Local Linear Transformations Research Articles

A novel Dual-Branch Asymmetric Encoder–Decoder Segmentation Network for accurate colonic crypt segmentation

Colorectal cancer (CRC) is a leading cause of cancer-related deaths, with colonic crypts (CC) being crucial in its development. Accurate segmentation of CC is essential for decisions CRC and developing diagnostic strategies. However, colonic crypts’ blurred boundaries and morphological diversity bring substantial challenges for automatic segmentation. To mitigate this problem, we proposed the Dual-Branch Asymmetric Encoder–Decoder Segmentation Network (DAUNet), a novel and efficient model tailored for confocal laser endomicroscopy (CLE) CC images. In DAUNet, we crafted a dual-branch feature extraction module (DFEM), employing Focus operations and dense depth-wise separable convolution (DDSC) to extract multiscale features, boosting semantic understanding and coping with the morphological diversity of CC. We also introduced the feature fusion guided module (FFGM) to adaptively combine features from both branches using cross-group spatial and channel attention to improve the model representation in focusing on specific lesion features. These modules are seamlessly integrated into the encoder for effective multiscale information extraction and fusion, and DDSC is further introduced in the decoder to provide rich representations for precise segmentation. Moreover, the local multi-layer perceptron (LMLP) module is designed to decouple and recalibrate features through a local linear transformation that filters out the noise and refines features to provide edge-enriched representation. Experimental evaluations on two datasets demonstrate that the proposed method achieves Intersection over Union (IoU) scores of 81.54% and 84.83%, respectively, which are on par with state-of-the-art methods, exhibiting its effectiveness for CC segmentation. The proposed method holds great potential in assisting physicians with precise lesion localization and region analysis, thereby improving the diagnostic accuracy of CRC.

Guided Filtering Combining Neighborhood Variance and Anisotropic Window

Aiming at the problem that guided filtering would cause halo near the edge and it is difficult to identify fine edges, a guided filtering combining neighborhood variance and anisotropic window is proposed. Firstly, the directional selectivity of the anisotropic Gaussian filter is used for the recognition of the fine edge, and the narrow spatial structure of the filter can benefit the information fusion of different pixels inside the local window to suppress the edge blur and halo effect. Secondly, based on the local structure similarity, the neighborhood variance is introduced to optimize the parameters of local linear transformation, so as to achieve the maximum diffusion at non-edge region while preserving strong edges. The experimental results on 102 Category Flower Dataset show that, compared with other edge-preserving filtering methods, the proposed method is superior to other methods in visual effect and quantitative evaluation (PSNR and SSIM), and the distortion of the test image is 46.72%, 48.64% and 29.61% smaller than guided filtering, weighted guided filtering and anisotropic guided filtering respectively. It can effectively suppress the occurrence of artifacts while recognizing precise edges.

Coarse-to-Fine Image Registration for Multi-Temporal High Resolution Remote Sensing Based on a Low-Rank Constraint

For multi-temporal high resolution remote sensing images, the image registration is important but difficult due to the high resolution and low-stability land-cover. Especially, the changing of land-cover, solar altitude angle, radiation intensity, and terrain fluctuation distortion in the overlapping areas can represent different image characteristics. These time-varying properties cause traditional registration methods with known reference information to fault. Therefore, in this paper we propose a comprehensive coarse-to-fine registration (CCFR) algorithm. First, we design a low-rank constraint-based batch reference extraction (LRC-BRE) method. Under the low-rank constraint, the stable features with highly spatial co-occurrence can be reconstructed via matrix decomposition, and are set as reference images to batch registration. Second, we improve the general feature registration with block feature matching and local linear transformation (BFM-LLT) operators including match outlier filtering (MOF) on regional mutual information and dual-weighted block fitting (DWBF). Finally, based on combining LRC-BRE and BFM-LLT, CCFR is integrated. Experimental results show that the proposed method has a good batch alignment effect, especially in the registration of large difference image pairs. The proposed CCFR achieves a significant performance improvement over many state-of-the-art registration algorithms.

Foggy Image Detection and Filtration Methods: Review

Image de-fogging in brightness defined to image calculated in a deprived climate like as fog, rain and ocean and pollutants or dust particles. To alter the fog and some other pollutants from the image, various methods are customized, some mainly utilized methods are DCP, Detection, and Classification of foggy images. Haze is an arrangement of dual components, air-light and DA (Direct Attenuation), low image quality and generates various issues in VS (Video Surveillance), Navigation and Target Tracking, etc. So, its removes from an image, several de-fogging approaches have been discussed in this paper. Image De-fogging can attain utilizing several and single image haze removal techniques. The famous methods are discussed in this paper used for image de-fogging in DCP, Depth-map for accurate estimation, Guided Filter, and Transmission methods. These techniques still efficient in removing haze from images have very high time complexity. The guided filter is a new region preservative filter with region enhancement and smoothing. The previous result was a local linear transformation of the Guided Image. It defines a review of the classification and detection technique of a hazy image. This method mitigates the limitations of filtration and DCP and at the same time preserves the image quality. At that time, described the existing image de-fogging methods containing image restoration, contrast improvement, and fusion-based image de-fogging methods.

Transferable Linear Discriminant Analysis.

Linear discriminant analysis (LDA) has been widely used as the technique of feature exaction. However, LDA may be invalid to address the data from different domains. The reasons are as follows: 1) the distribution discrepancy of data may disturb the linear transformation matrix so that it cannot extract the most discriminative feature and 2) the original design of LDA does not consider the unlabeled data so that the unlabeled data cannot take part in the training process for further improving the performance of LDA. To address these problems, in this brief, we propose a novel transferable LDA (TLDA) method to extend LDA into the scenario in which the data have different probability distributions. The whole learning process of TLDA is driven by the philosophy that the data from the same subspace have a low-rank structure. The matrix rank in TLDA is the key learning criterion to conduct local and global linear transformations for restoring the low-rank structure of data from different distributions and enlarging the distances among different subspaces. In doing so, the variations of distribution discrepancy within the same subspace can be reduced, i.e., data can be aligned well and the maximally separated structure can be achieved for the data from different subspaces. A simple projected subgradient-based method is proposed to optimize the objective of TLDA, and a strict theory proof is provided to guarantee a quick convergence. The experimental evaluation on public data sets demonstrates that our TLDA can achieve better classification performance and outperform the state-of-the-art methods.

Material Affine Connections for Growing Solids

The present paper aims to develop geometrical approach for finite incompatible deformations arising in growing solids. The phenomena of incompatibility is modeled by specific affine connection on material manifold, referred to as material connection. It provides complete description of local incompatible deformations for simple materials. Meanwhile, the differential-geometric representation of such connection is not unique. It means that one can choose different ways for analytical definition of connection for single given physical problem. This shows that, in general, affine connection formalism provides greater potential than is required to the theory of simple materials (first gradient theory). For better understanding of this inconsistence it is advisable to study different ways for material connection formalization in details. It is the subject of present paper. Affine connection endows manifolds with geometric properties, in particular, with parallel transport on them. For simple materials the parallel transport is elegant mathematical formalization of the concept of a materially uniform (in particular, a stress-free) non-Euclidean reference shape. In fact, one can obtain a connection of physical space by determining the parallel transport as a transformation of the tangent vector, which corresponds to the structure of the physical space containing shapes of the body. One can alternatively construct affine connection of material manifold by defining parallel transport as the transformation of the tangent vector, in which its inverse image with respect to locally uniform embeddings does not change. Utilizing of the conception of material connections and the corresponding methods of non-Euclidean geometry may significantly simplify formulation of the initial-boundary value problems of the theory of incompatible deformations. Connection on the physical manifold is compatible with metric and Levi-Civita relations holds for it. Connection on the material manifold is considered in three alternative variants. The first leads to Weitzenbock space (the space of absolute parallelism or teleparallelism, i.e., space with zero curvature and nonmetricity, but with non-zero torsion) and gives a clear interpretation of the material connection in terms of the local linear transformations which transform an elementary volume of simple material into uniform state. The second one allows to choose the Riemannian space structure (with zero torsion and nonmetricity, but nonzero curvature) in material manifold and it is the most convenient way for deriving of field equations. The third variant is based on Weyl manifold with specified volume form and non-vanishing nonmetricity.

Connector Tensor Networks: A Renormalization-Type Approach to Quantum Certification

As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from severe scalability issues and can only be computed for systems of a very modest size, of around $6$ sites. In order to address large many-body systems, we propose a renormalisation-type approach based on a class of local linear transformations, called connectors, which can be used to coarse-grain the system in a way that preserves the property under investigation. Repeated coarse-graining produces a system of manageable size, whose properties can then be explored by means of usual techniques for small systems. In case of a successful detection of the desired property, the method outputs a linear witness which admits an exact tensor network representation, composed of connectors. We demonstrate the power of our method by certifying using a normal desktop computer entanglement, Bell nonlocality and supra-quantum Bell nonlocality in systems with hundreds of sites.

An Integrated Approach to Registration and Fusion of Hyperspectral and Multispectral Images

Combining a hyperspectral (HS) image and a multispectral (MS) image - an example of image fusion - can result in a spatially and spectrally high-resolution image. Despite the plethora of fusion algorithms in remote sensing, a necessary prerequisite, namely registration, is mostly ignored. This limits their application to well-registered images from the same source. In this article, we propose and validate an integrated registration and fusion approach (code available at https://github.com/zhouyuanzxcv/Hyperspectral). The registration algorithm minimizes a least-squares (LSQ) objective function with the point spread function (PSF) incorporated together with a nonrigid freeform transformation applied to the HS image and a rigid transformation applied to the MS image. It can handle images with significant scale differences and spatial distortion. The fusion algorithm takes the full high-resolution HS image as an unknown in the objective function. Assuming that the pixels lie on a low-dimensional manifold invariant to local linear transformations from spectral degradation, the fusion optimization problem leads to a closed-form solution. The method was validated on the Pavia University, Salton Sea, and the Mississippi Gulfport datasets. When the proposed registration algorithm is compared to its rigid variant and two mutual information-based methods, it has the best accuracy for both the nonrigid simulated dataset and the real dataset, with an average error less than 0.15 pixels for nonrigid distortion of maximum 1 HS pixel. When the fusion algorithm is compared with current state-of-the-art algorithms, it has the best performance on images with registration errors as well as on simulations that do not consider registration effects.

Feedback Unilateral Grid-Based Clustering Feature Matching for Remote Sensing Image Registration

In feature-based image matching, implementing a fast and ultra-robust feature matching technique is a challenging task. To solve the problems that the traditional feature matching algorithm suffers from, such as long running time and low registration accuracy, an algorithm called feedback unilateral grid-based clustering (FUGC) is presented which is able to improve computation efficiency, accuracy and robustness of feature-based image matching while applying it to remote sensing image registration. First, the image is divided by using unilateral grids and then fast coarse screening of the initial matching feature points through local grid clustering is performed to eliminate a great deal of mismatches in milliseconds. To ensure that true matches are not erroneously screened, a local linear transformation is designed to take feedback verification further, thereby performing fine screening between true matching points deleted erroneously and undeleted false positives in and around this area. This strategy can not only extract high-accuracy matching from coarse baseline matching with low accuracy, but also preserves the true matching points to the greatest extent. The experimental results demonstrate the strong robustness of the FUGC algorithm on various real-world remote sensing images. The FUGC algorithm outperforms current state-of-the-art methods and meets the real-time requirement.

A post-processing algorithm for spectral CT material selective images using learned dictionaries

In spectral computed tomography (spectral CT), the additional information about the energy dependence of the linear attenuation coefficients can be exploited to produce material selective images. These images have proven to be useful for various applications such as quantitative imaging or clinical diagnosis. However, noise amplification on material decomposed images remains a fundamental problem which limits the utility of basis material images. In this work, we present a new post-processing algorithm for material selective images which is based on dictionary denoising and specifically tailored to take the properties of the basis material images into account. Dictionary denoising is a powerful noise reduction technique which separates image features from noise by modeling small image patches as a sparse linear combination of dictionary atoms. These dictionary atoms are learned from training images prior to the denoising process. We have adapted the dictionary denoising algorithm to make use of the structural correlation as well as the anti-correlated noise which is typically present in material selective images. Dictionary denoising is first applied to the virtual monochromatic image for which the anti-correlated noise maximally cancels out (minimum noise image) in order to identify the structures and edges of the material selective images. In a second step, the basis material images are compiled by finding local linear transformations between the minimum noise image and the basis material images. Numerical simulations as well as an experimental measurement show that our algorithm achieves improved image quality compared to two other post-processing methods, namely conventional dictionary denoising and bilateral filtering. As a post-processing method, it can be combined with image-based as well as projection-based material decomposition techniques. Our algorithm therefore has the potential to improve the usability of basis material images for various tasks such as artifact reduction, quantitative imaging and clinical diagnosis.

A kernel approach to implementation of local linear discriminant analysis for face recognition

The multiple linear model is used successfully to extend the linear model to nonlinear problems. However, the conventional multilinear models fail to learn the global structure of a training data set because the local linear models are independent of each other. Furthermore, the local linear transformations are learned in the original space. Therefore, the performance of multilinear methods is strongly dependent on the results of partition. This paper presents a kernel approach for the implementation of the local linear discriminant analysis for face recognition problems. In the original space, we utilize a set of local linear transformations with interpolation to approximate an optimal global nonlinear transformation. Based on the local linear models in the original space, we derive an explicit kernel mapping to map the training data into a high‐dimensional transformed space. The optimal transformation is learned globally in the transformed space. Experimental results show that the proposed method is more robust to the partition results than the conventional multilinear methods. Compared with the general nonlinear kernels that utilize a black‐box mapping, our proposed method can reduce the negative effects caused by the potential overfitting problem. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Multi-metrics Classification Machine

Distance and its related decision rules are important in classification problems. kNN classifies a data point by the labels of its k-nearest neighbors and can be ameliorated by metric learning. For SVM, representative hyperplanes are found to refer to the location of every class and any point can be labeled by its perpendicular distance from the hyperplanes. Inspired by metric learning and SVM, a multi-metric classification machine, called MMCM, with a new prediction mechanism is proposed based on a novel distance relationship discerned by multi-metrics learning of the specificity information of each class. MMCM aims to find multi-metrics, namely the multiple local linear transformations for each class, to map data points into a new feature space, in which the distance between a point and its corresponding class centroid is minimized and data points of other classes are far from the centroid. An example with unknown label is classified according to the label of its nearest centroid. The primary problem is slacked as a linear optimization problem and kernel is introduced to make a nonlinear transformation. Enormous experiments verify MMCM's competitive performance both on binary classification and multi-class classification compared to state-of-the-art classification methods.

Piecewise linear transformation in diffusive flux discretization

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along material discontinuities using only cell concentration values. This is often resolved by introducing auxiliary node, edge, or face concentration values that are explicitly interpolated from the surrounding cell concentrations. We propose to discretize the diffusive flux after applying a local piecewise linear coordinate transformation that effectively removes the discontinuities. The resulting scheme does not need any auxiliary concentrations and is therefore remarkably simpler, while being second-order accurate under the assumption that the structure of the domain is locally layered.

Local linear dynamics assignment in IDA-PBC

In this paper, the technique of local linear dynamics assignment is presented, which complements the powerful Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) methodology. In IDA-PBC, nonlinear state feedback controllers are designed by matching the system’s dynamics with a desired Port-Hamiltonian (PH) state representation. The latter consists of an energy function, which serves as the closed-loop Lyapunov function, as well as matrices, describing the virtual internal exchange and dissipation of the energy. A major difficulty in IDA-PBC is how to determine reasonable values for the large number of free design parameters. Local linear dynamics assignment offers a solution to this problem with a number of advantages. (i) Invoking the closed-loop Jacobian linearization to fix the parameter values provides transparency with respect to the resulting local dynamic behavior. (ii) An appropriate state transformation isolates the coordinates available for energy shaping. (iii) A related local linear state transformation makes the resulting system of design equations linear. (iv) Assigning a Hurwitz closed-loop Jacobian and ensuring positive semi-definiteness of the closed-loop dissipation matrix, the tedious definiteness check of the energy is omitted. The design steps are illustrated with the Ball on Wheel example.

Fast Facial Image Super-Resolution via Local Linear Transformations for Resource-Limited Applications

Most popular learning-based super-resolution (SR) approaches suffer from complicated learning structures and highly intensive computation, especially in resource-limited applications. We propose a novel frontal facial image SR approach by using multiple local linear transformations to approximate the nonlinear mapping between low-resolution (LR) and high-resolution (HR) images in the pixel domain. We adopt Procrustes analysis to obtain orthogonal matrices representing the learned linear transformations, which cannot only well capture appearance variations in facial patches but also greatly simplify the transformation computation to matrices manipulation. An HR image can be directly reconstructed from a single LR image without need of the large training data, thus avoiding the use of a large redundant LR and HR patch database. Experimental results show that our approach is computationally fast as well the SR quality compares favorably with the state-of-the-art approaches from both subjective and objective evaluations. Besides, our approach is insensitive to the size of training data and robust to a wide range of facial variations like occlusions. More importantly, the proposed method is also much more effective than other comparative methods to reconstruct real-world images captured from the Internet and webcams.

Nonparametric regression function estimation for errors-in-variables models with validation data

This paper develops estimation approach for nonparametric regression analysis with measurement error in covariables assuming the availability of inde- pendent validation data on covariables in addition to primary data on the response variable and surrogate covariables. Without specifying any error model structure between the surrogate and true covariables, we propose an estimator which inte- grates local linear regression and Fourier transformation method. An estimator combined by two local linear kernel estimators, is flrstly used to calibrate the con- ditional expectation of unknown objective regression function given the surrogate covariates, and then the flnal estimator can be derived by passing a trigonometric series approach suggested by Delaigle et al. (2006). Under mild conditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.

Linearization of T-S fuzzy systems and robust H ∞ control

Takagi-Sugeno (T-S) fuzzy model is difficult to be linearized because of membership functions included. So, novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system. The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models. The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily. After the linearization of T-S fuzzy model, a robust H∞ controller with the robustness of sliding model control (SMC) is designed. As a result, controlled T-S fuzzy system shows the performance of H∞ control and the robustness of SMC.

Local linear transformation embedding

Dimensionality reduction is vital in many fields and locally linear embedding (LLE) is one of the most important approaches. However, LLE is unavoidable to derive the nonuniform wraps and folds when the data are of low sample density or unevenly sampled. LLE would also fail when the data are contaminated by even small noises. We have analyzed the performance of LLE and pointed out the reason why LLE fails. An improved algorithm, local linear transformation embedding (LLTE), is then proposed. Local linear transformation is performed on nearby points. The ‘Three-stage LLTE’ is also provided when the data has outliers. Comparing with LLE and Local tangent space alignment (LTSA), LLTE could derive more practical embedding than LLE and has wider application prospect than LTSA. Meanwhile, it exploits the tight relations between LLE/LLTE and LTSA. Several experiments and numerical results demonstrate the potential of our algorithm.

Measuring two-photon orbital angular momentum entanglement

We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of twin photons from a down-conversion source. Our estimate for the Schmidt number is substantially lower but still confirms the presence of high-dimensional entanglement.

Probabilistic Forecasting of the 3-h ap Index

Measurements of the solar wind are now available for nearly 40 years or four solar cycles. Several magnetic indexes are available for all of this time, and in most cases, some time before. Particle fluxes at geostationary orbit are available for nearly two solar cycles. Such data can be used to establish empirical relations between properties of the solar wind and indexes of magnetospheric and ionospheric activity. These relations are often expressed in terms of linear prediction filters, local linear filters, neural networks, or nonlinear transformations of solar wind data. The properties of these filters provide insight into the physical properties of the system and also can be used as real time predictors of future activity. All of these methods depend on real-time monitoring of the solar wind somewhere between the Earth's bow shock and the L1 point. Consequently, they provide no more than 1 h of advance warning. Longer term predictions depend on remote sensing of the Sun or solar wind and new models that transform these observations into properties of the solar wind at the Earth. Thus far, the only example of such remote sensing and empirical modeling is the Wang-Sheeley-Arge model. This model predicts the temporal profiles of solar wind speed, interplanetary magnetic field (IMF) magnitude, and IMF polarity at 1 AU. Unfortunately, geomagnetic activity indexes, and their prediction filters, also depend on the GSM Bz component of the IMF which so far is unpredictable. Fortunately, the solar wind often has large-scale structures that can be detected remotely. These structures organize the properties of the solar wind including IMF Bz, and hence affect the probability of geomagnetic activity at different times relative to the structure. Thus, it is possible to utilize the predictable properties of the solar wind to parameterize the probability distribution for a magnetic index and to accurately specify the probability of high geomagnetic activity given the correct identification of a solar wind structure.