Watershed is a widespread technique for image segmentation. Many researchers apply the method implemented in open source libraries without a deep understanding of its characteristics and limitations. In the review, we describe benchmarking outcomes of six open-source marker-controlled watershed implementations for the segmentation of 2D and 3D images. Even though the considered solutions are based on the same algorithm by flooding having O(n)computational complexity, these implementations have significantly different performance. In addition, building of watershed lines grows processing time. High memory consumption is one more bottleneck for dealing with huge volumetric images. Sometimes, the usage of more optimal software is capable of mitigating the issues with the long processing time and insufficient memory space. We assume parallel processing is capable of overcoming the current limitations. However, the development of concurrent approaches for the watershed segmentation remains a challenging problem.

Image segmentation is a crucial step of almost any Digital Rock workflow. In this paper, we propose an approach for generation of a labelled dataset and investigate an application of three popular convolutional neural networks (CNN) architectures for segmentation of 3D microtomographic images of samples of various rocks. Our dataset contains eight pairs of images of five specimens of sand and sandstones. For each sample, we obtain a single set of microtomographic shadow projections, but run reconstruction twice: one regular high-quality reconstruction, and one using just a quarter of all available shadow projections. Thoughtful manual Indicator Kriging (IK) segmentation of the full-quality image is used as the ground truth for segmentation of images with reduced quality. We assess the generalization capability of CNN by splitting our dataset into training and validation sets by five different manners. In addition, we compare neural networks results with segmentation by IK and thresholding. Segmentation outcomes by 2D and 3D U-nets are comparable to IK, but the deep neural networks operate in automatic mode, and there is big room for improvements in solutions based on CNN. The main difficulties are associated with the segmentation of fine structures that are relatively uncommon in our dataset.

A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly-and doubly-closed-shell nuclei are compared with available experimental data.

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We present image processing algorithms for a new technique of ceramic proppant crush resistance characterization. To obtain the images of the proppant material before and after the test we used X-ray microtomography. We propose a watershed-based unsupervised algorithm for segmentation of proppant particles, as well as a set of parameters for the characterization of 3D particle size, shape, and porosity. An effective approach based on central geometric moments is described. The approach is used for calculation of particles’ form factor, compactness, equivalent ellipsoid axes lengths, and lengths of projections to these axes. Obtained grain size distribution and crush resistance fit the results of conventional test measured by sieves. However, our technique has a remarkable advantage over traditional laboratory method since it allows to trace the destruction at the level of individual particles and their fragments; it grants to analyze morphological features of fines. We also provide an example describing how the approach can be used for verification of statistical hypotheses about the correlation between particles’ parameters and their crushing under load.

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Watershed is a widely used image segmentation algorithm. Most researchers understand just an idea of this method: a grayscale image is considered as topographic relief, which is flooded from initial basins. However, frequently they are not aware of the options of the algorithm and the peculiarities of its realizations. There are many watershed implementations in software packages and products. Even if these packages are based on the identical algorithm–watershed, by flooding their outcomes, processing speed, and consumed memory, vary greatly. In particular, the difference among various implementations is noticeable for huge volumetric images; for instance, tomographic 3D images, for which low performance and high memory requirements of watershed might be bottlenecks. In our review, we discuss the peculiarities of algorithms with and without waterline generation, the impact of connectivity type and relief quantization level on the result, approaches for parallelization, as well as other method options. We present detailed benchmarking of seven open-source and three commercial software implementations of marker-controlled watershed for semantic or instance segmentation. We compare those software packages for one synthetic and two natural volumetric images. The aim of the review is to provide information and advice for practitioners to select the appropriate version of watershed for their problem solving. In addition, we forecast future directions of software development for 3D image segmentation by watershed.