., & Oliveira, H. P. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-32239-7_11 · Cited by 50 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodSkeletonization using an extended Euclidean distance transform
Wright, M., Cipolla, R., & Giblin, P. (1995) · Image and Vision Computing · doi:10.1016/0262-8856(95)99723-e · Cited by 42 · cited 1× · see citing works
“Euclidean distance transform has been used on multiple occasions [42, 55], but remains a discrete operation and, to the best of our knowledge, an end-to-end differentiable approximation remains to be developed, preventing the use in a loss function for training neural networks.”
MethodTree Shape Priors with Connectivity Constraints Using Convex Relaxation on General Graphs
Stühmer, J., Schröder, P., & Cremers, D. (2013) · IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2013.290 · Cited by 40 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodJoint Segmentation and Path Classification of Curvilinear Structures
Mosinska, A., Koziński, M., & Fua, P. (2019) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2019.2921327 · Cited by 38 · cited 1× · see citing works
“trained networks which perform segmentation and path classification simultaneously [30].”
Generalized Connectivity Constraints for Spatio-temporal 3D Reconstruction
Oswald, M. R., Stühmer, J., & Cremers, D. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10593-2_3 · Cited by 32 · cited 1× · see citing works
“For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [44], graph representation priors to natural images [2], higher-order cliques which connect superpixels [53] and adversarial learni…”
MethodPromoting Connectivity of Network-Like Structures by Enforcing Region Separation
Öner, D., Koziński, M., Citraro, L., Dadap, N. C., Konings, A. G., & Fua, P. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3074366 · Cited by 28 · see citing works
Image-Conditioned Graph Generation for Road Network ExtractionPreprint
Belli, D., & Kipf, T. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.14388 · Cited by 26 · cited 3× · see citing works
“SMD captures a Wasserstein distance between two graphs.”
BackgroundMethodAutomated analysis of whole brain vasculature using machine learningPreprint
Todorov, M. I., Paetzold, J. C., Schoppe, O., Tetteh, G., Efremov, V., Völgyi, K., Duering, M., Dichgans, M., Piraud, M., Menze, B. H., et al. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/613257 · Cited by 16 · cited 4× · see citing works
“In 3D, a synthetic vessel dataset with an added Gaussian noise term [39] and the Vessap dataset of multi-channel volumetric scans of brain vessels is used [48, 34].”
BackgroundMethodInfluentialSelf-citationA Multi-task Network to Detect Junctions in Retinal Vasculature
Uslu, F., & Bharath, A. A. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-00934-2_11 · Cited by 14 · cited 1× · see citing works
“In stark contrast to previous works, where segmentation and centerline prediction has been learned jointly as multi-task learning [50, 47], we are not interested in learning the centerline.”
ResultEfficient Algorithms for Moral Lineage Tracing
Rempfler, M., Lange, J.-H., Jug, F., Blasse, C., Myers, E. W., Menze, B. H., & Andres, B. (2017) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.503 · Cited by 12 · see citing works
Self-citationTopoAL: An Adversarial Learning Approach for Topology-Aware Road Segmentation
Vasu, S., Koziński, M., Citraro, L., & Fua, P. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58583-9_14 · Cited by 12 · see citing works
A Distance-Based Loss for Smooth and Continuous Skin Layer Segmentation in Optoacoustic Images
Gerl, S., Paetzold, J. C., He, H., Ezhov, I., Shit, S., Kofler, F., Bayat, A., Tetteh, G., Ntziachristos, V., & Menze, B. H. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-59725-2_30 · Cited by 11 · see citing works
Self-citationPaetzold, J. C., Schoppe, O., Al-Maskari, R., Tetteh, G., Efremov, V., Todorov, M. I., Cai, R., Mai, H., Rong, Z., Ertuerk, A., et al. (2019) · Cited by 10 · see citing works
Self-citationTowards Reliable Evaluation of Algorithms for Road Network Reconstruction from Aerial Images
Citraro, L., Koziński, M., & Fua, P. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58604-1_42 · Cited by 9 · cited 2× · see citing works
“Additionally we compute the F1 score of junction-based metric [7].”
BackgroundMethod
Flagged first, then by citations
3 of the 64 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- [40][40] Azriel Rosenfeld. Digital topology. The American Mathematical Monthly , 86(8):621-630, 1979. 11 -
Cited by
Sorted by citations
Zeng, A., Wu, C., Lin, G., Xie, W., Hong, J., Meiping, H., Zhuang, J., Bi, S., Pan, D., Ullah, N., et al. (2023) · Computerized Medical Imaging and Graphics · doi:10.1016/j.compmedimag.2023.102287 · Cited by 141 · see citing works
AngioNet: a convolutional neural network for vessel segmentation in X-ray angiography
Iyer, K., Najarian, C., Fattah, A., Arthurs, C. J., Soroushmehr, S. M. R., Subban, V., Sankardas, M. A., Nadakuditi, R. R., Nallamothu, B. K., & Figueroa, C. A. (2021) · Scientific Reports · doi:10.1038/s41598-021-97355-8 · Cited by 114 · see citing works
Payette, K., de Dumast, P., Kebiri, H., Ezhov, I., Paetzold, J. C., Shit, S., Iqbal, A., Khan, R., Kottke, R., Grehten, P., et al. (2021) · Zurich Open Repository and Archive (University of Zurich) · doi:10.3929/ethz-b-000495621 · Cited by 105 · see citing works
Self-citationAdaptive t-vMF dice loss: An effective expansion of dice loss for medical image segmentation
Kato, S., & Hotta, K. (2023) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2023.107695 · Cited by 60 · see citing works
Human treelike tubular structure segmentation: A comprehensive review and future perspectives
Li, H., Tang, Z., Yang, N., & Yang, G. (2022) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2022.106241 · Cited by 42 · see citing works
Lu, X., & Weng, Q.-H. (2025) · Isprs Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2025.07.013 · Cited by 42 · see citing works
Geometry-Aware Neural Solver for Fast Bayesian Calibration of Brain Tumor Models
Ezhov, I., Mot, T., Shit, S., Lipková, J., Paetzold, J. C., Kofler, F., Pellegrini, C., Kollovieh, M., Navarro, F., Li, H., et al. (2021) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2021.3136582 · Cited by 29 · see citing works
Self-citationParrott, C. M., Abueidda, D., & James, K. A. (2023) · Journal of Mechanical Design · doi:10.1115/1.4056929 · Cited by 27 · see citing works
Simulating the Cellular Context in Synthetic Datasets for Cryo-Electron Tomography
Martínez-Sánchez, A., Lamm, L., Jasnin, M., & Phelippeau, H. (2024) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2024.3398401 · Cited by 27 · see citing works
“Authors in [54] proposes clDice (centerline Dice) for tube-like structures in 2D images, here we extend this metric to 3D for processing filament-like structures.”
BackgroundPatel, T. R., Patel, A., Veeturi, S. S., Shah, M., Waqas, M., Monteiro, A., Baig, A. A., Pinter, N. K., Levy, E. I., Siddiqui, A. H., et al. (2023) · Neurosurgical FOCUS · doi:10.3171/2023.3.focus2374 · Cited by 25 · see citing works
vesselFM: A Foundation Model for Universal 3D Blood Vessel Segmentation
Wittmann, B., Wattenberg, Y., Amiranashvili, T., Shit, S., & Menze, B. (2025) · 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr52734.2025.01944 · Cited by 25 · see citing works
“Masks contained in M syn encompass a broad range of realistic vascular patterns, capturing variations in blood vessel scale, density, curvature, and tortuosity.”
Self-citationAutomatic segmentation of mandibular canal using transformer based neural networks
Lv, J., Zhang, L., Xu, J., Li, W., Li, G., & Zhou, H. (2023) · Frontiers in Bioengineering and Biotechnology · doi:10.3389/fbioe.2023.1302524 · Cited by 24 · see citing works
CoordConv-Unet: Investigating CoordConv for Organ Segmentation
Jurdi, R. E., Petitjean, C., Honeine, P., & Abdallah, F. (2021) · IRBM · doi:10.1016/j.irbm.2021.03.002 · Cited by 22 · see citing works
Deep learning based coronary vessels segmentation in X-ray angiography using temporal information
He, H., Banerjee, A., Choudhury, R. P., & Grau, V. (2025) · Medical Image Analysis · doi:10.1016/j.media.2025.103496 · Cited by 17 · see citing works
Whole mandibular canal segmentation using transformed dental CBCT volume in Frenet frame
Zhao, H., Chen, J., Yun, Z., Feng, Q., Zhong, L., & Yang, W. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e17651 · Cited by 14 · see citing works
“To further maintain the connectivity of the mandibular canal, we use clDice loss [22] to train the mandibular canal segmentation network.”
BackgroundMethodInfluentialCIDN: A context interactive deep network with edge-aware for X-ray angiography images segmentation
Zhang, M., Wang, H., Wang, L., Saif, A., & Wassan, S. (2023) · Alexandria Engineering Journal · doi:10.1016/j.aej.2023.12.034 · Cited by 14 · see citing works
TopoTxR: A topology-guided deep convolutional network for breast parenchyma learning on DCE-MRIs
Wang, F., Zou, Z., Sakla, N. M., Partyka, L., Rawal, N., Singh, G., Zhao, W., Ling, H., Huang, C. Z., Prasanna, P., et al. (2024) · Medical Image Analysis · doi:10.1016/j.media.2024.103373 · Cited by 14 · see citing works
Supervised segmentation with domain adaptation for small sampled orbital CT images
Suh, S., Cheon, S., Choi, W., Chung, Y. W., Cho, W., Paik, J., Kim, S. E., Chang, D.-J., & Lee, Y. O. (2022) · Journal of Computational Design and Engineering · doi:10.1093/jcde/qwac029 · Cited by 13 · see citing works
Yaman, S., Aslan, Ö., Güler, H., Şengür, A., Hafeez‐Baig, A., Tan, R., Deo, R. C., Barua, P. D., & Acharya, U. R. (2025) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2025.108858 · Cited by 13 · see citing works
Automatic segmentation and quantification of the optic nerve on MRI using a 3D U-Net
van Elst, S., de Bloeme, C. M., Noteboom, S., de Jong, M. C., Moll, A. C., Göricke, S. L., de Graaf, P., & Caan, M. W. A. (2023) · Journal of medical imaging · doi:10.1117/1.jmi.10.3.034501 · Cited by 12 · see citing works
“, continuous values between 0 and 1)(41) or adapting the loss function specifically to tubular structure segmentation, such as using a centerline Dice loss.(40) These approaches could enhance the segmentation accuracy and improve its quantitative evaluation.”
MethodCardiovascular medical image and analysis based on 3D vision: A comprehensive survey
Wang, Z., Yi, R., Wen, X., Zhu, C., & Xu, K. (2024) · Meta-Radiology · doi:10.1016/j.metrad.2024.100102 · Cited by 11 · see citing works
Alblas, D., Suk, J., Brüne, C., Yeung, K. K., & Wolterink, J. M. (2025) · Medical Image Analysis · doi:10.1016/j.media.2025.103467 · Cited by 11 · see citing works
Learning Euler's Elastica Model for Medical Image SegmentationPreprint
Chen, X., Luo, X., Zhao, Y., Zhang, S., Wang, G., & Zheng, Y. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.00526 · Cited by 11 · see citing works
Image Segmentation of Retinal Blood Vessels Based on Dual-Attention Multiscale Feature Fusion
Gao, J., Huang, Q., Gao, Z., & Chen, S. (2022) · Computational and Mathematical Methods in Medicine · doi:10.1155/2022/8111883 · Cited by 10 · see citing works
“In [24], a computationally e ffi cient, di ff erentiable loss function (soft-clDice) was proposed for training arbitrary neural segmentation networks.”
RetractedSegmentation of cardiac tissues and organs for CCTA images based on a deep learning model
Cai, S., Lu, Y., Li, B., Gao, Q., Xu, L., Hu, X., & Zhang, L. J. (2023) · Frontiers in Physics · doi:10.3389/fphy.2023.1266500 · Cited by 10 · see citing works
E2MISeg: Enhancing edge-aware 3D medical image segmentation via feature progressive co-aggregation
Jiang, L., Xu, W., Zheng, X., Zhang, Z., Jiang, Z., Jiang, C. W., Chen, Y., Ji, Y., Liu, S., Liu, J.-W., et al. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.128861 · Cited by 8 · see citing works
An analysis of the influence of transfer learning when measuring the tortuosity of blood vessels
da Silva, M. V., Ouellette, J., Lacoste, B., & Comin, C. H. (2022) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2022.107021 · Cited by 8 · see citing works
“Despite the development of additional performance metrics such as clDice [38], the influence of segmentation on downstream tasks, such as blood vessel morphometry, has rarely been addressed.”
GVC-Net: Global Vascular Context Network for Cerebrovascular Segmentation Using Sparse Labels
Li, M., Li, S., Han, Y., & Zhang, T. (2022) · IRBM · doi:10.1016/j.irbm.2022.05.001 · Cited by 8 · see citing works
TSNet: Vessel segmentation with sequential frame temporal information in coronary angiography
Yu, H., Gao, H., Li, G., Qin, Z., Jia, D., Wang, G., & Wang, S. (2025) · Computerized Medical Imaging and Graphics · doi:10.1016/j.compmedimag.2025.102540 · Cited by 6 · see citing works
Taming Connectedness in Machine-Learning-Based Topology Optimization with Connectivity Graphs
Behzadi, M. M., Chen, J., & Ilieş, H. T. (2023) · Computer-Aided Design · doi:10.1016/j.cad.2023.103634 · Cited by 5 · see citing works
“Similar modifications to loss functions, incorporating topology-aware terms, have been explored in other domains, as demonstrated in [16].”
Li, J., Huang, Y., Ye, X., & Yang, H. (2025) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2025.110045 · Cited by 5 · see citing works
Yun, Z., Xu, Q., Wang, G., Jin, S., Lin, G., Feng, Q., & Yuan, J. (2022) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2022.106631 · Cited by 5 · see citing works
Han, T., Xiong, J., Lin, T. S., An, T., Wang, C., Zhu, J., Li, Z., Lu, L., Zhang, Y., & Teng, G. (2024) · EngMedicine · doi:10.1016/j.engmed.2024.100004 · Cited by 4 · see citing works
Xiong, J., Lyu, P., Fang, W., Li, X., Wang, C., & Zhu, J. (2023) · International Conference on Control, Robotics and Intelligent System (CCRIS) · doi:10.1145/3622896.3622913 · Cited by 4 · see citing works
“proposed the use of cldice loss [14] to supervise the network and effectively preserve the topological nature of tubular structure segmentation.”
A shape-supervised feature fusion U-Net for tubular structure segmentation
Yue, J., Jin, S., Wang, S., Zeng, J., Shan, S., Liu, B., Jiang, N., & Zhou, F. (2024) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2024.109522 · Cited by 4 · see citing works
Jenssen, H. B., Nainamalai, V., Pelanis, E., Kumar, R. P., Abildgaard, A., Kolrud, F. K., Edwin, B., Jiang, J., Vettukattil, J. J., Elle, O. J., et al. (2025) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2025.107822 · Cited by 4 · see citing works
Boundary-aware dynamic re-weighting for semi-supervised medial image segmentation
Jiang, W., Li, J., Li, Y., Wei, X., Huang, J., Quellec, G., Si, W., & Ou, C. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.128175 · Cited by 4 · see citing works
A deep-learning framework reveals whole-body perturbations at cell level
Kaltenecker, D., Horvath, I., Al-Maskari, R., Chen, Y., Kolabas, Z. I., Hoeher, L., Todorov, M., Minde, D.-P., Kapoor, S., Turhan, S. G., et al. (2026) · Nature · doi:10.1038/s41586-026-10535-2 · Cited by 5 · see citing works
Self-citationHuang, Z., Wang, S., Alley, R. B., & Parizek, B. R. (2025) · Remote Sensing of Environment · doi:10.1016/j.rse.2025.114964 · Cited by 3 · see citing works
Tractable large-scale deep reinforcement learning
Sarang, N., & Poullis, C. (2023) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2023.103689 · Cited by 3 · see citing works
Meta-Tubular-Net: A Robust Topology-Aware Re-Weighting Network for Retinal Vessel Segmentation
Huang, S., Li, J., Shen, N., & Xu, T. (2022) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2024.106060 · Cited by 3 · see citing works
Tiefenthaler, M., Mangesius, S., Pereverzyev, S., Gizewski, E. R., & Neumann, L. (2025) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2025.108952 · Cited by 3 · see citing works
Chang, G. H., Wu, M., Yen, L.-H., Huang, D., Lin, Y., Luo, Y.-R., Liu, Y.-D., Xu, B., Leong, K. W., Lai, W., et al. (2023) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2023.107991 · Cited by 3 · see citing works
coDice: connectivity-preserving dice loss for 2D/3D tubular structure segmentation
Dong, J., Lv, Y., Bai, X., Tian, M., Zhang, C., Zhuang, X., Jernberg, T., & Wang, C. (2025) · SPIE Medical Imaging: Image Processing · doi:10.1117/12.3047030 · Cited by 2 · see citing works
“Standard 2D and 3D U-Nets are used as the backbone networks, 12,13 and these networks are trained from scratch every time using softDice, 10,14 clDice 9 or coDice.”
Chierici, A. P., Guzzi, L., Goffart, S., Kamoun, N., Gargiulo, M., Chevallier, P., Iannelli, A., Anty, R., Delingette, H., Lareyre, F., et al. (2025) · Cureus · doi:10.7759/cureus.86072 · Cited by 2 · see citing works
“Centerline dice score (clDice): Evaluates overlap for tubular structures, focusing on segmentation masks and morphological skeletons [26].”
Skea-Topo: A skeleton-aware loss function for topologically accurate boundary segmentation
Liu, C., Ma, B., Xie, Y., Ban, X., Huang, H., Wang, H. H., Xue, W., & Xu, K. (2025) · Pattern Recognition · doi:10.1016/j.patcog.2025.112265 · Cited by 2 · see citing works
DPANet: curve-like structure segmentation based on dual-path attention network
Song, P., Zhang, H., Junfeng, 景. J., Li, P., & Pan, Q. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.129030 · Cited by 2 · see citing works
UCAN: U-shaped context aggregation network for thin crack segmentation under topological constraints
Chen, J., Zhu, G., Zhang, Y., Chen, Z., Huang, Q., & Li, J. (2024) · Robotic Intelligence and Automation · doi:10.1108/ria-08-2023-0097 · Cited by 2 · see citing works
Center-Guided and Connectivity-Preserving Network for Grain Size Measurement
Yu, H., Shang, E., Li, X., Xie, H., Zhu, Z. S., Song, Z., Liang, X. P., Song, K., Yan, Y., Li, X., et al. (2021) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2021.3135331 · Cited by 2 · see citing works
Hepatic artery segmentation with 3D convolutional neural networks
Kock, F., Chlebus, G., Thielke, F., Schenk, A., & Meine, H. (2022) · SPIE Medical Imaging: Computer-Aided Diagnosis · doi:10.1117/12.2607253 · Cited by 2 · see citing works
“…and precision have been adapted so that Centerline Precision = TP predSkel TP predSkel + FP predSkel (1) and Centerline Sensitivity = TP refSkel TP refSkel + FN (2) are defined such that the computations are not done voxelwise but with skeletonized vessel masks as proposed by Shit et al. (2021).”
ExpertSegmentation: Segmentation for microscopy with domain-informed targets via custom loss
Prakash, N., Gasper, P. J., & Usseglio‐Viretta, F. L. E. (2025) · Acta Materialia · doi:10.1016/j.actamat.2025.120993 · Cited by 1 · see citing works
Zhou, Z., Zhang, Z., Hu, J., Zhang, Y., Mao, X., Chen, G., Qian, X., Peng, B., Dai, B., & Dai, Y. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.128096 · Cited by 1 · see citing works
A$$\nu $$-Net: Automatic Detection and Segmentation of Aneurysm
Shit, S., Ezhov, I., Paetzold, J. C., & Menze, B. H. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-72862-5_5 · Cited by 1 · see citing works
Self-citationThielke, F., Kock, F., Gerken, A., Abolmaali, N., Schenk, A., & Meine, H. (2023) · SPIE Medical Imaging: Image Processing · doi:10.1117/12.2654157 · Cited by 1 · see citing works
Sam-Octa: Prompting Segment-Anything for Octa Image SegmentationPreprint
Xinrunchen, X., Wang, C., Ning, H., Li, S., & Shen, M. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4893639 · Cited by 1 · see citing works
rNCA: Self-Repairing Segmentation Masks
Silbernagel, M., Alonso, A., Petersen, J., Ibragimov, B., de Bruijne, M., & Wyburd, M. K. (2025) · arXiv · doi:10.48550/arxiv.2512.13397
Topological Regularization for Dense Prediction
Fu, D., & Nelson, B. J. (2022) · International Conference on Machine Learning and Applications · doi:10.1109/icmla55696.2022.00014
“There has been a recent broad effort to develop persistent homology-based losses and regularization terms in a variety of contexts, including the development of applicationspecific losses [26], [27], [28], [29] as well as general implementations and theory to make this tool increasingly available [6], [7], [8], [9], […”
BackgroundEsteves, S. C., Vacavant, A., & Merveille, O. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4573124
SAM-OCTA: Prompting Segment-Anything for OCTA Image SegmentationPreprint
Xinrunchen, X., Ning, H., Li, S., & Shen, M. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4844681
Intelligent segmentation of pelvic lymph nodes and accessory accompanying pelvic artery
Zhang, H., Zhang, Y., & Wang, Z. (2024) · Elsevier eBooks · doi:10.1016/b978-0-443-33875-5.00006-2
Deep leaning-based interactive segmentation of three-dimensional blood vessel images
Li, Y., Zhang, Q., Zhou, H., An, Y., Li, X., Li, X., Zhou, H., & Li, A. (2025) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2025.107507
A novel multiscale 3D segmentation network based on vascular skeleton assistance
Wang, Y. M., Zhou, S., Xinyang, S., Chen, T., & Zhang, J. (2025) · International Conference on Graphics and Image Processing (ICGIP) · doi:10.1117/12.3057741
Centerline dice metric implementation is not streamlined
Podobnik, G., & Vrtovec, T. (2025) · SPIE Medical Imaging: Image Processing · doi:10.1117/12.3047456
“6,10 The authors of clDice 4 have, concurrently with their paper, released its open-source Python-based implementation, which resorts to volumetric-based skeletonization.”
- Authors
- Shit, S., Paetzold, J. C., Sekuboyina, A., Ezhov, I., Unger, A., Zhylka, A., Pluim, J. P. W., Bauer, U., & Menze, B. H.
- Affiliations
- Technical University of Munich (DE)
- Eindhoven University of Technology (NL)
- ORCID
- Venue
- 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
- Publisher
- IEEE
- Published
- 2021-06
- Pages
- 16555-16564
- ISSN
- 1063-6919 (ISSN-L)
- OpenAlex
- W3010789210
- Cited by
- 60
- References
- 64
- Citations by year
- 2025: 20 · 2024: 9 · 2023: 15 · 2022: 9 · 2021: 6 · 2020: 1
- FWCI
- 3.19
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- TU/e Research Portal (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Medical Image Segmentation Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Retinal Imaging and Analysis
- Keywords
- topology preservation, tubular structure segmentation, skeletonization, homotopy equivalence, differentiable loss function, vessel segmentation, neuron segmentation, road network segmentation, graph similarity, connectedness
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
