clDice - a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation

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, e.g. preserving connectedness: in case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed clDice, which is calculated on the intersection of the segmentation masks and their (morphological) skeletons. Crucially, we theoretically prove that clDice guarantees topological correctness for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable soft-clDice as a loss function for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss for segmentation on four public datasets (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.

[1]  Dimitris Samaras,et al.  Topology-Preserving Deep Image Segmentation , 2019, NeurIPS.

[2]  Rangasami L. Kashyap,et al.  Building Skeleton Models via 3-D Medial Surface/Axis Thinning Algorithms , 1994, CVGIP Graph. Model. Image Process..

[3]  T. Yung Kong,et al.  On Topology Preservation in 2-D and 3-D Thinning , 1995, Int. J. Pattern Recognit. Artif. Intell..

[4]  Ullrich Köthe,et al.  Probabilistic image segmentation with closedness constraints , 2011, 2011 International Conference on Computer Vision.

[5]  Kálmán Palágyi,et al.  A 3-subiteration 3D thinning algorithm for extracting medial surfaces , 2002, Pattern Recognit. Lett..

[6]  Frank Y. Shih,et al.  A skeletonization algorithm by maxima tracking on Euclidean distance transform , 1995, Pattern Recognit..

[7]  Max A. Viergever,et al.  Ridge-based vessel segmentation in color images of the retina , 2004, IEEE Transactions on Medical Imaging.

[8]  Yuan Zhang,et al.  Retinal vessel segmentation of color fundus images using multiscale convolutional neural network with an improved cross-entropy loss function , 2018, Neurocomputing.

[9]  Florent Ségonne,et al.  Active Contours Under Topology Control—Genus Preserving Level Sets , 2008, International Journal of Computer Vision.

[10]  Thomas Brox,et al.  3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation , 2016, MICCAI.

[11]  Mingchen Gao,et al.  Deep vessel tracking: A generalized probabilistic approach via deep learning , 2016, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI).

[12]  Jan Dirk Wegner,et al.  A Higher-Order CRF Model for Road Network Extraction , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[13]  Pascal Fua,et al.  Promoting Connectivity of Network-Like Structures by Enforcing Region Separation , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  A. L. Allegra Mascaro,et al.  Whole-Brain Vasculature Reconstruction at the Single Capillary Level , 2017, Scientific Reports.

[15]  Vladimir Kolmogorov,et al.  Graph cut based image segmentation with connectivity priors , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[16]  Cherng Min Ma,et al.  On topology preservation in 3D thinning , 1994 .

[17]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[18]  Eugene W. Myers,et al.  Efficient Algorithms for Moral Lineage Tracing , 2017, 2017 IEEE International Conference on Computer Vision (ICCV).

[19]  Bjoern H. Menze,et al.  DeepVesselNet: Vessel Segmentation, Centerline Prediction, and Bifurcation Detection in 3-D Angiographic Volumes , 2018, Frontiers in Neuroscience.

[20]  Dimitris Samaras,et al.  Topology cuts: A novel min-cut/max-flow algorithm for topology preserving segmentation in N-D images , 2008, Comput. Vis. Image Underst..

[21]  Jaime S. Cardoso,et al.  A Deep Learning Design for Improving Topology Coherence in Blood Vessel Segmentation , 2019, MICCAI.

[22]  Daniel Cremers,et al.  Generalized Connectivity Constraints for Spatio-temporal 3D Reconstruction , 2014, ECCV.

[23]  Marwan N. Sabbagh,et al.  Morphological and Pathological Evolution of the Brain Microcirculation in Aging and Alzheimer’s Disease , 2012, PloS one.

[24]  M. H. A. Newman,et al.  Combinatorial Topology. Vol. 1 , 1958 .

[25]  Roberto Cipolla,et al.  Skeletonization using an extended Euclidean distance transform , 1995, Image Vis. Comput..

[26]  Pascal Fua,et al.  Joint Segmentation and Path Classification of Curvilinear Structures , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Francis K. H. Quek,et al.  A review of vessel extraction techniques and algorithms , 2004, CSUR.

[28]  Vasilis Ntziachristos,et al.  A distance-based loss for smooth and continuous skin layer segmentation in optoacoustic images , 2020, MICCAI.

[29]  Pascal Fua,et al.  Reconstructing Curvilinear Networks Using Path Classifiers and Integer Programming , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[30]  Gábor Székely,et al.  Tissue metabolism driven arterial tree generation , 2012, Medical Image Anal..

[31]  Ghassan Hamarneh,et al.  Topology Aware Fully Convolutional Networks for Histology Gland Segmentation , 2016, MICCAI.

[32]  Pascal Fua,et al.  Towards Reliable Evaluation of Algorithms for Road Network Reconstruction from Aerial Images , 2020, European Conference on Computer Vision.

[33]  Herbert Edelsbrunner,et al.  Computational Topology - an Introduction , 2009 .

[34]  Daniel Cremers,et al.  Tree Shape Priors with Connectivity Constraints Using Convex Relaxation on General Graphs , 2013, ICCV.

[35]  Bjoern H Menze,et al.  Shape-Aware Complementary-Task Learning for Multi-Organ Segmentation , 2019, MLMI@MICCAI.

[36]  Geoffrey E. Hinton,et al.  Machine Learning for Aerial Image Labeling , 2013 .

[37]  Xin Wang,et al.  Learning tree-structured representation for 3D coronary artery segmentation , 2019, Comput. Medical Imaging Graph..

[38]  Bjoern H Menze,et al.  Machine learning analysis of whole mouse brain vasculature , 2020, Nature Methods.

[39]  Anil A. Bharath,et al.  A Multi-task Network to Detect Junctions in Retinal Vasculature , 2018, MICCAI.

[40]  Adam P. Harrison,et al.  3D Convolutional Neural Networks with Graph Refinement for Airway Segmentation Using Incomplete Data Labels , 2017, MLMI@MICCAI.

[41]  J. Whitehead,et al.  Combinatorial homotopy. II , 1949 .

[42]  Davide Belli,et al.  Image-Conditioned Graph Generation for Road Network Extraction , 2019, ArXiv.

[43]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[44]  Gábor Székely,et al.  Joint 3-D vessel segmentation and centerline extraction using oblique Hough forests with steerable filters , 2015, Medical Image Anal..

[45]  Chandan Singh,et al.  Large Scale Image Segmentation with Structured Loss Based Deep Learning for Connectome Reconstruction , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  Xiao Han,et al.  A Topology Preserving Level Set Method for Geometric Deformable Models , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[47]  Sébastien Ourselin,et al.  Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations , 2017, DLMIA/ML-CDS@MICCAI.

[48]  Sebastian Nowozin,et al.  Global connectivity potentials for random field models , 2009, 2009 IEEE Conference on Computer Vision and Pattern Recognition.

[49]  Allan Hanbury,et al.  Metrics for evaluating 3D medical image segmentation: analysis, selection, and tool , 2015, BMC Medical Imaging.

[50]  Herbert Edelsbrunner,et al.  Topological Persistence and Simplification , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[51]  Bjoern H Menze,et al.  Cellular and Molecular Probing of Intact Human Organs , 2020, Cell.

[52]  A. Schedl,et al.  Cerebrovascular dysfunction and microcirculation rarefaction precede white matter lesions in a mouse genetic model of cerebral ischemic small vessel disease. , 2010, The Journal of clinical investigation.

[53]  Pascal Fua,et al.  Beyond the Pixel-Wise Loss for Topology-Aware Delineation , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[54]  Nils Daniel Forkert,et al.  Vascular Segmentation in TOF MRA Images of the Brain Using a Deep Convolutional Neural Network , 2017, CVII-STENT/LABELS@MICCAI.

[55]  Pascal Fua,et al.  TopoAL: An Adversarial Learning Approach for Topology-Aware Road Segmentation , 2020, ECCV.

[56]  Ilkay Öksüz,et al.  A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology , 2019, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[57]  Bjoern H. Menze,et al.  Automated analysis of whole brain vasculature using machine learning , 2019, bioRxiv.

[58]  Seyed-Ahmad Ahmadi,et al.  V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation , 2016, 2016 Fourth International Conference on 3D Vision (3DV).