Distance Regularization Research Articles

Distance regularization energy terms in level set image segment model: A survey

The level set is a classical image segmentation model. In order to achieve its stable evolution, the level set function should be a signed distance function (SDF). However, due to the common appearance of irregularities, it must periodically be initialized in order to remain a SDF near the zero level set. Distance regularization terms have been used to maintain the stable evolution of the level set function. We provide a survey of the various distance regularization potential functions. Firstly, we summarize many kinds of distance regularization potential functions studied in the literature. We then divide them into five classes according to the type of potential function. Secondly, we analyze the properties of every class of potential functions and their diffusion rate functions. Finally, to demonstrate the effectiveness of the distance regularization potential functions, we apply them with a region based level set energy functional for image segmentation. Experimental analyses are conducted to compare the segmentation performance of various distance regularization potential functions when combined with the classical Chan Vese model.

Deep learning-based simultaneous registration and unsupervised non-correspondence segmentation of medical images with pathologies

PurposeThe registration of medical images often suffers from missing correspondences due to inter-patient variations, pathologies and their progression leading to implausible deformations that cause misregistrations and might eliminate valuable information. Detecting non-corresponding regions simultaneously with the registration process helps generating better deformations and has been investigated thoroughly with classical iterative frameworks but rarely with deep learning-based methods.MethodsWe present the joint non-correspondence segmentation and image registration network (NCR-Net), a convolutional neural network (CNN) trained on a Mumford–Shah-like functional, transferring the classical approach to the field of deep learning. NCR-Net consists of one encoding and two decoding parts allowing the network to simultaneously generate diffeomorphic deformations and segment non-correspondences. The loss function is composed of a masked image distance measure and regularization of deformation field and segmentation output. Additionally, anatomical labels are used for weak supervision of the registration task. No manual segmentations of non-correspondences are required.ResultsThe proposed network is evaluated on the publicly available LPBA40 dataset with artificially added stroke lesions and a longitudinal optical coherence tomography (OCT) dataset of patients with age-related macular degeneration. The LPBA40 data are used to quantitatively assess the segmentation performance of the network, and it is shown qualitatively that NCR-Net can be used for the unsupervised segmentation of pathologies in OCT images. Furthermore, NCR-Net is compared to a registration-only network and state-of-the-art registration algorithms showing that NCR-Net achieves competitive performance and superior robustness to non-correspondences.ConclusionNCR-Net, a CNN for simultaneous image registration and unsupervised non-correspondence segmentation, is presented. Experimental results show the network’s ability to segment non-correspondence regions in an unsupervised manner and its robust registration performance even in the presence of large pathologies.

A distance regularization scheme for topology optimization with parametric level sets using cut elements

A distance regularization scheme for topology optimization with parametric level sets using cut elements

Adaptive Graph Representation for Clustering

Many graph construction methods cannot consider both local and global data structures in the construction of initial graph. Meanwhile, redundant features or even outliers and data with important characteristics are addressed equally in the graph optimization process. These lead to the learned representation graph may not capture the optimal structure. This paper proposes a novel graph learning method, called ACLWN, to overcome these problems. ACLWN is composed of an adaptive representation graph construction model named ARG, and an adaptive weighted sparse representation graph learning model named AWSG. In ARG, manifold learning and sparse representation are employed to capture the local structure of data. In AWSG, an adaptive weighted matrix is proposed to strengthen the important features and improve the robustness of the low-dimensional representation graph. Moreover, constraints such as non-negative low-rank, sparsity and distance regularization terms are imposed to capture the local and global structures of data. Comprehensive experimental results show that our method outperforms the compared state-of-the-art methods. The low-dimensional representation graph constructed by ACLWN is more suitable for clustering.

The mosaic of AII amacrine cell bodies in rat retina is indistinguishable from a random distribution.

The vertebrate retina contains a large number of different types of neurons that can be distinguished by their morphological properties. Assuming that no location should be without a contribution from the circuitry and function linked to a specific type of neuron, it is expected that the dendritic trees of neurons belonging to a type will cover the retina in a regular manner. Thus, for most types of neurons, the contribution to visual processing is thought to be independent of the exact location of individual neurons across the retina. Here, we have investigated the distribution of AII amacrine cells in rat retina. The AII is a multifunctional amacrine cell found in mammals and involved in synaptic microcircuits that contribute to visual processing under both scotopic and photopic conditions. Previous investigations have suggested that AIIs are regularly distributed, with a nearest-neighbor distance regularity index of ~4. It has been argued, however, that this presumed regularity results from treating somas as points, without taking into account their actual spatial extent which constrains the location of other cells of the same type. When we simulated random distributions of cell bodies with size and density similar to real AIIs, we confirmed that the simulated distributions could not be distinguished from the distributions observed experimentally for AIIs in different regions and eccentricities of the retina. The developmental mechanisms that generate the observed distributions of AIIs remain to be investigated.

On the distance spectrum of minimal cages and associated distance biregular graphs

A (k,g)-cage is a k-regular simple graph of girth g with minimum possible number of vertices. In this paper, (k,g)-cages which are Moore graphs are referred as minimal (k,g)-cages. A simple connected graph is called distance regular (DR) if all its vertices have the same intersection array. A bipartite graph is called distance biregular (DBR) if all the vertices of the same partite set admit the same intersection array. It is known that minimal (k,g)-cages are DR graphs and their subdivisions are DBR graphs. In this paper, for minimal (k,g)-cages we give a formula for distance spectral radius in terms of k and g, and also determine polynomials of degree ⌊g2⌋, which is the diameter of the graph. This polynomial gives all distance eigenvalues when the variable is substituted by adjacency eigenvalues. We show that a minimal (k,g)-cage of diameter d has d+1 distinct distance eigenvalues, and this partially answers a problem posed in [1]. We prove that every DBR graph is a 2-partitioned transmission regular graph and then give a formula for its distance spectral radius. By this formula we obtain the distance spectral radius of subdivision of minimal (k,g)-cages. Finally we determine the full distance spectrum of subdivision of some minimal (k,g)-cages.

Magnetic Resonance Imaging Segmentation via Weighted Level Set Model Based on Local Kernel Metric and Spatial Constraint.

Magnetic resonance imaging (MRI) segmentation is a fundamental and significant task since it can guide subsequent clinic diagnosis and treatment. However, images are often corrupted by defects such as low-contrast, noise, intensity inhomogeneity, and so on. Therefore, a weighted level set model (WLSM) is proposed in this study to segment inhomogeneous intensity MRI destroyed by noise and weak boundaries. First, in order to segment the intertwined regions of brain tissue accurately, a weighted neighborhood information measure scheme based on local multi information and kernel function is designed. Then, the membership function of fuzzy c-means clustering is used as the spatial constraint of level set model to overcome the sensitivity of level set to initialization, and the evolution of level set function can be adaptively changed according to different tissue information. Finally, the distance regularization term in level set function is replaced by a double potential function to ensure the stability of the energy function in the evolution process. Both real and synthetic MRI images can show the effectiveness and performance of WLSM. In addition, compared with several state-of-the-art models, segmentation accuracy and Jaccard similarity coefficient obtained by WLSM are increased by 0.0586, 0.0362 and 0.1087, 0.0703, respectively.

Disparity Computation Through PDE and Data-Driven CeNN Technique

This paper proposes a variational approach by minimizing the energy functional to compute the disparity from a given pair of consecutive images. The partial differential equation (PDE) is modeled from the energy function to address the minimization problem. We incorporate a distance regularization term in the PDE model to preserve the boundaries' discontinuities. The proposed PDE is numerically solved by a cellular neural network (CeNN) algorithm. This CeNN based scheme is stable and consistent. The effectiveness of the proposed algorithm is shown by a detailed experimental study along with its superiority over some of the existing algorithms.

Multi-level Distance Regularization for Deep Metric Learning

We propose a novel distance-based regularization method for deep metric learning called Multi-level Distance Regularization (MDR). MDR explicitly disturbs a learning procedure by regularizing pairwise distances between embedding vectors into multiple levels that represents a degree of similarity between a pair. In the training stage, the model is trained with both MDR and an existing loss function of deep metric learning, simultaneously; the two losses interfere with the objective of each other, and it makes the learning process difficult. Moreover, MDR prevents some examples from being ignored or overly influenced in the learning process. These allow the parameters of the embedding network to be settle on a local optima with better generalization. Without bells and whistles, MDR with simple Triplet loss achieves the-state-of-the-art performance in various benchmark datasets: CUB-200-2011, Cars-196, Stanford Online Products, and In-Shop Clothes Retrieval. We extensively perform ablation studies on its behaviors to show the effectiveness of MDR. By easily adopting our MDR, the previous approaches can be improved in performance and generalization ability.

AW-SDRLSE: Adaptive Weighting and Scalable Distance Regularized Level Set Evolution for Lymphoma Segmentation on PET Images.

Accurate lymphoma segmentation on Positron Emission Tomography (PET) images is of great importance for medical diagnoses, such as for distinguishing benign and malignant. To this end, this paper proposes an adaptive weighting and scalable distance regularized level set evolution (AW-SDRLSE) method for delineating lymphoma boundaries on 2D PET slices. There are three important characteristics with respect to AW-SDRLSE: 1) A scalable distance regularization term is proposed and a parameter q can control the contour's convergence rate and precision in theory. 2) A novel dynamic annular mask is proposed to calculate mean intensities of local interior and exterior regions and further define the region energy term. 3) As the level set method is sensitive to parameters, we thus propose an adaptive weighting strategy for the length and area energy terms using local region intensity and boundary direction information. AW-SDRLSE is evaluated on 90 cases of real PET data with a mean Dice coefficient of 0.8796. Comparative results demonstrate the accuracy and robustness of AW-SDRLSE as well as its performance advantages as compared with related level set methods. In addition, experimental results indicate that AW-SDRLSE can be a fine segmentation method for improving the lymphoma segmentation results obtained by deep learning (DL) methods significantly.

Multiscale Attention Guided Network for COVID-19 Diagnosis Using Chest X-Ray Images.

Coronavirus disease 2019 (COVID-19) is one of the most destructive pandemic after millennium, forcing the world to tackle a health crisis. Automated lung infections classification using chest X-ray (CXR) images could strengthen diagnostic capability when handling COVID-19. However, classifying COVID-19 from pneumonia cases using CXR image is a difficult task because of shared spatial characteristics, high feature variation and contrast diversity between cases. Moreover, massive data collection is impractical for a newly emerged disease, which limited the performance of data thirsty deep learning models. To address these challenges, Multiscale Attention Guided deep network with Soft Distance regularization (MAG-SD) is proposed to automatically classify COVID-19 from pneumonia CXR images. In MAG-SD, MA-Net is used to produce prediction vector and attention from multiscale feature maps. To improve the robustness of trained model and relieve the shortage of training data, attention guided augmentations along with a soft distance regularization are posed, which aims at generating meaningful augmentations and reduce noise. Our multiscale attention model achieves better classification performance on our pneumonia CXR image dataset. Plentiful experiments are proposed for MAG-SD which demonstrates its unique advantage in pneumonia classification over cutting-edge models. The code is available at https://github.com/JasonLeeGHub/MAG-SD.

RPCA-induced self-representation for subspace clustering

The self-expressiveness property of the data, i.e., each sample is linearly represented as a combination of other samples, has recently aroused much attention in the community of data mining and machine learning and shown great promising for subspace clustering. However, real-world data are usually contaminated by noise and outliers. The true similarity between samples directly learned from the original data may deviate from the intrinsic structure of the data, and subsequent clustering results will be severely affected. Hence naively taking a corrupted dictionary, i.e., data itself, will not always obtain the desired clustering performance. To address the above issues, this paper proposes a robust principal component analysis induced self-representation clustering method via adaptively learning the similarity graph from the clean data in the self-representation framework, where the original data are recovered, and the representation coefficients are obtained simultaneously in a unified framework. Specifically, we jointly integrate a nonnegative constraint and a distance regularization into the proposed framework, which guarantees the learned affinity matrix can simultaneously capture the global and local structure of data. Experimental results on both synthetic data and several famous multimedia datasets demonstrate that the proposed method performs much better against state-of-the-arts.

Automorphisms of a Distance Regular Graph with Intersection Array $\{21,18,12,4;1,1,6,21\}$

А. А. Махнев и М. С. Нирова нашли массивы пересечений дистанционно регулярных графов с $\lambda=2$ и числом вершин, не большим 4096. Для графов диаметра $4$ наиболее интересен массив $\{21,18,12,4;1,1,6,21\}$ из этого списка. В данной работе найдены возможные порядки и подграфы неподвижных точек автоморфизмов дистанционно регулярного графа с массивом пересечений $\{21,18,12,4;1,1,6,21\}$. Библиография: 5 названий.

A Computational Model of Thrombus Growth Based on Level Set Method

The computational model of thrombosis is of great importance that decides the simulation performance. In the present study, a hybrid particle-continuum model with plasma, vascular wall, and thrombus being continuum material and platelets being discrete particles, was developed to simulate the thrombus growth. In the computational model, the thrombus growth was reformulated as a novel continuum surface expansion problem implemented by a level set function due to its capability of effectively handling the topological changes comprising splitting and merging, rather than a traditional particle accumulation problem. Additionally, a Gaussian-based function and distance regularization function, served as speed functions to drive the thrombus growth, were proposed and compared in our study. Experiments demonstrated that the growing thrombus could retain the particle texture of platelets by both level set speed functions, while the distance regularization function performed better in improving computational complexity and surface tracking behaviors. Both simulations demonstrated better visuality in the progress of thrombosis, and the geometry shape of the virtual primary thrombi were similar to the realistic counterpart.

Automorphisms of a Distance Regular Graph with Intersection Array $$\{21,18,12,4;1,1,6,21\}$$

Automorphisms of a Distance Regular Graph with Intersection Array $$\{21,18,12,4;1,1,6,21\}$$

Individual tooth detection and identification from dental panoramic X-ray images via point-wise localization and distance regularization

Dental panoramic X-ray imaging is a popular diagnostic method owing to its very small dose of radiation. For an automated computer-aided diagnosis system in dental clinics, automatic detection and identification of individual teeth from panoramic X-ray images are critical prerequisites. In this study, we propose a point-wise tooth localization neural network by introducing a spatial distance regularization loss. The proposed network initially performs center point regression for all the anatomical teeth (i.e., 32 points), which automatically identifies each tooth. A novel distance regularization penalty is employed on the 32 points by considering L2 regularization loss of Laplacian on spatial distances. Subsequently, teeth boxes are individually localized using a multitask neural network on a patch basis. A multitask offset training is employed on the final output to improve the localization accuracy. Our method successfully localizes not only the existing teeth but also missing teeth; consequently, highly accurate detection and identification are achieved. The experimental results demonstrate that the proposed algorithm outperforms state-of-the-art approaches by increasing the average precision of teeth detection by 15.71 % compared to the best performing method. The accuracy of identification achieved a precision of 0.997 and recall value of 0.972. Moreover, the proposed network does not require any additional identification algorithm owing to the preceding regression of the fixed 32 points regardless of the existence of the teeth.

Nonassociativity of the Norton Algebras of Some Distance Regular Graphs

A Norton algebra is an eigenspace of a distance regular graph endowed with a commutative nonassociative product called the Norton product, which is defined as the projection of the entrywise product onto this eigenspace. The Norton algebras are useful in finite group theory as they have interesting automorphism groups. We provide a precise quantitative measurement for the nonassociativity of the Norton product on the eigenspace of the second largest eigenvalue of the Johnson graphs, Grassman graphs, Hamming graphs, and dual polar graphs, based on the formulas for this product established in previous work of Levstein, Maldonado and Penazzi. Our result shows that this product is as nonassociative as possible except for two cases, one being the trivial vanishing case while the other having connections with the integer sequence A000975 on OEIS and the so-called double minus operation studied recently by Huang, Mickey, and Xu.

Reconstruction of Three-Dimensional Object from Two-Dimensional Images by Utilizing Distance Regularized Level Algorithm and Mesh Object Generation

Three-dimensional (3D) reconstruction from images is a most beneficial method of object regeneration by using a photo-realistic way that can be used in many fields. For industrial fields, it can be used to visualize the cracks within alloys or walls. In medical fields, it has been used as 3D scanner to reconstruct some human organs such as internal nose for plastic surgery or to reconstruct ear canal for fabricating a hearing aid device, and others. These applications need high accuracy details and measurement that represent the main issue which should be taken in consideration, also the other issues are cost, movability, and ease of use which should be taken into consideration. This work has presented an approach for design and constructed a low-cost three-dimensional object scanner. We have proposed a 3D canal reconstruction system (ear or nose) based on using 2D images for reconstruction 3D object. A low-cost EndoScope with a proposed program based upon utilized the segmentation algorithm type “Distance Regularized Level” to segment active edges from images then generate mesh object in order to generate 3D structure for small canals or cracks. The results show good accuracy of the reconstructed object in both details and their measurements which are related to the success in the reconstruction of algorithm that yields good three-dimensional meshes object.

Face clustering via learning a sparsity preserving low-rank graph

Face clustering aims to group the face images without any label information into clusters, and has recently attracted considerable attention in machine learning and data mining. Many graph based clustering methods have been proposed and among which sparse representation (SR) and low-rank representation (LRR) are two representative methods for affinity graph construction. The clustering result may be inaccurate if the affinity graph is constructed with low quality. In this paper, we propose a novel face clustering method via learning a sparsity preserving low-rank graph (LSPLRG), where the initial affinity graph is derived on the sparse coefficients without any a priori graph or similarity matrix. In addition, an adaptive weighted matrix is imposed on the data reconstruction errors to enhance the role of important features, while a constraint on the representation matrix is to reduce the redundant features. By integrating the local distance regularization term into LRR, LSPLRG could exploit the global and local structures of data simultaneously. These appealing properties allow LSPLRG to well capture the intrinsic structure of data, and thus has potential to improve clustering performance. Experiments conducted on several face image databases demonstrate the effectiveness and robustness of LSPLRG compared with several state-of-the-art subspace clustering methods.

Active contours driven by order-statistic filtering and coherence-enhancing diffusion filter for fast image segmentation

A robust active contour model driven by an order-statistic filtering and coherence-enhancing diffusion (OSFCED) filter for fast image segmentation is proposed. The main idea of the order-statistic filtering is to construct the edge force function (EFF) to quickly and adaptively attract evolving curves to target boundaries while a coherence-enhancing diffusion (CED) filter aims at filtering noise and enhancing target boundaries so that the segmentation efficiency can be improved. In addition, the computation of the EFF and CED function is completed before iterations. Therefore, the computational cost of the proposed model is low during curve evolution. Furthermore, the addition of optimized distance regularization term and optimized length term makes curve evolution smoother and more stable. Experiments performed show that the proposed model is robust to initial contour, parameter and has higher segmentation efficiency for images with intensity inhomogeneity.