Codes with symmetric distances

Ultrasound (US) imaging has been widely used in breast tumor diagnosis and treatment intervention. Automatic delineation of the tumor is a crucial first step, especially for the computer-aided diagnosis (CAD) and US-guided breast procedure. However, the intrinsic properties of US images such as low contrast and blurry boundaries pose challenges to the automatic segmentation of the breast tumor. Therefore, the purpose of this study is to propose a segmentation algorithm that can contour the breast tumor in US images. To utilize the neighbor information of each pixel, a Hausdorff distance based fuzzy c-means (FCM) method was adopted. The size of the neighbor region was adaptively updated by comparing the mutual information between them. The objective function of the clustering process was updated by a combination of Euclid distance and the adaptively calculated Hausdorff distance. Segmentation results were evaluated by comparing with three experts' manual segmentations. The results were also compared with a kernel-induced distance based FCM with spatial constraints, the method without adaptive region selection, and conventional FCM. Results from segmenting 30 patient images showed the adaptive method had a value of sensitivity, specificity, Jaccard similarity, and Dice coefficient of 93.60 ± 5.33%, 97.83 ± 2.17%, 86.38 ± 5.80%, and 92.58 ± 3.68%, respectively. The region-based metrics of average symmetric surface distance (ASSD), root mean square symmetric distance (RMSD), and maximum symmetric surface distance (MSSD) were 0.03 ± 0.04 mm, 0.04 ± 0.03 mm, and 1.18 ± 1.01 mm, respectively. All the metrics except sensitivity were better than that of the non-adaptive algorithm and the conventional FCM. Only three region-based metrics were better than that of the kernel-induced distance based FCM with spatial constraints. Inclusion of the pixel neighbor information adaptively in segmenting US images improved the segmentation performance. The results demonstrate the potential application of the method in breast tumor CAD and other US-guided procedures.

To generate fully automated and fast 4D-flow MRI-based 3D segmentations of the aorta using deep learning for reproducible quantification of aortic flow, peak velocity, and dimensions. A total of 1018 subjects with aortic 4D-flow MRI (528 with bicuspid aortic valve, 376 with tricuspid aortic valve and aortic dilation, 114 healthy controls) comprised the data set. A convolutional neural network was trained to generate 3D aortic segmentations from 4D-flow data. Manual segmentations served as the ground truth (N = 499 training, N = 101 validation, N = 418 testing). Dice scores, Hausdorff distance, and average symmetrical surface distance were calculated to assess performance. Aortic flow, peak velocity, and lumen dimensions were quantified at the ascending, arch, and descending aorta and compared using Bland-Altman analysis. Interobserver variability of manual analysis was assessed on a subset of 40. Convolutional neural network segmentation required 0.438 ± 0.355 seconds versus 630 ± 254 seconds for manual analysis and demonstrated excellent performance with a median Dice score of 0.951 (0.930-0.966), Hausdorff distance of 2.80 (2.13-4.35), and average symmetrical surface distance of 0.176 (0.119-0.290). Excellent agreement was found for flow, peak velocity, and dimensions with low bias and limits of agreement less than 10% difference versus manual analysis. For aortic volume, limits of agreement were moderate within 16.3%. Interobserver variability (median Dice score: 0.950; Hausdorff distance: 2.45; and average symmetrical surface distance: 0.145) and convolutional neural network-based analysis (median Dice score: 0.953-0.959; Hausdorff distance: 2.24-2.91; and average symmetrical surface distance: 0.145-1.98 to observers) demonstrated similar reproducibility. Deep learning enabled fast and automated 3D aortic segmentation from 4D-flow MRI, demonstrating its potential for efficient clinical workflows. Future studies should investigate its utility for other vasculature and multivendor applications.

Purpose:To validate and compare the deformable image registration and parotid contour propagation process for head and neck magnetic resonance imaging in patients treated with radiotherapy using 3 different approaches—the commercial MIM, the open-source Elastix software, and an optimized version of it.Materials and Methods:Twelve patients with head and neck cancer previously treated with radiotherapy were considered. Deformable image registration and parotid contour propagation were evaluated by considering the magnetic resonance images acquired before and after the end of the treatment. Deformable image registration, based on free-form deformation method, and contour propagation available on MIM were compared to Elastix. Two different contour propagation approaches were implemented for Elastix software, a conventional one (DIR_Trx) and an optimized homemade version, based on mesh deformation (DIR_Mesh). The accuracy of these 3 approaches was estimated by comparing propagated to manual contours in terms of average symmetric distance, maximum symmetric distance, Dice similarity coefficient, sensitivity, and inclusiveness.Results:A good agreement was generally found between the manual contours and the propagated ones, without differences among the 3 methods; in few critical cases with complex deformations, DIR_Mesh proved to be more accurate, having the lowest values of average symmetric distance and maximum symmetric distance and the highest value of Dice similarity coefficient, although nonsignificant. The average propagation errors with respect to the reference contours are lower than the voxel diagonal (2 mm), and Dice similarity coefficient is around 0.8 for all 3 methods.Conclusion:The 3 free-form deformation approaches were not significantly different in terms of deformable image registration accuracy and can be safely adopted for the registration and parotid contour propagation during radiotherapy on magnetic resonance imaging. More optimized approaches (as DIR_Mesh) could be preferable for critical deformations.

This paper reports a novel approach to 3D kidney segmentation from a single prior shape in magnetic resonance imaging (MRI) datasets. The proposed method is based on a hierarchic surface deformation algorithm, to generate a pre-personalized model, followed by an anamorphing segmentation algorithm, to extract the kidney capsule. Accuracy and precision are assessed by comparing our method over 20 kidney reconstructions segmented manually by 3 different observers on native MRI images. The experimental results show a volumetric overlap error of 6.39±2.47%, a relative volume difference of 1.87±1.39%, an average symmetric surface distance of 0.80±0.23mm, a root mean squared symmetric distance of 1.03±0.33mm and a maximum symmetric surface distance of 4.18±3.45mm. With our method, the capsules of both kidneys are segment in less than 40 seconds.

Background: Over the past few years, researchers have devoted efforts to enhance the robustness and randomness of the original DES cipher. These enhancements focused on improving multiple perspectives of the algorithm to deliver robust DES variants against typical attacks. Method: Recent publications and patent databases have been reviewed to investigate the potential enhancements in DES cipher algorithm. The enhancements have targeted the main components of DES including the F-function, S-boxes arrangements, and the key length. Result: This paper introduces a DES variant named Hashed Data Encryption Standard (HDES). The main idea behind HDES cryptographic algorithm is to provide a trade-off between fast encryption while ensuring a degree of randomness in the encrypted data. HDES employs several techniques including the use of a hash function and secure arrangements of S-boxes. The idea of using the hash is to create a fingerprint of the plaintext. This fingerprint is used to generate a seed and the subsequent round seeds. Conclusion: The randomness analysis of HDES and its counterparts DES and DESX have shown performance merits of HDES in terms of entropy difference, cipher data randomness, symmetric distance and encryption time. Keywords: Encryption algorithm, randomness test, symmetric distance, data cipher difference, encryption time, DES, HDES, DESX.

A method was previously developed to identify participant-specific parameters in a model of trabecular bone adaptation from longitudinal computed tomography (CT) imaging. In this study, we use these numerical methods to estimate changes in astronaut bone health during the distinct phases of spaceflight and recovery on Earth. Astronauts (N = 16) received high-resolution peripheral quantitative CT (HR-pQCT) scans of their distal tibia prior to launch (L), upon their return from an approximately six-month stay on the international space station (R+0), and after six (R+6) and 12 (R+12) months of recovery. To model trabecular bone adaptation, we determined participant-specific parameters at each time interval and estimated their bone structure at R+0, R+6, and R+12. To assess the fit of our model to this population, we compared static and dynamic bone morphometry as well as the Dice coefficient and symmetric distance at each measurement. In general, modeled and observed static morphometry were highly correlated (R2> 0.94) and statistically different (p < 0.0001) but with errors close to HR-pQCT precision limits. Dynamic morphometry, which captures rates of bone adaptation, was poorly estimated by our model (p < 0.0001). The Dice coefficient and symmetric distance indicated a reasonable local fit between observed and predicted bone volumes. This work applies a general and versatile computational framework to test bone adaptation models. Future work can explore and test increasingly sophisticated models (e.g., those including load or physiological factors) on a participant-specific basis.

Effective and accurate segmentation of the aortic valve (AV) from sequenced ultrasound (US) images remains a technical challenge because of intrinsic factors of ultrasound images that impact the quality and the continuous changes of shape and position of segmented objects. In this paper, a novel shape-constraint gradient Chan-Vese (GCV) model is proposed for segmenting the AV from time serial echocardiography. The GCV model is derived by incorporating the energy of the gradient vector flow into a CV model framework, where the gradient vector energy term is introduced by calculating the deviation angle between the inward normal force of the evolution contour and the gradient vector force. The flow force enlarges the capture range and enhances the blurred boundaries of objects. This is achieved by adding a circle-like contour (constructed using the AV structure region as a constraint shape) as an energy item to the GCV model through the shape comparison function. This shape-constrained energy can enhance the image constraint force by effectively connecting separate gaps of the object edge as well as driving the evolution contour to quickly approach the ideal object. Because of the slight movement of the AV in adjacent frames, the initial constraint shape is defined by users, with the other constraint shapes being derived from the segmentation results of adjacent sequence frames after morphological filtering. The AV is segmented from the US images by minimizing the proposed energy function. To evaluate the performance of the proposed method, five assessment parameters were used to compare it with manual delineations performed by radiologists (gold standards). Three hundred and fifteen images acquired from nine groups were analyzed in the experiment. The area-metric overlap error rate was 6.89% ± 2.88%, the relative area difference rate 3.94% ± 2.63%, the average symmetric contour distance 1.08 ± 0.43 mm, the root mean square symmetric contour distance 1.37 ± 0.52 mm, and the maximum symmetric contour distance was 3.57 ± 1.72 mm. Compared with the CV model, as a result of the combination of the gradient vector and neighborhood shape information, this semiautomatic segmentation method significantly improves the accuracy and robustness of AV segmentation, making it feasible for improved segmentation of aortic valves from US images that have fuzzy boundaries.

A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a dynamic security partition assessment method, aiming to develop accurate and incrementally updated DSA models with simple structures. Firstly, the power grid is self-adaptively partitioned into several local regions based on the mean shift algorithm. The input of the mean shift algorithm is a symmetric electrical distance matrix, and the distance metric is the Chebyshev distance. Secondly, high-level features of operating conditions are extracted based on the stacked denoising autoencoder. The symmetric electrical distance matrix is modified to represent fault locations in local regions. Finally, DSA models are constructed for fault locations in each region based on the radial basis function neural network (RBFNN) and Chebyshev distance. An online incremental updating strategy is designed to enhance the model adaptability. With the simulation software PSS/E 33.4.0, the proposed dynamic security partition assessment method is verified in a simplified provincial system and a large-scale practical system in China. Test results demonstrate that the Chebyshev distance can improve the partition quality of the mean shift algorithm by approximately 50%. The RBFNN-based partition assessment model achieves an accuracy of 98.96%, which is higher than the unified assessment with complex models. The proposed incremental updating strategy achieves an accuracy of over 98% and shortens the updating time to 30 s, which can meet the efficiency of online application.

ObjectivesDevelopment and verification of a convolutional neural network (CNN)-based deep learning (DL) model for mandibular canal (MC) localization on multicenter cone beam computed tomography (CBCT) images.MethodsIn this study, a total 1056 CBCT scans in multiple centers were collected. Of these, 836 CBCT scans of one manufacturer were used for development of CNN model (training set: validation set: internal testing set = 640:360:36) and an external testing dataset of 220 CBCT scans from other four manufacturers were tested. The convolution module was built using a stack of Conv + InstanceNorm + LeakyReLU. Average symmetric surface distance (ASSD) and symmetric mean curve distance (SMCD) were used for quantitative evaluation of this model for both internal testing data and partial external testing data. Visual scoring (1–5 points) were performed to evaluate the accuracy and generalizability of MC localization for all external testing data. The differences of ASSD, SMCD and visual scores among the four manufacturers were compared for external testing dataset. The time of manual and automatic MC localization were recorded.ResultsFor the internal testing dataset, the average ASSD and SMCD was 0.486 mm and 0.298 mm respectively. For the external testing dataset, 86.8% CBCT scans’ visual scores ≥ 4 points; the average ASSD and SMCD of 40 CBCT scans with visual scores ≥ 4 points were 0.438 mm and 0.185 mm respectively; there were significant differences among the four manufacturers for ASSD, SMCD and visual scores (p < 0.05). And the time for bilateral automatic MC localization was 8.52s (± 0.97s).ConclusionsIn this study, a CNN model was developed for automatic MC localization, and external testing of large sample on multicenter CBCT images showed its excellent clinical application potential.

A randomized parallel algorithm for Voronoi diagrams based on symmetric convex distance functions

In this paper, we propose and validate an automatic pipeline for subcortical surface generation by making use of the average symmetrical surface distance (ASSD) loss in active shape modeling (ASM). A group of template surfaces are first generated via large deformation diffeomorphic metric mapping based surface deformation. ASM is then employed to obtain the mean shape and shape variation parameters of the template surfaces. To obtain the optimal shape variation parameters which best fit the target structure after acting upon the mean shape, a recently proposed derivative-free optimization method (the slow-fast learning method) is adopted. The ASSD loss, in addition to the typically utilized Dice similarity coefficient loss, is employed during the learning process to help enhance the boundary accuracy. We successfully validate the importance of the ASSD loss through ablation analysis. In addition, we show the effectiveness of the slow-fast learning method by comparing it with other state-of-the-art derivative-free optimization algorithms. Our proposed pipeline is found to be capable of yielding subcortical surfaces with high accuracy, correct anatomical topology, and sufficient smoothness. Clinical Relevance- This work provides a useful tool for generating subcortical surfaces which are important biomarkers for a variety of brain disorders.

We propose a new and easy approach to evaluate structural dissimilarities between frames issued from molecular dynamics, and we test this methodology on human hemagglutinin. This protein is responsible for the entry of the influenza virus into the host cell by endocytosis, and this virus causes seasonal epidemics of infectious disease, which can be estimated to result in hundreds of thousands of deaths each year around the world. We computed the three interfaces between the three protomers of the hemagglutinin H1 homotrimer (PDB code: 1RU7) for each of its conformations generated from molecular dynamics simulation. For each conformation, we considered the set of residues involved in the union of these three interfaces. The dissimilarity between each pair of conformations was measured with our new methodology, the symmetric difference distance between the associated set of residues. The main advantages of the full procedure are: (i) it is parameter free; (ii) no spatial alignment is needed and (iii) it is simple enough so that it can be implemented by a beginner in programming. It is shown to be a relevant tool to follow the evolution of the conformation along the molecular dynamics trajectories.

A genetic map is an ordering of genetic markers calculated from a population of known lineage. While traditionally a map has been generated from a single population for each species, recently researchers have created maps from multiple populations. In the face of these new data, we address the need to find a consensus map--a map that combines the information from multiple partial and possibly inconsistent input maps. We model each input map as a partial order and formulate the consensus problem as finding a median partial order. Finding the median of multiple total orders (preferences or rankings)is a well studied problem in social choice. We choose to find the median using the weighted symmetric difference distance, a more general version of both the symmetric difference distance and the Kemeny distance. Finding a median order using this distance is NP-hard. We show that for our chosen weight assignment, a median order satisfies the positive responsiveness, extended Condorcet,and unanimity criteria. Our solution involves finding the maximum acyclic subgraph of a weighted directed graph. We present a method that dynamically switches between an exact branch and bound algorithm and a heuristic algorithm, and show that for real data from closely related organisms, an exact median can often be found. We present experimental results using seven populations of the crop plant Zea mays.

We extend the classical system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces. Trace inclusion and equivalence give rise to asymmetrical and symmetrical linear distances, while simulation and bisimulation give rise to asymmetrical and symmetrical branching distances. We study the relationships among these distances and we provide a full logical characterization of the distances in terms of quantitative versions of LTL and mu-calculus. We show that, while trace inclusion (respectively, equivalence) coincides with simulation (respectively, bisimulation) for deterministic boolean transition systems, linear and branching distances do not coincide for deterministic metric transition systems. Finally, we provide algorithms for computing the distances over finite systems, together with a matching lower complexity bound.

Preoperative radiological identification of mandibular canals is essential for maxillofacial surgery. This study demonstrates the reproducibility of a deep learning system (DLS) by evaluating its localisation performance on 165 heterogeneous cone beam computed tomography (CBCT) scans from 72 patients in comparison to an experienced radiologist's annotations. We evaluated the performance of the DLS using the symmetric mean curve distance (SMCD), the average symmetric surface distance (ASSD), and the Dice similarity coefficient (DSC). The reproducibility of the SMCD was assessed using the within-subject coefficient of repeatability (RC). Three other experts rated the diagnostic validity twice using a 0-4 Likert scale. The reproducibility of the Likert scoring was assessed using the repeatability measure (RM). The RC of SMCD was 0.969 mm, the median (interquartile range) SMCD and ASSD were 0.643 (0.186) mm and 0.351 (0.135) mm, respectively, and the mean (standard deviation) DSC was 0.548 (0.138). The DLS performance was most affected by postoperative changes. The RM of the Likert scoring was 0.923 for the radiologist and 0.877 for the DLS. The mean (standard deviation) Likert score was 3.94 (0.27) for the radiologist and 3.84 (0.65) for the DLS. The DLS demonstrated proficient qualitative and quantitative reproducibility, temporal generalisability, and clinical validity.