Expectation maximization strategies for multi-atlas multi-label segmentation.

Atlas-based segmentation is a powerful method for automatic structural segmentation of several sub-structures in many organs. However, such an approach has been very scarcely used in the context of muscle segmentation, and so far no study has assessed such a method for the automatic delineation of individual muscles of the quadriceps femoris (QF). In the present study, we have evaluated a fully automated multi-atlas method and a semi-automated single-atlas method for the segmentation and volume quantification of the four muscles of the QF and for the QF as a whole. The study was conducted in 32 young healthy males, using high-resolution magnetic resonance images (MRI) of the thigh. The multi-atlas-based segmentation method was conducted in 25 subjects. Different non-linear registration approaches based on free-form deformable (FFD) and symmetric diffeomorphic normalization algorithms (SyN) were assessed. Optimal parameters of two fusion methods, i.e., STAPLE and STEPS, were determined on the basis of the highest Dice similarity index (DSI) considering manual segmentation (MSeg) as the ground truth. Validation and reproducibility of this pipeline were determined using another MRI dataset recorded in seven healthy male subjects on the basis of additional metrics such as the muscle volume similarity values, intraclass coefficient, and coefficient of variation. Both non-linear registration methods (FFD and SyN) were also evaluated as part of a single-atlas strategy in order to assess longitudinal muscle volume measurements. The multi- and the single-atlas approaches were compared for the segmentation and the volume quantification of the four muscles of the QF and for the QF as a whole. Considering each muscle of the QF, the DSI of the multi-atlas-based approach was high 0.87±0.11 and the best results were obtained with the combination of two deformation fields resulting from the SyN registration method and the STEPS fusion algorithm. The optimal variables for FFD and SyN registration methods were four templates and a kernel standard deviation ranging between 5 and 8. The segmentation process using a single-atlas-based method was more robust with DSI values higher than 0.9. From the vantage of muscle volume measurements, the multi-atlas-based strategy provided acceptable results regarding the QF muscle as a whole but highly variable results regarding individual muscle. On the contrary, the performance of the single-atlas-based pipeline for individual muscles was highly comparable to the MSeg, thereby indicating that this method would be adequate for longitudinal tracking of muscle volume changes in healthy subjects. In the present study, we demonstrated that both multi-atlas and single-atlas approaches were relevant for the segmentation of individual muscles of the QF in healthy subjects. Considering muscle volume measurements, the single-atlas method provided promising perspectives regarding longitudinal quantification of individual muscle volumes.

Neuroimaging provides great utility in complex spinal surgeries, particularly when anatomical geometry is distorted by pathology (tumour, degeneration, etc.). Spinal cord MRI diffusion tractography can be used to generate streamlines; however, it is unclear how well they correspond with white matter tract locations along the cord microstructure. The goal of this work was to evaluate the spatial correspondence of DTI tractography with anatomical MRI in healthy anatomy (where anatomical locations can be well defined in T1-weighted images). Ten healthy volunteers were scanned on a 3T system. T1-weighted (1 × 1 × 1 mm) and diffusion-weighted images (EPI readout, 2 × 2 × 2 mm, 30 gradient directions) were acquired and subsequently registered (Spinal Cord Toolbox (SCT)). Atlas-based (SCT) anatomic label maps of the left and right lateral corticospinal tracts were identified for each vertebral region (C2-C6) from T1 images. Tractography streamlines were generated with a customized approach, enabling seeding of specific spinal tract regions corresponding to individual vertebral levels. Spatial correspondence of generated fibre streamlines with anatomic tract segmentations was compared in unseeded regions of interest (ROIs). Spatial correspondence of the lateral corticospinal tract streamlines was good over a single vertebral ROI (Dice's similarity coefficient (DSC) = 0.75 ± 0.08, Hausdorff distance = 1.08 ± 0.17 mm). Over larger ROI, fair agreement between tractography and anatomical labels was achieved (two levels: DSC = 0.67 ± 0.13, three levels: DSC = 0.52 ± 0.19). DTI tractography produced good spatial correspondence with anatomic white matter tracts, superior to the agreement between multiple manual tract segmentations (DSC ~ 0.5). This supports further development of spinal cord tractography for computer-assisted neurosurgery.

The honey bee is the most essential pollinator and a key contributor to the natural ecosystem. There are numerous ways for thousands of bees in a hive to communicate with one another. Individual trajectories and social interactions are thus complex behavioral features that can provide valuable information for an ecological study. To study honey bee behavior, the key challenges that have resulted from unreliable studies include complexity (high density of similar objects, small objects, and occlusion), the variety of background scenes, the dynamism of individual bee movements, and the similarity between the bee body and the background in the beehive. This study investigated the tracking of individual bees in a beehive environment using a deep learning approach and a Kalman filter. Detection of multiple bees and individual object segmentation were performed using Mask R-CNN with a ResNet-101 backbone network. Subsequently, the Kalman filter was employed for tracking multiple bees by tracking the body of each bee across a sequence of image frames. Three metrics were used to assess the proposed framework: mean average precision (mAP) for multiple-object detection and segmentation tasks, CLEAR MOT for multiple object tracking tasks, and MOTS for multiple object tracking and segmentation tasks. For CLEAR MOT and MOTS metrics, accuracy (MOTA and MOTSA) and precision (MOTP and MOTSP) are considered. By employing videos from a custom-designed observation beehive, recorded at a frame rate of 30 frames per second (fps) and utilizing a continuous frame rate of 10 fps as input data, our system displayed impressive performance. It yielded satisfactory outcomes for tasks involving segmentation and tracking of multiple instances of bee behavior. For the multiple-object segmentation task based on Mask R-CNN, we achieved a 0.85 mAP. For the multiple-object-tracking task with the Kalman filter, we achieved 77.48% MOTA, 79.79% MOTSP, and 79.56% recall. For the overall system for multiple-object tracking and segmentation tasks, we achieved 77.00% MOTSA, 75.60% MOTSP, and 80.30% recall.

This paper proposes a fully automated atlas-based pancreas segmentation method from CT volumes utilizing atlas localization by regression forest and atlas generation using blood vessel information. Previous probabilistic atlas-based pancreas segmentation methods cannot deal with spatial variations that are commonly found in the pancreas well. Also, shape variations are not represented by an averaged atlas. We propose a fully automated pancreas segmentation method that deals with two types of variations mentioned above. The position and size of the pancreas is estimated using a regression forest technique. After localization, a patient-specific probabilistic atlas is generated based on a new image similarity that reflects the blood vessel position and direction information around the pancreas. We segment it using the EM algorithm with the atlas as prior followed by the graph-cut. In evaluation results using 147 CT volumes, the Jaccard index and the Dice overlap of the proposed method were 62.1% and 75.1%, respectively. Although we automated all of the segmentation processes, segmentation results were superior to the other state-of-the-art methods in the Dice overlap.

The Fuzzy C Means (FCM) and Expectation Maximization (EM) algorithms are the most prevalent methods for automatic segmentation of MR brain images into three classes Gray Matter (GM), White Matter (WM) and Cerebrospinal Fluid (CSF). The major difficulties associated with these conventional methods for MR brain image segmentation are the Intensity Non-uniformity (INU) and noise. In this paper, EM and FCM with spatial information and bias correction are proposed to overcome these effects. The spatial information is incorporated by convolving the posterior probability during E-Step of the EM algorithm with mean filter. Also, a method of pixel re-labeling is included to improve the segmentation accuracy. The proposed method is validated by extensive experiments on both simulated and real brain images from standard database. Quantitative and qualitative results depict that the method is superior to the conventional methods by around 25% and over the state-of-the art method by 8%.

To support real-time tracking of objects in video sequences, there has been considerable effort directed at developing optical flow and general motion-based image segmentation algorithms. The goal is to segment multiple moving objects in the image based on their relative motion. This task can be complicated by the presence of lighting variations. Furthermore, a combination of multiple motions and complex lighting effects can lead to dramatic image variations that may not be adequately accounted for by a single motion-based segmentation algorithm. We propose to fuse the results of multiple motion segmentation algorithms to improve the system robustness. Our approach uses the expectation maximization (EM) algorithm as a fusion engine. It also uses principal components analysis (PCA) to perform dimensionality reduction to improve the performance of the EM algorithm and reduce the processing burden. The performance of the proposed fusion algorithm has been demonstrated in the smart airbag application of monitoring occupants in a moving automobile to determine if they are too close to the instrument panel (airbag). Through fusion of the outputs of multiple algorithms we are able to reduce the percentage of pixels missed on the target by 35.

In this work, an expectation maximization (EM) algorithm is derived for maximum likelihood estimation of the autocorrelation function of a linear distortion channel as well as the level of additive noise, under the assumption that the source signal comes from a mixture of Gaussian sources. To facilitate parameter initialization in the EM algorithm, a correlation-matching based estimation algorithm is developed for the channel autocorrelation function. The proposed EM algorithm was evaluated on speech-derived simulated data of multiple autoregressive Gaussian sources and real speech of isolated digits under signal-to-noise ratios (SNRs) of 20 dB down to 0 dB. The algorithm is shown to produce convergent estimation results as well as estimates of signal statistics that lead to significantly improved classification accuracy under additive and convolutive noise conditions.

The development of segmentation algorithms for different anatomical structures and imaging protocols is an important task in medical image processing. The validation of these methods, however, is often treated as a subordinate task. Since manual delineations, which are widely used as a surrogate for the ground truth, exhibit an inherent uncertainty, it is preferable to use multiple reference segmentations for an objective validation. This requires a consistent framework that should fulfill three criteria: 1) it should treat all reference masks equally a priori and not demand consensus between the experts; 2) it should evaluate the algorithmic performance in relation to the inter-reference variability, i.e., be more tolerant where the experts disagree about the true segmentation; 3) it should produce results that are comparable for different test data. We show why current state-of-the-art frameworks as the one used at several MICCAI segmentation challenges do not fulfill these criteria and propose a new validation methodology. A score is computed in an adaptive way for each individual segmentation problem, using a combination of volume- and surface-based comparison metrics. These are transformed into the score by relating them to the variability between the reference masks which can be measured by comparing the masks with each other or with an estimated ground truth. We present examples from a study on liver tumor segmentation in CT scans where our score shows a more adequate assessment of the segmentation results than the MICCAI framework.

BackgroundFlexural three-point bending tests are useful for characterizing the mechanical properties of plant stems. These tests can be performed with minimal sample preparation, thus allowing tests to be performed relatively quickly. The best-practice for such tests involves long spans with supports and load placed at nodes. This approach typically provides only one flexural stiffness measurement per specimen. However, by combining flexural tests with analytic equations, it is possible to solve for the mechanical characteristics of individual stem segments.ResultsA method is presented for using flexural tests to obtain estimates of flexural stiffness of individual segments. This method pairs physical test data with analytic models to obtain a system of equations. The solution of this system of equations provides values of flexural stiffness for individual stalk segments. Uncertainty in the solved values for flexural stiffness were found to be strongly dependent upon measurement errors. Row-wise scaling of the system of equations reduced the influence of measurement error. Of many possible test combinations, the most advantageous set of tests for performing these measurements were identified. Relationships between measurement uncertainty and solution uncertainty were provided for two different testing methods.ConclusionsThe methods presented in this paper can be used to measure the axial variation in flexural stiffness of plant stem segments. However, care must be taken to account for the influence of measurement error as the individual segment method amplifies measurement error. An alternative method involving aggregate flexural stiffness values does not amplify measurement error, but provides lower spatial resolution.

Design and analysis of direction of arrival using hybrid expectation-maximization and MUSIC for wireless communication

Many diseases show dichotomous phenotypic variation but do not follow a simple Mendelian pattern of inheritance. Variances of these binary diseases are presumably controlled by multiple loci and environmental variants. A least-squares method has been developed for mapping such complex disease loci by treating the binary phenotypes (0 and 1) as if they were continuous. However, the least-squares method is not recommended because of its ad hoc nature. Maximum Likelihood (ML) and Bayesian methods have also been developed for binary disease mapping by incorporating the discrete nature of the phenotypic distribution. In the ML analysis, the likelihood function is usually maximized using some complicated maximization algorithms (e.g. the Newton-Raphson or the simplex algorithm). Under the threshold model of binary disease, we develop an Expectation Maximization (EM) algorithm to solve for the maximum likelihood estimates (MLEs). The new EM algorithm is developed by treating both the unobserved genotype and the disease liability as missing values. As a result, the EM iteration equations have the same form as the normal equation system in linear regression. The EM algorithm is further modified to take into account sexual dimorphism in the linkage maps. Applying the EM-implemented ML method to a four-way-cross mouse family, we detected two regions on the fourth chromosome that have evidence of QTLs controlling the segregation of fibrosarcoma, a form of connective tissue cancer. The two QTLs explain 50-60% of the variance in the disease liability. We also applied a Bayesian method previously developed (modified to take into account sex-specific maps) to this data set and detected one additional QTL on chromosome 13 that explains another 26% of the variance of the disease liability. All the QTLs detected primarily show dominance effects.

Atlas-based segmentation is a popular generic technique for automated delineation of structures in volumetric data sets. Several studies have shown that multi-atlas based segmentation methods outperform schemes that use only a single atlas, but running multiple registrations on large volumetric data is too time-consuming for routine clinical use. We propose a generally applicable adaptive local multi-atlas segmentation method (ALMAS) that locally decides how many and which atlases are needed to segment a target image. Only the selected parts of atlases are registered. The method is iterative and automatically stops when no further improvement is expected. ALMAS was applied to segmentation of the heart on chest CT scans and compared to three existing atlas-based methods. It performed significantly better than single-atlas methods and as good as multi-atlas methods at a much lower computational cost.

This paper makes two contributions: the first is the proposal of a new model-The associative hierarchical random field (AHRF), and a novel algorithm for its optimization; the second is the application of this model to the problem of semantic segmentation. Most methods for semantic segmentation are formulated as a labeling problem for variables that might correspond to either pixels or segments such as super-pixels. It is well known that the generation of super pixel segmentations is not unique. This has motivated many researchers to use multiple super pixel segmentations for problems such as semantic segmentation or single view reconstruction. These super-pixels have not yet been combined in a principled manner, this is a difficult problem, as they may overlap, or be nested in such a way that the segmentations form a segmentation tree. Our new hierarchical random field model allows information from all of the multiple segmentations to contribute to a global energy. MAP inference in this model can be performed efficiently using powerful graph cut based move making algorithms. Our framework generalizes much of the previous work based on pixels or segments, and the resulting labelings can be viewed both as a detailed segmentation at the pixel level, or at the other extreme, as a segment selector that pieces together a solution like a jigsaw, selecting the best segments from different segmentations as pieces. We evaluate its performance on some of the most challenging data sets for object class segmentation, and show that this ability to perform inference using multiple overlapping segmentations leads to state-of-the-art results.

Segmentation of vegetation LiDAR point clouds is an important method for obtaining individual tree structure parameters. The current individual tree segmentation methods are mainly for airborne LiDAR point clouds, which use elevation information to form a grid map for segmentation, or use canopy vertices as seed points for clustering. Side-view LiDAR (vehicle LiDAR and hand-held LiDAR) can acquire more information about the lower layer of trees, but it is a challenge to perform the individual tree segmentation because the structure of side-view LiDAR point clouds is more complex. This paper proposes an individual tree segmentation method called Shadow-cut to extract the contours of the street tree point cloud. Firstly, we separated the region of the trees using the binary classifier (e.g., support vector machine) based on point cloud geometric features. Then, the optimal projection of the 3D point clouds to the 2D image is calculated and the optimal projection is the case where the pixels of the individual tree image overlap the least. Finally, after using the image segmentation algorithm to extract the tree edges in the 2D image, the corresponding 3D individual tree point cloud contours are matched with the pixels of individual tree edges in the 2D image. We conducted experiments with the proposed method on LiDAR data of urban street trees, and the correctness, completeness, and quality of the proposed individual tree segmentation method reached 91.67%, 85.33%, and 79.19%, which were superior to the CHM-based method by 2.70%, 6.19%, and 7.12%, respectively. The results show that this method is a practical and effective solution for individual tree segmentation in the LiDAR point clouds of street trees.

Recently, the expectation maximisation (EM) algorithm has been applied to a lot of problems of estimating parameters and learning and there are some theoretical analyses, however, prediction error is not mentioned yet. We are trying to evaluate the learning error when a machine learns with the EM algorithm and the probability distribution of the estimated parameters is mentioned here as the first step for the learning curve.