Topology Preservation Research Articles

Towards estimating cardiac motion using low-rank representation and topology preservation for ultrafast ultrasound data.

Estimation of the cardiac motion is very important in order to detect heart diseases. This work presents a cardiac motion estimation approach using ultrafast ultrasound data. We optimize a variational framework which has the benefits of combining low-rank data representation with topology preservation. We show through the analysis of experimental results that this combination offers a radical reduction in computational time and noise while ensuring preservation of the anatomical structure of the heart under complex deformations. Although in this work we use the heart as a study case, our solution is promising to analyze other organs experiencing motion.

Adaptive registration of diffusion tensor images on lie groups

With diffusion tensor imaging (DTI), more exquisite information on tissue microstructure is provided for medical image processing. In this paper, we present a locally adaptive topology preserving method for DTI registration on Lie groups. The method aims to obtain more plausible diffeomorphisms for spatial transformations via accurate approximation for the local tangent space on the Lie group manifold. In order to capture an exact geometric structure of the Lie group, the local linear approximation is efficiently optimized by using the adaptive selection of the local neighborhood sizes on the given set of data points. Furthermore, numerical comparative experiments are conducted on both synthetic data and real DTI data to demonstrate that the proposed method yields a higher degree of topology preservation on a dense deformation tensor field while improving the registration accuracy.

Use of Self Organizing Map to Obtain ECG Data Templates for Its Compression and Reconstruction

An electrocardiogram (ECG) is a recording of electrical impulses generated by the electrical activity of the heart and is used as a diagnostic tool to analyze various heart diseases. For economical storage and fast transmission over low-bandwidth channels, ECG data need to be compressed. For the efficient compression of ECG signals, the topology preservation feature of self-organizing maps (SOM) is used. It is observed that a compression ratio up to 1:20 can be achieved with a very low-percentage root-mean-square difference, i.e. below 1.6, by creating templates of ECG patterns in the form of weight vectors of neurons. The templates obtained in this manner are then used to reconstruct the ECG signal. This analysis shows that the reconstructed signal is perfectly matched to the original signal.

Discriminative Analysis Dictionary Learning

Dictionary learning (DL) has been successfully applied to various pattern classification tasks in recent years. However, analysis dictionary learning (ADL), as a major branch of DL, has not yet been fully exploited in classification due to its poor discriminability. This paper presents a novel DL method, namely Discriminative Analysis Dictionary Learning (DADL), to improve the classification performance of ADL. First, a code consistent term is integrated into the basic analysis model to improve discriminability. Second, a triplet constraint-based local topology preserving loss function is introduced to capture the discriminative geometrical structures embedded in data. Third, correntropy induced metric is employed as a robust measure to better control outliers for classification. Then, half-quadratic minimization and alternate search strategy are used to speed up the optimization process so that there exist closed-form solutions in each alternating minimization stage. Experiments on several commonly used databases show that our proposed method not only significantly improves the discriminative ability of ADL, but also outperforms state-of-the-art synthesis DL methods.

A non-rigid point matching method with local topology preservation for accurate bladder dose summation in high dose rate cervical brachytherapy

GEC-ESTRO guidelines for high dose rate cervical brachytherapy advocate the reporting of the D2cc (the minimum dose received by the maximally exposed 2cc volume) to organs at risk. Due to large interfractional organ motion, reporting of accurate cumulative D2cc over a multifractional course is a non-trivial task requiring deformable image registration and deformable dose summation. To efficiently and accurately describe the point-to-point correspondence of the bladder wall over all treatment fractions while preserving local topologies, we propose a novel graphic processing unit (GPU)-based non-rigid point matching algorithm. This is achieved by introducing local anatomic information into the iterative update of correspondence matrix computation in the ‘thin plate splines-robust point matching’ (TPS-RPM) scheme. The performance of the GPU-based TPS-RPM with local topology preservation algorithm (TPS-RPM-LTP) was evaluated using four numerically simulated synthetic bladders having known deformations, a custom-made porcine bladder phantom embedded with twenty one fiducial markers, and 29 fractional computed tomography (CT) images from seven cervical cancer patients. Results show that TPS-RPM-LTP achieved excellent geometric accuracy with landmark residual distance error (RDE) of 0.7 ± 0.3 mm for the numerical synthetic data with different scales of bladder deformation and structure complexity, and 3.7 ± 1.8 mm and 1.6 ± 0.8 mm for the porcine bladder phantom with large and small deformation, respectively. The RDE accuracy of the urethral orifice landmarks in patient bladders was 3.7 ± 2.1 mm. When compared to the original TPS-RPM, the TPS-RPM-LTP improved landmark matching by reducing landmark RDE by 50 ± 19%, 37 ± 11% and 28 ± 11% for the synthetic, porcine phantom and the patient bladders, respectively. This was achieved with a computational time of less than 15 s in all cases with GPU acceleration. The efficiency and accuracy shown with the TPS-RPM-LTP indicate that it is a practical and promising tool for bladder dose summation in adaptive cervical cancer brachytherapy.

Experimental Approach for Performance Analysis of Thinning Algorithms for Offline Handwritten Devnagri Numerals

Objectives: Performance and efficiency of thinning algorithms is essential in the field of image analysis and recognition. The present paper aims at experimental approach for performance analysis of different thinning algorithms for offline handwritten devnagri numeral script on multiparameter scale. Methods/Statistical Analysis: Algorithms based on datasets are reviewed and three algorithms based on their characteristics and strengths are implemented and their performance is evaluated based on pixel count in output image, compression ratio, pixel removal parameter, connectivity, triangle counts, unit pixel width, and information loss and topology preservation measure. Findings: Experimental findings indicate the strength and weakness of each thinning algorithm. Application/Improvements: The novelty of work is use of large parameter set for experimental performance evaluation. The findings and subsequent discussion aim at providing parametric strength of different thinning algorithms.

Kernel learning over the manifold of symmetric positive definite matrices for dimensionality reduction in a BCI application

In this paper, we propose a kernel for nonlinear dimensionality reduction over the manifold of Symmetric Positive Definite (SPD) matrices in a Motor Imagery (MI)-based Brain Computer Interface (BCI) application. The proposed kernel, which is based on Riemannian geometry, tries to preserve the topology of data points in the feature space. Topology preservation is the main challenge in nonlinear dimensionality reduction (NLDR). Our main idea is to decrease the non-Euclidean characteristics of the manifold by modifying the volume elements. We apply a conformal transform over data-dependent isometric mapping to reduce the negative eigen fraction to learn a data dependent kernel over the Riemannian manifolds. Multiple experiments were carried out using the proposed kernel for a dimensionality reduction of SPD matrices that describe the EEG signals of dataset IIa from BCI competition IV. The experiments show that this kernel adapts to the input data and leads to promising results in comparison with the most popular manifold learning methods and the Common Spatial Pattern (CSP) technique as a reference algorithm in BCI competitions. The proposed kernel is strong, particularly in the cases where data points have a complex and nonlinear separable distribution.

A three-dimensional coupled Nitsche and level set method for electrohydrodynamic potential flows in moving domains

In this paper we present a new algorithm for computing three-dimensional electrohydrodynamic flow in moving domains which can undergo topological changes. We consider a non-viscous, irrotational, perfect conducting fluid and introduce a way to model the electrically charged flow with an embedded potential approach. To numerically solve the resulting system, we combine a level set method to track both the free boundary and the surface velocity potential with a Nitsche finite element method for solving the Laplace equations. This results in an algorithmic framework that does not require body-conforming meshes, works in three dimensions, and seamlessly tracks topological change. Assembling this coupled system requires care: while convergence and stability properties of Nitsche's methods have been well studied for static problems, they have rarely been considered for moving domains or for obtaining the gradients of the solution on the embedded boundary. We therefore investigate the performance of the symmetric and non-symmetric Nitsche formulations, as well as two different stabilization techniques. The global algorithm and in particular the coupling between the Nitsche solver and the level set method are also analyzed in detail. Finally we present numerical results for several time-dependent problems, each one designed to achieve a specific objective: (a) The oscillation of a perturbed sphere, which is used for convergence studies and the examination of the Nitsche methods; (b) The break-up of a two lobe droplet with axial symmetry, which tests the capability of the algorithm to go past flow singularities such as topological changes and preservation of an axi-symmetric flow, and compares results to previous axi-symmetric calculations; (c) The electrohydrodynamical deformation of a thin film and subsequent jet ejection, which will account for the presence of electrical forces in a non-axi-symmetric geometry.

Unsupervised Feature Selection with Controlled Redundancy (UFeSCoR)

Features selected by a supervised/ unsupervised technique often include redundant or correlated features. While use of correlated features may result in an increase in the design and decision making cost, removing redundancy completely can make the system vulnerable to measurement errors. Most feature selection schemes do not account for redundancy at all, while a few supervised methods try to discard correlated features. We propose a novel unsupervised feature selection scheme ( UFeSCoR ), which not only discards irrelevant features, but also selects features with controlled redundancy. Here, the number of selected features can also be directed. Our algorithm optimizes an objective function, which tries to select a specified number of features, with a controlled level of redundancy, such that the topology of the original data set can be maintained in the reduced dimension. Here, we have used Sammon’s error as a measure of preservation of topology. We demonstrate the effectiveness of the algorithm in terms of choosing relevant features, controlling redundancy, and selecting a given number of features using several data sets. We make a comparative study with five unsupervised feature selection methods. Our results reveal that the proposed method can select useful features with controlled redundancy.

On topology preservation of mixed operators in triangular, square, and hexagonal grids

A crucial issue in digital topology is to ensure topology preservation of binary image operators. Several sufficient conditions have already been proposed (i.e., for operators that never change a white pixel to black one and a black pixel to a white one, respectively), however not much attention has been paid on mixed operators, which can modify both black and white pixels. In this paper, we intend to fill in this gap by presenting some sufficient criteria on the latter family of operators considering all the possible regular partitionings of the plane (i.e., triangular, square, and hexagonal grids).

Topology preserving non-rigid image registration using time-varying elasticity model for MRI brain volumes

In this paper, we present a new non-rigid image registration method that imposes a topology preservation constraint on the deformation. We propose to incorporate the time varying elasticity model into the deformable image matching procedure and constrain the Jacobian determinant of the transformation over the entire image domain. The motion of elastic bodies is governed by a hyperbolic partial differential equation, generally termed as elastodynamics wave equation, which we propose to use as a deformation model. We carried out clinical image registration experiments on 3D magnetic resonance brain scans from IBSR database. The results of the proposed registration approach in terms of Kappa index and relative overlap computed over the subcortical structures were compared against the existing topology preserving non-rigid image registration methods and non topology preserving variant of our proposed registration scheme. The Jacobian determinant maps obtained with our proposed registration method were qualitatively and quantitatively analyzed. The results demonstrated that the proposed scheme provides good registration accuracy with smooth transformations, thereby guaranteeing the preservation of topology.

Collaborative-Learning-Automata-Based Channel Assignment With Topology Preservation for Wireless Mesh Networks Under QoS Constraints

Wireless mesh networks have emerged as a new technology for providing cost-effective broadband Internet access to users living in different communities across the globe. However, due to changes in a network topology across different paths, it is a challenging task to handle heavy data traffic in a multichannel environment. To address this issue, we propose a new collaborative-learning-automata-based channel assignment with topology preservation in this paper. In the proposed scheme, learning automata (LA) are deployed at the nearest mesh routers to collaborate with each other for information sharing and data transmission while learning from an environment. For each performed action, the LA get a reward or a penalty from the environment. Based on the inputs from the environment, the LA update their action probability vector and then decide the next action. The performance of the proposed scheme is evaluated with respect to various metrics such as throughput, data delivery ratio, switching and buffering delays, effective transmission, and effective channel utilization.

Laguerre approximation of random foams

Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam’s cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.

Constrained Self Organizing Maps for Data Clusters Visualization

High dimensional data visualization is one of the main tasks in the field of data mining and pattern recognition. The self organizing maps (SOM) is one of the topology visualizing tool that contains a set of neurons that gradually adapt to input data space by competitive learning and form clusters. The topology preservation of the SOM strongly depends on the learning process. Due to this limitation one cannot guarantee the convergence of the SOM in data sets with clusters of arbitrary shape. In this paper, we introduce Constrained SOM (CSOM), the new version of the SOM by modifying the learning algorithm. The idea is to introduce an adaptive constraint parameter to the learning process to improve the topology preservation and mapping quality of the basic SOM. The computational complexity of the CSOM is less than those with the SOM. The proposed algorithm is compared with similar topology preservation algorithms and the numerical results on eight small to large real-world data sets demonstrate the efficiency of the proposed algorithm.

A new incremental neural network for simultaneous clustering and classification

In this paper, an Incremental Neural Network for Classification and Clustering (INNCC) is proposed. The main advantages of this neural network are the linkage between data topology preservation and classes representation by using the cluster posterior probabilities of classes. It is a constructive model without prior conditions such as a suitable number of nodes. A new neuron is inserted when new data are not represented by existing neurons. In training step, both supervised and unsupervised learning are used. The training dataset contains few samples with class labels and several unlabeled ones. The Support Vector Machines (SVM) operates in the training step to assess the INNCC classification result. The proposed approach has been tested on synthetic and real datasets. Obtained results are very promising.

A survey on skeletonization algorithms and their applications

Skeletonization provides an effective and compact representation of objects, which is useful for object description, retrieval, manipulation, matching, registration, tracking, recognition, and compression. It also facilitates efficient assessment of local object properties, e.g., scale, orientation, topology, etc. Several computational approaches are available in literature toward extracting the skeleton of an object, some of which are widely different in terms of their principles. In this paper, we present a comprehensive and concise survey of different skeletonization algorithms and discuss their principles, challenges, and benefits. Topology preservation, parallelization, and multi-scale skeletonization approaches are discussed. Finally, various applications of skeletonization are reviewed and the fundamental challenges of assessing the performance of different skeletonization algorithms are discussed.

Digital Topology and Geometry in Medical Imaging: A Survey.

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

Topology preserving advection of implicit interfaces on Cartesian grids

Accurate representation of implicit interface topology is important for the numerical computation of two phase flow on Cartesian grids. A new method is proposed for the construction of signed distance function by geometrically projecting interface topology onto the Cartesian grid using a multi-level projection framework. The method involves a stepwise improvement in the approximation to the signed distance function based on pointwise, piecewise and locally smooth reconstructions of the interface. We show that this approach provides accurate representation of the projected interface and its topology on the Cartesian grid, including the distance from the interface and the interface normal and curvature. The projected interface can be in the form of either a connected set of marker particles that evolve with Lagrangian advection, or a discrete set of points associated with an implicit interface that evolves with the advection of a scalar function. The signed distance function obtained with geometric projection is independent of the details of the scaler field, in contrast to the conventional approach where advection and reinitialization cannot be decoupled. As a result, errors introduced by reinitialization do not amplify advection errors, which leads to substantial improvement in both volume conservation and topology representation.

Topological preservation techniques for nonlinear process monitoring

This work proposes a novel approach for the offline development and online implementation of data-driven process monitoring (PM) using topological preservation techniques, specifically self-organizing maps (SOM). Previous topological preservation PM applications have been restricted due to the lack of monitoring and diagnosis tools. In the proposed approach, the capabilities of SOM are further extended so that all aspects of PM can be performed in a single environment. First for fault detection, using SOM's vector quantization abilities, an SOM-based Gaussian mixture model (GMM) is proposed to define the normal region. For identification, an SOM-based contribution plot is proposed to identify the variables most responsible for the fault. This is done by analyzing the residual of the faulty point and an SOM model of the normal region used in fault detection. The data points are projected on the model by locating the best matching unit (BMU) of the point. Finally, for fault diagnosis a procedure is formulated involving the concept of multiple self-organizing maps (MSOM), creating a map for each fault. This allows the ability to include new faults without directly affecting previously characterized faults. A Tennessee Eastman Process (TEP) application is performed on dynamic faults such as random variations, sticky valves and a slow drift in kinetics. Previous studies of the TEP have considered particular feed-step-change faults. Results indicate an excellent performance when compared to linear and nonlinear distance preservation techniques and standard nonlinear SOM approaches in fault diagnosis and identification.

Topology-preserving flocking of nonlinear agents using optimistic planning

We consider the generalized flocking problem in multiagent systems, where the agents must drive a subset of their state variables to common values, while communication is constrained by a proximity relationship in terms of another subset of variables. We build a flocking method for general nonlinear agent dynamics, by using at each agent a near-optimal control technique from artificial intelligence called optimistic planning. By defining the rewards to be optimized in a well-chosen way, the preservation of the interconnection topology is guaranteed, under a controllability assumption. We also give a practical variant of the algorithm that does not require to know the details of this assumption, and show that it works well in experiments on nonlinear agents.