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We present a method for segmenting cracks in images of masonry buildings damaged by earthquakes. Existing methods of crack detection fail to preserve the continuity of cracks, and their performance deteriorates with imprecise training labels. We address these problems by adapting an approach previously proposed for reconstructing roads in aerial images, in which a Convolutional Neural Network is trained with a loss function specifically designed to encourage the continuity of thin structures and to accommodate imprecise annotations. We evaluate combinations of three loss functions (the Mean Squared Error, the Dice loss and the new connectivity-oriented loss) on two datasets using TernausNet, a deep network shown to attain state-of-the-art accuracy in crack detection. We herein show that combining these three losses significantly improves the topology of the predictions quantitatively and qualitatively. We also propose a new continuity metric, named Cracks Per Patch (CPP), and share a new dataset of images of earthquake-affected urban scenes accompanied by crack annotations. The dataset and implementations are publicly available for future studies and benchmarking (https://github.com/eesd-epfl/topo%5fcrack%5fdetection and https://doi.org/10.5281/zenodo.6769028). • Evaluation of a loss function for crack detection using deep learning that emphasize the correct representation of crack topology. • A solution for continuity crack detection problems using deep learning that does not require pixel-precise labels. • New metric to assess continuity preservation in crack prediction. • New training dataset of real-world post-earthquake building images containing labeled cracks. [ABSTRACT FROM AUTHOR]

Determining the relationship between the cause of damage and the subsequent structural behavior of infrastructure systems requires an accurate characterization of the propagation of cracks, which represents the evolution of the damage state. When no information about the cause of damage is available, kinematic approaches can be used to describe the motion of crack contours. Current image-based approaches to derive crack kinematics use digital image correlation (DIC) on a set of sequential images as the crack propagates. However, DIC is invasive in that the structure surfaces must be painted with random speckle patterns, limiting its use primarily to controlled experiments. In this paper, we propose a novel image-based methodology for computing crack opening in Mode I or Mode II. As an input, this method takes a binary image from a semantic segmentation of an image of a crack pattern. This binary image is used to detect the opposite edges along the crack, which are then registered using an optimization algorithm based on the Euclidean transformation model and non-linear least squares. As a final output, this method produces displacement maps in the tangential and normal directions to the crack skeleton. To demonstrate its performance, we validate our methodology first with synthetic crack patterns and then with real crack patterns. Because this methodology for determining crack openings requires only simple data (just a binary crack pattern image), it is straightforward, robust, and adaptable, thus contributing to the development of structural image-based damage assessments. The computational codes and datasets are available to the public for future research and benchmarking on https://github.com/eesd-epfl/crack%5fkinematics and https://doi.org/10.5281/zenodo.6632071. • A novel method for determining crack opening in Mode I and Mode II from images. • A crack kinematics formulation as a registration problem of the two crack edges. • A simple algorithm for registering 2D point sets based on non-linear least squares. • A dataset of binary crack patterns with known displacements for benchmarking. [ABSTRACT FROM AUTHOR]