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Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target ground truth labels of training examples by uniform random labels. However, it can cause undesirable misleading gradients due to the large loss associated with incorrect labels. We propose a first-order optimization method (Label-Noised Trim-SGD) that uses the label noise with the example trimming in order to remove the outliers based on the loss. The proposed algorithm is simple yet enables us to impose a large label-noise and obtain a better regularization effect than the original methods. The quantitative analysis is performed by comparing the behavior of the label noise, the example trimming, and the proposed algorithm. We also present empirical results that demonstrate the effectiveness of our algorithm using the major benchmarks and the fundamental networks, where our method has successfully outperformed the state-of-the-art optimization methods.

We present a stochastic first-order optimization algorithm, named block-cyclic stochastic coordinate descent (BCSC), that adds a cyclic constraint to stochastic block-coordinate descent in the selection of both data and parameters. It uses different subsets of the data to update different subsets of the parameters, thus limiting the detrimental effect of outliers in the training set. Empirical tests in image classification benchmark datasets show that BCSC outperforms state-of-the-art optimization methods in generalization leading to higher accuracy within the same number of update iterations. The improvements are consistent across different architectures and datasets, and can be combined with other training techniques and regularizations.

Characterization of tissue architecture is important to understand cell function and mechanisms in vivo. Spatial transcriptomics (ST), by recovering the transcriptome of a cell or tissue section while maintaining the two-dimensional location of the cell or tissue, can provide detailed insights into the cellular function in association with tissue architecture. Still, however, algorithmic development for ST has focused on identifying cells or spots with the same cell types located nearby and, therefore, cannot detect a tissue structure often composed of multiple cell types. Here, we present Vesalius to decipher tissue anatomy from ST data by converting transcriptomic information into a color code for image segmentation. Vesalius successfully detected tissue architecture in mouse embryo and brain from high resolution ST data by incorporating image processing algorithms. In contrast, previous spatial clustering approaches developed for low resolution ST data were unable to recover these structures. Intriguingly, Vesalius identifies genes linked to the morphology of tissue structures. In short, Vesalius is a tool to perform high-resolution in silico anatomization and molecular characterization from ST data.

We present a method to infer a dense depth map from a color image and associated sparse depth measurements. Our main contribution lies in the design of an annealing process for determining co-visibility (occlusions, disocclusions) and the degree of regularization to impose on the model. We show that regularization and co-visibility are related via the fitness (residual) of model to data and both can be unified into a single framework to improve the learning process. Our method is an adaptive weighting scheme that guides optimization by measuring the residual at each pixel location over each training step for (i) estimating a soft visibility mask and (ii) determining the amount of regularization. We demonstrate the effectiveness our method by applying it to several recent unsupervised depth completion methods and improving their performance on public benchmark datasets, without incurring additional trainable parameters or increase in inference time. Code available at: https://github.com/alexklwong/adaframe-depth-completion.

In this work, we present an image segmentation algorithm based on the convolutional neural network framework where the scale space theory is incorporated in the course of training procedure. The construction of data augmentation is designed to apply the scale space to the training data in order to effectively deal with the variability of regions of interest in geometry and appearance such as shape and contrast. The proposed data augmentation algorithm via scale space is aimed to improve invariant features with respect to both geometry and appearance by taking into consideration of their diffusion process. We develop a segmentation algorithm based on the convolutional neural network framework where the network architecture consists of encoding and decoding substructures in combination with the data augmentation scheme via the scale space induced by the heat equation. The quantitative analysis using the cardiac MRI dataset indicates that the proposed algorithm achieves better accuracy in the delineation of the left ventricles, which demonstrates the potential of the algorithm in the application of the whole heart segmentation as a compute-aided diagnosis system for the cardiac diseases.

Humans can recognize objects well even if they only show the shape of objects or an object is composed of several components. But, most of the classifiers in the deep learning framework are trained through original images without removing complex elements inside the object. And also, they do not remove things other than the object to be classified. So the classifiers are not as effective as the human classification of objects because they are trained with the original image which has many objects that the classifier does not want to classify. In this respect, we found out which pre-processing can improve the performance of the classifier the most by comparing the results of using data through other pre-processing. In this paper, we try to limit the amount of information in the object to a minimum. To restrict the information, we use anisotropic diffusion and isotropic diffusion, which are used for removing the noise in the images. By using the anisotropic diffusion and the isotropic diffusion for the pre-processing, only shapes of objects were passed to the classifier. With these diffusion processes, we can get similar classification accuracy compared to when using the original image, and we found out that although the original images are diffused too much, the classifier can classify the objects centered on discriminative parts of the objects.

Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose L2 penalty on the model parameters resulting in the decay of parameters, called weight-decay, and the decay rate is generally constant to all the model parameters in the course of optimization. In contrast to the previous approach based on the constant rate of weight-decay, we propose to consider the residual that measures dissimilarity between the current state of model and observations in the determination of the weight-decay for each parameter in an adaptive way, called adaptive weight-decay (AdaDecay) where the gradient norms are normalized within each layer and the degree of regularization for each parameter is determined in proportional to the magnitude of its gradient using the sigmoid function. We empirically demonstrate the effectiveness of AdaDecay in comparison to the state-of-the-art optimization algorithms using popular benchmark datasets: MNIST, Fashion-MNIST, and CIFAR-10 with conventional neural network models ranging from shallow to deep. The quantitative evaluation of our proposed algorithm indicates that AdaDecay improves generalization leading to better accuracy across all the datasets and models.

We propose a deep learning framework for anisotropic diffusion which is based on a complex algorithm for a single image. Our network can be applied not only to a single image but also to multiple images. Also by blurring the image, the noise in the image is reduced. But the important features of objects remain. To apply anisotropic diffusion to deep learning, we use total variation for our loss function. Also, total variation is used in image denoising pre-process.[1] With this loss, our network makes successful anisotropic diffusion images. In these images, the whole parts are blurred, but edge and important features remain. The effectiveness of the anisotropic diffusion image is shown with the classification task.

We propose a first-order stochastic optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework. The adaptive regularization is imposed by stochastic process in determining batch size for each model parameter at each optimization iteration. The stochastic batch size is determined by the update probability of each parameter following a distribution of gradient norms in consideration of their local and global properties in the neural network architecture where the range of gradient norms may vary within and across layers. We empirically demonstrate the effectiveness of our algorithm using an image classification task based on conventional network models applied to commonly used benchmark datasets. The quantitative evaluation indicates that our algorithm outperforms the state-of-the-art optimization algorithms in generalization while providing less sensitivity to the selection of batch size which often plays a critical role in optimization, thus achieving more robustness to the selection of regularity.

The reduction of unnecessary details is important in a variety of imaging tasks. Imagedenoising can be generally formulated as a diffusion process that iteratively suppresses undesirableimage features with high variance. We propose a recursive diffusion process that simultaneouslycomputes the local geometrical property of the image features and determines the size and shapeof the diffusion kernel, leading to an anisotropic scale-space. In the construction of the proposedanisotropic scale-space, image features due to undesirable noise are suppressed while significantgeometrical image features such as edges and corners are preserved across the scale-space.The diffusion kernels are iteratively determined based on the local geometrical properties ofthe image features. We demonstrate the effectiveness and robustness of the proposed algorithmin the detection of curvilinear features using simple yet effective synthetic and real images.The algorithm is quantitatively evaluated based on the identification of fissures in lung CT imagery.The experimental results indicate that the proposed algorithm can be used for the detection of linearor curvilinear structures in a variety of images ranging from satellite to medical images.

We formulate an energy for segmentation that is designed to have preference for segmenting the coarse over fine structure of the image, without smoothing across boundaries of regions. The energy is formulated by integrating a continuum of scales from a scale space computed from the heat equation within regions. We show that the energy can be optimized without computing a continuum of scales, but instead from a single scale. This makes the method computationally efficient in comparison to energies using a discrete set of scales. We apply our method to texture and motion segmentation. Experiments on benchmark datasets show that a continuum of scales leads to better segmentation accuracy over discrete scales and other competing methods.

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized at convergence. We also introduce the use of a Huber loss function in both data fidelity and regularization terms, and present an efficient convex optimization algorithm based on the alternating direction method of multipliers (ADMM) using the equivalent relation between the Huber function and the proximal operator of the one-norm. We illustrate and validate our adaptive Huber-Huber model on synthetic and real images in segmentation, motion estimation, and denoising problems.

The objective of our study was to measure thyroid volumes using semiautomated 3D CT and to compare the 3D CT volumes with volumes measured using 2D ultrasound, 2D CT, and the water displacement method.In 47 patients, 2D ultrasound volumes and 2D CT volumes of the thyroid gland were estimated using the ellipsoid volume formula, and 3D CT volumes were calculated using semiautomated reconstructive techniques. All volume data were compared with thyroid specimen volumes obtained using the water displacement method and were statistically analyzed using the one-way ANOVA, the Pearson correlation coefficient (R), linear regression, and the concordance correlation coefficient (CCC). The processing time of semiautomated 3D CT thyroid volumetry was measured.The paired mean differences ± SD between the three imaging-determined volumes and the specimen volumes were 0.8 ± 3.1 mL for 2D ultrasound, 4.0 ± 4.7 mL for 2D CT, and 0.2 ± 2.5 mL for 3D CT. A significant difference in the mean thyroid volume was found between 2D CT and specimen volumes (p = 0.016) compared with the other pairs (p = 0.937 for 2D ultrasound mean volume vs specimen mean volume, and p = 0.999 for 3D CT mean volume vs specimen mean volume). Between specimen volume and 2D ultrasound volume, specimen volume and 2D CT volume, and specimen volume and 3D CT volume, R values were 0.885, 0.724, and 0.929, respectively, and CCC values were 0.876, 0.598, and 0.925, respectively. The mean processing time of semiautomated 3D CT thyroid volumetry was 7.0 minutes.Thyroid volumes measured using 2D ultrasound or semiautomated 3D CT are substantially close to thyroid specimen volumes measured using the water displacement method. Semiautomated 3D CT thyroid volumetry can provide a more reliable measure of thyroid volume than 2D ultrasound.

We propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures using a new physically motivated motion estimation scheme. Our method estimates motion by regularizing only within structures so that differing motions among different structures are not mixed. It simultaneously satisfies the physical constraints at the interface between a fluid and a medium that the normal component of the fluid's motion must match the normal component of the medium's motion and the No-Slip condition, which states that the tangential velocity approaches zero near the interface. We show that these conditions lead to partial differential equations with Robin boundary conditions at the interface, which couple the motion between structures. We show that propagating a segmentation across frames using our motion estimation scheme leads to more accurate segmentation than traditional motion estimation that does not use physical constraints. Our method is suited to interactive segmentation, prominently used in commercial applications for cardiac analysis, where segmentation propagation is used to predict a segmentation in the next frame. We show that our method leads to more accurate predictions than a popular and recent interactive method used in cardiac segmentation.

We propose a mathematical framework for simultaneously delineating the boundary of object and estimating its temporal motion in the application of lesion detection in a dynamic contrast-enhanced (DCE) breast MRI sequence where both the appearance and the shape of region of interest is assumed to change in time. A unified energy functional for a joint segmentation and registration is proposed based on the assumption that the statistical properties of dynamic intensity curves within a region of interest are homogeneous. Our algorithm is designed to provide the morphological properties of the enhanced region and its dynamic intensity profiles, called kinetic signatures, in the analysis of DCE imagery since these features are considered as significant cues in understanding images. The proposed energy comprises a combination of a segmentation energy and a registration energy. The segmentation energy is developed based on a convex formulation being insensitive to the initialization. The registration energy is designed to compensate motion artifacts that are usually involved in the temporal imaging procedure. The major objective of this work is to provide a mathematical framework for a joint segmentation and registration on a dynamic sequence of images, and we demonstrate the mutual benefit of the estimation of temporal deformations for the registration step and the localization of regions of interest for the segmentation step. The effectiveness of the developed algorithm has been demonstrated on a number of clinical DCE breast MRI data in the application of breast lesion detection and the results show its potential to improve the accuracy and the efficiency in the diagnosis of breast cancer.

Cardiac magnetic resonance imaging (MRI) has been extensively used in the diagnosis of cardiovascular disease and its quantitative evaluation. Cardiac MRI techniques have been progressively improved, providing high-resolution anatomical and functional information. One of the key steps in the assessment of cardiovascular disease is the quantitative analysis of the left ventricle (LV) contractile function. Thus, the accurate delineation of LV boundary is of great interest to improve diagnostic performance. In this work, we present a novel segmentation algorithm of LV from cardiac MRI incorporating an implicit shape prior without any training phase using level sets in a variational framework. The segmentation of LV still remains a challenging problem due to its subtle boundary, occlusion, and inhomogeneity. In order to overcome such difficulties, a shape prior knowledge on the anatomical constraint of LV is integrated into a region-based segmentation framework. The shape prior is introduced based on the anatomical shape similarity between endocardium and epicardium. The shape of endocardium is assumed to be mutually similar under scaling to the shape of epicardium. An implicit shape representation using signed distance function is introduced and their discrepancy is measured in a probabilistic way. Our shape constraint is imposed by a mutual similarity of shapes without any training phase that requires a collection of shapes to learn their statistical properties. The performance of the proposed method has been demonstrated on fifteen clinical datasets, showing its potential as the basis in the clinical diagnosis of cardiovascular disease.

We propose a multilabel segmentation that aims to partition a texture image into multiple regions based on a homogeneity condition using local entropy measured at varying scales. For multi-label segmentation, a bipartitioning segmentation scheme is recursively applied to confined regions obtained by previous segmentation steps. The empirical entropy is measured in the local neighbourhoods at varying scales, which is used as a characteristic feature in determining the spatial regularity of elementary texture structures. The experimental results on a variety of texture images demonstrate the efficiency and robustness of the proposed algorithm.

Purpose: Coronary CT angiography (CCTA) is a high-resolution three-dimensional imaging technique for the evaluation of coronary arteries in suspected or confirmed coronary artery disease (CAD). Coregistration of serial CCTA scans would allow precise superimposition of images obtained at two different points in time, which could aid in recognition of subtle changes and precise monitoring of coronary plaque progression or regression. To this end, the authors aimed at developing a fully automatic nonlinear volume coregistration for longitudinal CCTA scan pairs. Methods: The algorithm combines global displacement and local deformation using nonlinear volume coregistration with a volume-preserving constraint. Histogram matching of intensities between two serial scans is performed prior to nonlinear coregistration with dense nonparametric local deformation in which sum of squared differences is used as a similarity measure. The approximate segmentation of coronary arteries obtained from commercially available software provides initial anatomical landmarks for the coregistration algorithm that help localize and emphasize the structure of interest. To avoid possible bias caused by incorrect segmentation, the authors convolve the Gaussian kernel with the segmented binary coronary tree mask and define an extended weighted region of interest. A multiresolution approach is employed to represent coarse-to-fine details of both volumes and the energy functionmore » is optimized using a gradient descent method. The authors applied the algorithm in ten paired CCTA datasets (20 scans in total) obtained within 10.7{+-}5.7 months from each other on a dual source CT scanner to monitor progression of CAD. Results: Serial CCTA coregistration was successful in 9/10 cases as visually confirmed. The global displacement and local deformation of target registration error obtained from four anatomical landmarks were 2.22{+-}1.15 and 1.56{+-}0.74 mm, respectively, and the inverse consistency error of local deformation was 0.14{+-}0.06 mm. The observer variability between two expert observers was 1.31{+-}0.91 mm. Conclusions: The proposed coregistration algorithm demonstrates potential to accurately register serial CCTA scans, which may allow direct comparison of calcified and noncalcified atherosclerotic plaque changes between the two scans.« less

Purpose: Cardiaccomputed tomography(CT) and single photon emission computed tomography(SPECT) provide clinically complementary information in the diagnosis of coronary artery disease (CAD). Fused anatomical and physiological data acquired sequentially on separate scanners can be coregistered to accurately diagnose CAD in specific coronary vessels. Methods: A fully automated registration method is presented utilizing geometric features from a reliable segmentation of gated myocardial perfusion SPECT (MPS) volumes, where regions of myocardium and blood pools are extracted and used as an anatomical mask to de-emphasize the inhomogeneities of intensity distribution caused by perfusion defects and physiological variations. A multiresolution approach is employed to represent coarse-to-fine details of both volumes. The extracted voxels from each level are aligned using a similarity measure with a piecewise constant image model and minimized using a gradient descent method. The authors then perform limited nonlinear registration of gated MPS to adjust for phase differences by automatic cardiac phase matching between CT and MPS. For phase matching, they incorporate nonlinear registration using thin-plate-spline-based warping. Rigid registration has been compared with manual alignment ( n = 45 ) on 20 stress/rest MPS and coronary CTA data sets acquired from two different sites and five stress CT perfusion data sets. Phase matching was also compared to expert visual assessment. Results: As compared with manual alignment obtained from two expert observers, the mean and standard deviation of absolute registration errors of the proposed method for MPS were 4.3 ± 3.5 , 3.6 ± 2.6 , and 3.6 ± 2.1 mm for translation and 2.1 ± 3.2 ° , 0.3 ± 0.8 ° , and 0.7 ± 1.2 ° for rotation at site A and 3.8 ± 2.7 , 4.0 ± 2.9 , and 2.2 ± 1.8 mm for translation and 1.1 ± 2.0 ° , 1.6 ± 3.1 ° , and 1.9 ± 3.8 ° for rotation at site B. The results for CT perfusion were 3.0 ± 2.9 , 3.5 ± 2.4 , and 2.8 ± 1.0 mm for translation and 3.0 ± 2.4 ° , 0.6 ± 0.9 ° , and 1.2 ± 1.3 ° for rotation. The registration error shows that the proposed method achieves registration accuracy of less than 1 voxel ( 6.4 × 6.4 × 6.4 mm ) misalignment. The proposed method was robust for different initializations in the range from − 80 to 70, − 80 to 70, and − 50 to 50 mm in the x -, y -, and z -axes, respectively. Validation results of finding best matching phase showed that best matching phases were not different by more than two phases, as visually determined. Conclusions: The authors have developed a fast and fully automated method for registration of contrastcardiacCT with gated MPS which includes nonlinear cardiac phase matching and is capable of registering these modalities with accuracy 10 mm in 87% of the cases.

We propose an unsupervised multiphase segmentation algorithm based on Bresson et al.'s fast global minimization of Chan and Vese's two-phase piecewise constant segmentation model. The proposed algorithm recursively partitions a region into two subregions, starting from the largest scale. The segmentation process automatically terminates and detects when all the regions cannot be partitioned further. The number of regions is not given and can be arbitrary. Furthermore, this method provides a full hierarchical representation that gives a structure of a given image.

The paper presents a variational framework to compute first and second order statistics of an ensemble of shapes undergoing deformations. Geometrically “meaningful” correspondence between shapes is established via a kernel descriptor that characterizes local shape properties. Such a descriptor allows retaining geometric features such as high-curvature structures in the average shape, unlike conventional methods where the average shape is usually smoothed out by generic regularization terms. The obtained shape statistics are integrated into segmentation as a prior knowledge. The effectiveness of the method is demonstrated through experimental results with synthetic and real images.

A non-rigid ultrasound image registration method is proposed in this work using the intensity as well as the local phase information under a variational framework. One application of this technique is to register two consecutive images in an ultrasound image sequence. Although intensity is the most widely used feature in traditional ultrasound image registration algorithms, speckle noise and lower image resolution make the registration process difficult. By integrating the intensity and the local phase information, we can find and track the non-rigid transformation of each pixel under diffeomorphism between the source and target images. Experiments using synthetic and cardiac images of in vivo mice and human subjects are conducted to demonstrate the advantages of the proposed method.

Image-guided percutaneous interventions have successfully replaced invasive surgical methods in some cardiologic practice, where the use of 3D-reconstructed cardiac images, generated by magnetic resonance imaging (MRI) and computed tomography (CT), plays an important role. To conduct computer-aided catheter ablation of atrial fibrillation accurately, multimodal information integration with electroanatomic mapping (EAM) data and MRI/CT images is considered in this work. Specifically, we propose a variational formulation for surface reconstruction and incorporate the prior shape knowledge, which results in a level set method. The proposed method enables simultaneous reconstruction and registration under nonrigid deformation. Promising experimental results show the potential of the proposed approach.

Textures within real images vary in brightness, contrast, scale, and skew as imaging conditions change. To enable recognition of textures in real images, it is necessary to employ a similarity measure that is invariant to these properties. Furthermore, since textures often appear on undulating surfaces, such invariances must necessarily be local rather than global. Despite these requirements, it is only relatively recently that texture recognition algorithms with local scale and affine invariance properties have begun to be reported. Typically, they comprise detecting feature points followed by geometric normalization prior to description. We describe a method based on invariant combinations of linear filters. Unlike previous methods, we introduce a novel family of filters, which provides scale invariance, resulting in a texture description invariant to local changes in orientation, contrast, and scale and robust to local skew. Significantly, the family of filters enables local scale invariants to be defined without using a scale selection principle or a large number of filters. A texture discrimination method based on the chi2 similarity measure applied to histograms derived from our filter responses outperforms existing methods for retrieval and classification results for both the Brodatz textures and the University of Illinois, Urbana-Champaign (UIUC) database, which has been designed to require local invariance.

In this work, we address the problem of segmenting multiple objects, under possible occlusions, in a level set framework. A variational energy that incorporates a piecewise constant representation of the image in terms of the object regions and the object spatial order is proposed. To resolve occluded boundaries, prior knowledge of the shape of objects is also introduced within the segmentation energy. By minimizing the above energy, we solve the segmentation with depth problem, i.e., estimating the object boundaries, the object intensities, and the spatial order. The segmentation with depth problem was originally dealt with by the Nitzberg-Mumford-Shiota (NMS) variational formulation, which proposes segmentation energies for each spatial order. We discuss the relationships and show the computational advantages of our formulation over the NMS model, mainly due to our treatment of spatial order estimation within a single energy. A novelty here is that the spatial order information available in the image model is used to dynamically impose prior shape constraints only to occluded boundaries. Also presented are experiments on synthetic and real images that have promising results.

We present a shape descriptor based on integral kernels. Shape is represented in an implicit form and it is characterized by a series of isotropic kernels that provide desirable invariance properties. The shape features are characterized at multiple scales which form a signature that is a compact description of shape over a range of scales. The shape signature is designed to be invariant with respect to group transformations which include translation, rotation, scaling, and reflection. In addition, the integral kernels that characterize local shape geometry enable the shape signature to be robust with respect to undesirable perturbations while retaining discriminative power. Use of our shape signature is demonstrated for shape matching based on a number of synthetic and real examples.

The image restoration and noise reduction are used to improve image quality and to develop more robust and high performance algorithms to solve denoising problems in the image processing. Every approach has their own limitations and more practicable properties with the specific conditions. This paper considers rotational transformation with non-local means denoising algorithm. The non-local means denoising algorithm use repetitive patterns in the image for noise reduction. Therefore, the affine transformations will extend search space of the problem and will cause of more qualitative results.

For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.

A fast and accurate segmentation algorithm in a hierarchical way based on a recursive superpixel technique is presented. We propose a superpixel energy formulation in which the trade-off between data fidelity and regularization is dynamically determined based on the local residual in the energy optimization procedure. We also present an energy optimization algorithm that allows a pixel to be shared by multiple regions to improve the accuracy and appropriate the number of segments. The qualitative and quantitative evaluations demonstrate that our algorithm, combining the proposed energy and optimization, outperforms the conventional k -means algorithm by up to 29.10% in F -measure. We also perform comparative analysis with state-of-the-art algorithms in the hierarchical segmentation. Our algorithm yields smooth regions throughout the hierarchy as opposed to the others that include insignificant details. Our algorithm overtakes the other algorithms in terms of balance between accuracy and computational time. Specifically, our method runs 36.48% faster than the region-merging approach, which is the fastest of the comparing algorithms, while achieving a comparable accuracy.

A major challenge when distinguishing glandular tissues on mammograms, especially for area-based estimations, lies in determining a boundary on a hazy transition zone from adipose to glandular tissues. This stems from the nature of mammography, which is a projection of superimposed tissues consisting of different structures. In this paper, the authors present a novel segmentation scheme which incorporates the learned prior knowledge of experts into a level set framework for fully automated mammographic density estimations.The authors modeled the learned knowledge as a population-based tissue probability map (PTPM) that was designed to capture the classification of experts' visual systems. The PTPM was constructed using an image database of a selected population consisting of 297 cases. Three mammogram experts extracted regions for dense and fatty tissues on digital mammograms, which was an independent subset used to create a tissue probability map for each ROI based on its local statistics. This tissue class probability was taken as a prior in the Bayesian formulation and was incorporated into a level set framework as an additional term to control the evolution and followed the energy surface designed to reflect experts' knowledge as well as the regional statistics inside and outside of the evolving contour.A subset of 100 digital mammograms, which was not used in constructing the PTPM, was used to validate the performance. The energy was minimized when the initial contour reached the boundary of the dense and fatty tissues, as defined by experts. The correlation coefficient between mammographic density measurements made by experts and measurements by the proposed method was 0.93, while that with the conventional level set was 0.47.The proposed method showed a marked improvement over the conventional level set method in terms of accuracy and reliability. This result suggests that the proposed method successfully incorporated the learned knowledge of the experts' visual systems and has potential to be used as an automated and quantitative tool for estimations of mammographic breast density levels.

We derive an easy-to-implement and efficient algorithm for solving multi-label image partitioning problems in the form of the problem addressed by Region Competition. These problems jointly determine a parameter for each of the regions in the partition. Given an estimate of the parameters, a fast approximate solution to the multi-label sub-problem is derived by a global update that uses smoothing and thresholding. The method is empirically validated to be robust to fine details of the image that plague local solutions. Further, in comparison to global methods for the multi-label problem, the method is more efficient and it is easy for a non-specialist to implement. We give sample Matlab code for the multi-label Chan-Vese problem in this paper! Experimental comparison to the state-of-the-art in multi-label solutions to Region Competition shows that our method achieves equal or better accuracy, with the main advantage being speed and ease of implementation.

In this work, we address the multi-label Mumford-Shah problem, i.e., the problem of jointly estimating a partitioning of the domain of the image, and functions defined within regions of the partition. We create algorithms that are efficient, robust to undesirable local minima, and are easy-to-implement. Our algorithms are formulated by slightly modifying the underlying statistical model from which the multi-label Mumford-Shah functional is derived. The advantage of this statistical model is that the underlying variables: the labels and the functions are less coupled than in the original formulation, and the labels can be computed from the functions with more global updates. The resulting algorithms can be tuned to the desired level of locality of the solution: from fully global updates to more local updates. We demonstrate our algorithm on two applications: joint multi-label segmentation and denoising, and joint multi-label motion segmentation and flow estimation. We compare to the state-of-the-art in multi-label Mumford-Shah problems and show that we achieve more promising results.

We propose an optimization scheme that achieves fast yet accurate computation of superpixels from an image. Our optimization is designed to improve the efficiency and robustness for the minimization of a composite energy functional in the expectation–minimization (EM) framework where we restrict the update of an estimate to avoid redundant computations. We consider a superpixel energy formulation that consists of L 2 -norm for the spatial regularity and L 1 -norm for the data fidelity in the demonstration of the robustness of the proposed algorithm. The quantitative and qualitative evaluations indicate that our superpixel algorithm outperforms SLIC and SEEDS algorithms. It is also demonstrated that our algorithm guarantees the convergence with less computational cost by up to 89% on average compared to the SLIC algorithm while preserving the accuracy. Our optimization scheme can be easily extended to other applications in which the alternating minimization is applicable in the EM framework.

We propose a variational approach to unsupervised texture segmentation that depends on very few parameters and is robust to imaging conditions. First, the uneven illumination in the observed image is removed by the proposed image decomposition model that approximates the illumination and well retains the textures and features in the image. Then, from the obtained intrinsic image, we introduce a new data, multiscale local entropy, which is the entropy of each location's neighborhood histogram with various scales. The proposed segmentation model uses multiscale local entropy as data. Together with a length penalizing term, minimizing the energy functional locates the contours so that the local entropy within each region is similar to one another. Since entropy is the only feature, there are very few parameters. Moreover, the segmentation model can be solved by a fast global minimization method. Experimental results on natural images show the proposed method is able to robustly segment various texture patterns with uneven illumination in the original images.

Coronary CT angiography (CCTA) is a high-resolution three-dimensional imaging technique for the evaluation of coronary arteries in suspected or confirmed coronary artery disease (CAD). Coregistration of serial CCTA scans would allow precise superimposition of images obtained at two different points in time, which could aid in recognition of subtle changes and precise monitoring of coronary plaque progression or regression. To this end, the authors aimed at developing a fully automatic nonlinear volume coregistration for longitudinal CCTA scan pairs.The algorithm combines global displacement and local deformation using nonlinear volume coregistration with a volume-preserving constraint. Histogram matching of intensities between two serial scans is performed prior to nonlinear coregistration with dense nonparametric local deformation in which sum of squared differences is used as a similarity measure. The approximate segmentation of coronary arteries obtained from commercially available software provides initial anatomical landmarks for the coregistration algorithm that help localize and emphasize the structure of interest. To avoid possible bias caused by incorrect segmentation, the authors convolve the Gaussian kernel with the segmented binary coronary tree mask and define an extended weighted region of interest. A multiresolution approach is employed to represent coarse-to-fine details of both volumes and the energy function is optimized using a gradient descent method. The authors applied the algorithm in ten paired CCTA datasets (20 scans in total) obtained within 10.7 +/- 5.7 months from each other on a dual source CT scanner to monitor progression of CAD.Serial CCTA coregistration was successful in 9/10 cases as visually confirmed. The global displacement and local deformation of target registration error obtained from four anatomical landmarks were 2.22 +/- 1.15 and 1.56 +/- 0.74 mm, respectively, and the inverse consistency error of local deformation was 0.14 +/- 0.06 mm. The observer variability between two expert observers was 1.31 +/- 0.91 mm.The proposed coregistration algorithm demonstrates potential to accurately register serial CCTA scans, which may allow direct comparison of calcified and noncalcified atherosclerotic plaque changes between the two scans.

This paper presents a novel method for the segmentation of regions of interest in mammograms. The algorithm concurrently delineates the boundaries of the breast boundary, the pectoral muscle, as well as dense regions that include candidate masses. The resulting representation constitutes an analysis of the global structure of the object in the mammogram. We propose a topographic representation called the isocontour map, in which a salient region forms a dense quasi-concentric pattern of contours. The topological and geometrical structure of the image is analyzed using an inclusion tree that is a hierarchical representation of the enclosure relationships between contours. The ?saliency? of a region is measured topologically as the minimum nesting depth. Features at various scales are analyzed in multiscale isocontour maps, and we demonstrate that the multiscale scheme provides an efficient way of achieving better delineations. Experimental results demonstrate that the proposed method has potential as the basis for a prompting system in mammogram mass detection.

Coronary CT angiography (CTA) with multi-slice helical scanners is becoming the integral part of major diagnostic pathways for coronary artery disease. In addition, coronary CTA has demonstrated substantial potential in quantitative coronary plaque characterization. If serial comparisons of plaque progression or regression are to be made, accurate 3D volume registration of these volumes would be particularly useful. In this work, we propose a coronary CTA volume registration of the paired coronary CTA scans using feature-based non-rigid volume registration. We achieve this with a combined registration strategy, which uses the global rigid registration as an initialization, followed by local registration using non-rigid volume registration with a volume preserving constraint. We exploit the extracted coronary trees to help localize and emphasize the region of interest as unnecessary regions hinder registration process, which results in wrong registration result. The extracted binary masks of each coronary tree may not be the same due to initial segmentation errors, which could lead to subsequent bias in the registration process. Therefore we utilize a blur mask which is generated by convolving the Gaussian function with the binary coronary tree mask to include the neighboring vessel region into account. A volume preserving constraint is imposed so that the total volume of the binary mask before and after co-registration remains constant. To validate the proposed method, we perform experiments with data from 3 patients with available serial CT scans (6 scans in total) and measure the distance of anatomical landmarks between the registered serial scans of the same patient.

Automated image segmentation has been playing a critical role in medical image analysis. Recentl, Level Set methods have shown an efficacy and efficiency in various imaging modalities. In this paper, we present a novel segmentation approach to jointly delineate the boundaries of epi- and endocardium of the left ventricle on the Magnetic Resonance Imaging (MRI) images in a variational framework using level sets, which is in great demand as a clinical application in cardiology. One strategy to tackle segmentation under undesirable conditions such as subtle boundaries and occlusions is to exploit prior knowledge which is specific to the object to segment, in this case the knowledge about heart anatomy. While most left ventricle segmentation approaches incorporate a shape prior obtained by a training process from an ensemble of examples, we exploit a novel shape constraint using an implicit shape prior knowledge, which assumes shape similarity between epi- and endocardium allowing a variation under the Gaussian distribution. Our approach does not demand a training procedure which is usually subject to the training examples and is also laborious and time-consuming in generating the shape prior. Instead, we model a shape constraint by a statistical distance between the shape of epi- and endocardium employing signed distance functions. We applied this technique to cardiac MRI data with quantitative evaluations performed on 10 subjects. The experimental results show the robustness and effectiveness of our shape constraint within a Mumford-Shah segmentation model in the segmentation of left ventricle from cardiac MRI images in comparison with the manual segmentation results.