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Thin-plate spline for robust point matching (TPS-RPM) algorithm is a famous and widely used approach in nonlinear shape registration. In this paper, we improve this approach by adopting an alternatively iterative strategy of globally affine and locally nonlinear registration. Concretely, in the affine registration step, we apply the Lie group parameterization method to globally align two shapes to assume the global similarity. In which, some suitable constraints are introduced to improve the robustness of algorithm. Then, in the locally nonlinear deformation step, we apply the thin-plate spline approach. By alternatively iterating these two steps, the proposed method not only preserves the advantages of spline methods, but also overcomes an overmatching phenomenon in shape registration. Finally, we test the proposed method on several conventional data sets with comparison of TPS-RPM. The experimental results validate that our method is really effective for nonlinear shape registration as well as more robust.

Spatial resolution is a critical imaging parameter in magnetic resonance imaging. The image super-resolution (SR) is an effective and cost efficient alternative technique to improve the spatial resolution of MR images. Over the past several years, the convolutional neural networks (CNN)-based SR methods have achieved state-of-the-art performance. However, CNNs with very deep network structures usually suffer from the problems of degradation and diminishing feature reuse, which add difficulty to network training and degenerate the transmission capability of details for SR. To address these problems, in this work, a progressive wide residual network with a fixed skip connection (named FSCWRN) based SR algorithm is proposed to reconstruct MR images, which combines the global residual learning and the shallow network based local residual learning. The strategy of progressive wide networks is adopted to replace deeper networks, which can partially relax the above-mentioned problems, while a fixed skip connection helps provide rich local details at high frequencies from a fixed shallow layer network to subsequent networks. The experimental results on one simulated MR image database and three real MR image databases show the effectiveness of the proposed FSCWRN SR algorithm, which achieves improved reconstruction performance compared with other algorithms.

Spatial resolution is one of the key parameters of magnetic resonance imaging (MRI). The image super-resolution (SR) technique offers an alternative approach to improve the spatial resolution of MRI due to its simplicity. Convolutional neural networks (CNN)-based SR algorithms have achieved state-of-the-art performance, in which the global residual learning (GRL) strategy is now commonly used due to its effectiveness for learning image details for SR. However, the partial loss of image details usually happens in a very deep network due to the degradation problem. In this work, we propose a novel residual learning-based SR algorithm for MRI, which combines both multi-scale GRL and shallow network block-based local residual learning (LRL). The proposed LRL module works effectively in capturing high-frequency details by learning local residuals. One simulated MRI dataset and two real MRI datasets have been used to evaluate our algorithm. The experimental results show that the proposed SR algorithm achieves superior performance to all of the other compared CNN-based SR algorithms in this work.

The computer-aided quantitative analysis for histopathological images has attracted considerable attention. The stain decomposition on histopathological images is usually recommended to address the issue of co-localization or aliasing of tissue substances. Although the convolutional neural networks (CNN) is a popular deep learning algorithm for various tasks on histopathological image analysis, it is only directly performed on histopathological images without considering stain decomposition. The bilinear CNN (BCNN) is a new CNN model for fine-grained classification. BCNN consists of two CNNs, whose convolutional-layer outputs are multiplied with outer product at each spatial location. In this work, we propose a novel BCNN-based method for classification of histopathological images, which first decomposes histopathological images into hematoxylin and eosin stain components, and then perform BCNN on the decomposed images to fuse and improve the feature representation performance. The experimental results on the colorectal cancer histopathological image dataset with eight classes indicate that the proposed BCNN-based algorithm is superior to the traditional CNN.

Nonlinear registration is an important technique to align two different images and widely applied in medical image analysis. In this paper, we develop a novel nonlinear registration framework based on the diffeomorphic demons, where a reciprocal regularizer is introduced to assume that the deformation between two images is an exact diffeomorphism. In detail, first, we adopt a bidirectional metric to improve the symmetry of the energy functional, whose variables are two reciprocal deformations. Secondly, we slack these two deformations into two independent variables and introduce a reciprocal regularizer to assure the deformations being the exact diffeomorphism. Then, we utilize an alternating iterative strategy to decouple the model into two minimizing subproblems, where a new closed form for the approximate velocity of deformation is calculated. Finally, we compare our proposed algorithm on two data sets of real brain MR images with two relative and conventional methods. The results validate that our proposed method improves accuracy and robustness of registration, as well as the gained bidirectional deformations are actually reciprocal.

Normalizing all images in a large data set into a common space is a key step in many clinical and research studies, e.g., for brain development, maturation, and aging. Recently, groupwise registration has been developed for simultaneous alignment of all images without selecting a particular image as template, thus potentially avoiding bias in the registration. However, most conventional groupwise registration methods do not explore the data distribution during the image registration. Thus, their performance could be affected by large inter-subject variations in the data set under registration. To solve this potential issue, we propose to use a graph to model the distribution of all image data sitting on the image manifold, with each node representing an image and each edge representing the geodesic pathway between two nodes (or images). Then, the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other. Thus, the topology of image distribution on the image manifold is always preserved during the groupwise registration. More importantly, by modeling the distribution of all images via a graph, we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph. We have evaluated our proposed groupwise registration method on both infant and adult data sets, by also comparing with the conventional group-mean based registration and the ABSORB methods. All experimental results show that our proposed method can achieve better performance in terms of registration accuracy and robustness.

In this study, the authors address a two-dimensional (2D) shape registration problem on data with anisotropic-scale deformation and noise. First, the model is formulated under the iterative closest point (ICP) framework, which is one of the most popular methods for shape registration. To overcome the effect of noise, the expectation maximisation algorithm is used to improve the model. Then, the structure of Lie groups is adopted to parameterise the proposed model, which provides a unified framework to deal with the shape registration problems. Such representation makes it possible to introduce some suitable constraints to the model, which improves the robustness of the algorithm. Thereby, the 2D shape registration problem is turned to an optimisation problem on the matrix Lie group. Furthermore, a sequence of quadratic programming is designed to approximate the solution for the model. Finally, several comparative experiments are carried out to validate that the authors’ algorithm performs well in terms of robustness, especially in the presence of outliers.

With a rapid evolution of computer science, digital image manipulation becomes much more easily. One of the most commonly tampering with a digital image is copy-move forgery, in which a part of image is copied and used to cover another part in a different location in the same image. In this paper, we present an efficient and robust quaternion discrete cosine transform (QDCT) based method to detect this artifact. First, the R,G,B component of a tampered image is divided into overlapping fixed-size blocks, and a quaternion is constructed by using each R,G,B component block. Secondly, QDCT is applied to each quaternion block and using Zig-zag scanning extract finite QDCT coefficients, thus, the feature vectors are extracted from finite QDCT coefficients of overlapping blocks, and reduced features are generated. Finally, feature vectors are sorted lexicographically. The duplicated image blocks will be matched by a preset threshold value. Experiment results show that our proposed scheme can efficiently detect the copy-move forgery.

In clinical practice, it is more prevalent to use only a single-modal neuroimaging for diagnosis of brain disorders, such as structural magnetic resonance imaging. A neuroimaging dataset generally suffers from the small-sample-size problem, which makes it difficult to train a robust and effective classifier. The learning using privileged information (LUPI) is a newly proposed paradigm, in which the privileged information is available only at the training phase to provide additional information about training samples, but unavailable in the testing phase. LUPI can effectively help construct a better predictive rule to promote classification performance. In this paper, we propose to apply LUPI for the single-modal neuroimaging based diagnosis of brain diseases along with multi-modal training data. Moreover, a boosted LUPI framework is developed, which performs LUPI-based random subspace learning and then ensembles all the LUPI classifiers with the multiple kernel boosting (MKB) algorithm. The experimental results on two neuroimaging datasets show that LUPI-based algorithms are superior to the traditional classifier models for single-modal neuroimaging based diagnosis of brain disorders, and the proposed boosted LUPI framework achieves best performance.

Feature representation is a key step for the classification of histopathological images. The principal component analysis network (PCANet) offers a new unsupervised feature learning algorithm for images via a simple deep network architecture. However, PCA is sensitive to noise and outliers, which may depress the representation learning of PCANet. Grassmann averages (GA) is a newly proposed dimensionality reduction algorithm, which is more robust and effective than PCA. Therefore, in this paper, we propose a GA network (GANet) algorithm to improve the robustness of learned features from images. Moreover, since quaternion algebra provides a mathematically elegant tool to well handle color images, a quaternion representation based GANet (QGANet) is developed to fuse color information and learn a superior representation for color histopathological images. The experimental results on two histopathological image datasets show that GANet outperforms PCANet, while QGANet achieves the best performance for the classification of color histopathological images.

In this paper, 2D affine registration problem was studied. First, combining with the procedure of traditional iterative closest point method, the registration problem was modeled as an optimization problem on Lie group $$GL(2,{\mathfrak{R}})$$. To assure the registration non-degenerate, some reasonable constraints were introduced into the model by Iwasawa decomposition. Then, a series of quadratic programming were used to approximate the registration problem and a novel affine registration algorithm was proposed. At last, several illustration and comparison experiments were presented to demonstrate the performance and efficiency of the proposed algorithm. Particularly, a way of selecting a good initial registration based on ICA method to achieve the global minimum was suggested.

Point set registration is important for calibration of multiple cameras, 3D reconstruction and recognition, etc. The iterative closest point (ICP) algorithm is accurate and fast for point set registration in a same scale, but it does not handle the case with different scales. This paper instead introduces a novel approach named the scaling iterative closest point (SICP) algorithm which integrates a scale matrix with boundaries into the original ICP algorithm for scaling registration. At each iterative step of this algorithm, we set up correspondence between two m-D point sets, and then use a simple and fast iterative algorithm with the singular value decomposition (SVD) method and the properties of parabola incorporated to compute scale, rotation and translation transformations. The SICP algorithm has been proved to converge monotonically to a local minimum from any given parameters. Hence, to reach desired global minimum, good initial parameters are required which are successfully estimated in this paper by analyzing covariance matrices of point sets. The SICP algorithm is independent of shape representation and feature extraction, and thereby it is general for scaling registration of m-D point sets. Experimental results demonstrate its efficiency and accuracy compared with the standard ICP algorithm.

The iterative closet point (ICP) method is a dominant method for data registration that has attracted extensive attention. In this paper, a unified mathematical model of ICP based on Lie group representation is established. Under the framework, the registration problem is formulated into an optimization problem over a certain Lie group. In order to simplify the model and to reduce the dimension of parameter space, the translation part of geometric transformation is eliminated by calibrating the centers of two data sets under registration. As a result, a fast algorithm by solving an iterative linear system is designed for the optimization problem on Lie groups. Moreover, PCA and ICA methods are jointly applied to estimate the initial registration to achieve the global minimum. Finally, several illustrations and comparison experiments are presented to test the performance of the proposed algorithm.

SUMMARY Weighted graph matching is computationally challenging due to the combinatorial nature of the set of permutations. In this paper, a new relaxation approach to weighted graph matching is proposed, by which a new matching algorithm, named alternate iteration algorithm, is designed. It is proved that the algorithm proposed is locally convergent. Experiments are presented to show the effectiveness of the proposed algorithm. eration algorithm.

Background Electroencephalography (EEG) based sleep staging is commonly used in clinical routine. Feature extraction and representation plays a crucial role in EEG-based automatic classification of sleep stages. Sparse representation (SR) is a state-of-the-art unsupervised feature learning method suitable for EEG feature representation. New method Collaborative representation (CR) is an effective data coding method used as a classifier. Here we use CR as a data representation method to learn features from the EEG signal. A joint collaboration model is established to develop a multi-view learning algorithm, and generate joint CR (JCR) codes to fuse and represent multi-channel EEG signals. A two-stage multi-view learning-based sleep staging framework is then constructed, in which JCR and joint sparse representation (JSR) algorithms first fuse and learning the feature representation from multi-channel EEG signals, respectively. Multi-view JCR and JSR features are then integrated and sleep stages recognized by a multiple kernel extreme learning machine (MK-ELM) algorithm with grid search. Results The proposed two-stage multi-view learning algorithm achieves superior performance for sleep staging. With a K-means clustering based dictionary, the mean classification accuracy, sensitivity and specificity are 81.10 ± 0.15%, 71.42 ± 0.66% and 94.57 ± 0.07%, respectively; while with the dictionary learned using the submodular optimization method, they are 80.29 ± 0.22%, 71.26 ± 0.78% and 94.38 ± 0.10%, respectively. Comparison with existing methods The two-stage multi-view learning based sleep staging framework outperforms all other classification methods compared in this work, while JCR is superior to JSR. Conclusions The proposed multi-view learning framework has the potential for sleep staging based on multi-channel or multi-modality polysomnography signals.

Recently, group wise registration has been investigated for simultaneous alignment of all images without selecting any individual image as the template, thus avoiding the potential bias in image registration. However, none of current group wise registration method fully utilizes the image distribution to guide the registration. Thus, the registration performance usually suffers from large inter-subject variations across individual images. To solve this issue, we propose a novel group wise registration algorithm for large population dataset, guided by the image distribution on the manifold. Specifically, we first use a graph to model the distribution of all image data sitting on the image manifold, with each node representing an image and each edge representing the geodesic pathway between two nodes (or images). Then, the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other. Thus, the topology of image distribution on the image manifold is always preserved during the group wise registration. More importantly, by modeling the distribution of all images via a graph, we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph. We have evaluated our proposed group wise registration method on both synthetic and real datasets, with comparison to the two state-of-the-art group wise registration methods. All experimental results show that our proposed method achieves the best performance in terms of registration accuracy and robustness.

In this paper, a 2D shape registration algorithm for noisy data is established by combining the Iterative Closest Point (ICP) method, Expectation Maximization (EM) method, and Lie Group representation. First, the problem is formulated by a minimization problem with two sets of variables: the point-to-point correspondence, and the transformation (i.e., rotation, scaling and translation) between two data sets. The conventional way for solving this model is by iterating alternatively the following two steps: 1) having the transformation fixed, solve the correspondence, and 2) having the correspondence fixed, solve the transformation. In our approach, to enhance the robustness, the EM algorithm is introduced to find the correspondence by a probability which covers the relationship of all points, instead of one-to-one closest correspondence in ICP. Meanwhile, Lie group is used to parameterize transformation, i.e., in the iteration, the rotation, scaling and translation are all elements within respective Lie groups, and we use the element of Lie algebra to represent that of Lie group near the identity via exponential map. This forms a unified framework for registration algorithms. Then, transformation is estimated by solving a quadratic programming. The experimental result in 2D shape registration demonstrates that, compared with Lie-ICP, our algorithm is robuster and more accurate.

Registration of 3D range data is to find the transformation that best maps one data set to the other. In this paper, Lie group parametric representation is combined with the Expectation Maximization (EM) method to provide a unified framework. First, having a transformation fixed, the EM algorithm is introduced to find the correspondence between two data sets through correspondence probability, which covers the relationship of all points, instead of using exact correspondence such as the classical Iterative Closest Point (ICP) method. With this type of ststistical correspondence, we could deal with the presence of the degradations such as outliers and incomplete point sets. Second, having the updated correspondence fixed, and introducing Lie group parametric representation, the transformation is updated by minimizing a quadratic programming. Then, an alternative iterative strategy by the above two steps is used to approximate the desired correspondence and transformation. The comparative experiment between our Lie-EM-ICP algorithm and Lie-ICP algorithm using point cloud is presented. Our algorithm is demonstrated to be accurate and robust, especially in the presence of incomplete point sets and outliers.

The ICP algorithm is accurate and fast for registration between two point sets in a same scale, but it doesn't handle the case with different scales. This paper instead introduces a novel approach named the scaling iterative closest point (SICP) algorithm which integrates a scale matrix with boundaries into the original ICP algorithm for scaling registration. This method uses a simple iterative algorithm with the SVD algorithm and the properties of parabola incorporated to compute the translation, rotation and scale transformations at each iterative step, and its convergence is rapid with only a few iterations. The SICP algorithm is independent of shape representation and feature extraction; thereby it is general for scaling registration. Experimental results demonstrate its robustness and fast speed compared with the standard ICP algorithm.

We propose a trimmed strategy for affine registration of point sets using the Lie group parameterization. All affine transformations form an affine Lie group, thus finding an optimal transformation in registration is reduced to finding an optimal element in the affine group. Given two point sets (with outliers) and an initial element in the transformation group, we seek the optimal group element iteratively by minimizing an energy functional. This is conducted by sequentially finding the closest correspondence of two point sets, estimating the overlap rate of two sets, and finding the optimal affine transformation via the exponential map of the affine group. This method improves the trimmed iterative closest point algorithm (TrICP) in two aspects: (1) We use the Lie group parameterization to implement TrICP. (2) We also extend TrICP to the case of affine transformations. The performance of the proposed algorithm is demonstrated by using the LiDAR data acquired in the Mount St. Helens area. Both visual inspections and evaluation index (root mean trimmed squared distance) indicate that our algorithm performs consistently better than TrICP and other related algorithms, especially in the presence of outliers and missing points.