Hyperbolic Wasserstein Distance for Shape Indexing

Shape space is an active research topic in computer vision and medical imaging fields. The distance defined in a shape space may provide a simple and refined index to represent a unique shape. This work studies the Wasserstein space and proposes a novel framework to compute the Wasserstein distance between general topological surfaces by integrating hyperbolic Ricci flow, hyperbolic harmonic map, and hyperbolic power Voronoi diagram algorithms. The resulting hyperbolic Wasserstein distance can intrinsically measure the similarity between general topological surfaces. Our proposed algorithms are theoretically rigorous and practically efficient. It has the potential to be a powerful tool for 3D shape indexing research. We tested our algorithm with human face classification and Alzheimer's disease (AD) progression tracking studies. Experimental results demonstrated that our work may provide a succinct and effective shape index.

A standardized measurement technique may improve the reliability of measurements of endometrial thickness and volume

OBJECTIVE

To investigate whether standardization of the multiplanar view (SMV) when evaluating the uterus using three-dimensional ultrasonography (3D-US) improves intra- and interobserver reliability and agreement with regard to endometrial measurement.

METHODS

Two-dimensional (2D) and 3D-US was used to measure endometrial thickness by two observers in 30 women undergoing assisted reproduction treatment. Endometrial volume was measured with Virtual Organ Computer-aided AnaLysis (VOCAL(™)) in the longitudinal (A) and coronal (C) planes using an unmodified multiplanar view (UMV) and a standardized multiplanar view (SMV). Measurement reliability was evaluated by intraclass correlation coefficient (ICC) and agreement was examined using Bland-Altman plots with limits of agreement (LoA). The ease of outlining the endometrial-myometrial interface was compared between the A- and C-planes using subjective assessment.

RESULTS

Endometrial volume measurements using the SMV and A-plane were more reliable (intra- and interobserver ICCs, 0.979 and 0.975, respectively) than were measurements of endometrial thickness using 2D-US (intra- and interobserver ICCs, 0.742 and 0.702, respectively) or 3D-US (intra- and interobserver ICCs, 0.890 and 0.784, respectively). The LoAs were narrower for SMV than for UMV. Reliability and agreement were not much different between the A- and C-planes. However the observers agreed that delineating the endometrial-myometrial interface using the A-plane was easier (first and second observer, 50.0 and 46.7%, respectively) or 'comparable' (50 and 53.3%, respectively), but never more difficult than using the C-plane.

CONCLUSIONS

Endometrial volume measurements are more reliable than endometrial thickness measurements and are best performed using SMV and the A-plane.

The Fisher-Markov selector: fast selecting maximally separable feature subset for multiclass classification with applications to high-dimensional data

Selecting features for multiclass classification is a critically important task for pattern recognition and machine learning applications. Especially challenging is selecting an optimal subset of features from high-dimensional data, which typically have many more variables than observations and contain significant noise, missing components, or outliers. Existing methods either cannot handle high-dimensional data efficiently or scalably, or can only obtain local optimum instead of global optimum. Toward the selection of the globally optimal subset of features efficiently, we introduce a new selector--which we call the Fisher-Markov selector--to identify those features that are the most useful in describing essential differences among the possible groups. In particular, in this paper we present a way to represent essential discriminating characteristics together with the sparsity as an optimization objective. With properly identified measures for the sparseness and discriminativeness in possibly high-dimensional settings, we take a systematic approach for optimizing the measures to choose the best feature subset. We use Markov random field optimization techniques to solve the formulated objective functions for simultaneous feature selection. Our results are noncombinatorial, and they can achieve the exact global optimum of the objective function for some special kernels. The method is fast; in particular, it can be linear in the number of features and quadratic in the number of observations. We apply our procedure to a variety of real-world data, including mid--dimensional optical handwritten digit data set and high-dimensional microarray gene expression data sets. The effectiveness of our method is confirmed by experimental results. In pattern recognition and from a model selection viewpoint, our procedure says that it is possible to select the most discriminating subset of variables by solving a very simple unconstrained objective function which in fact can be obtained with an explicit expression.

How best to measure the levator hiatus: evidence for the non-Euclidean nature of the 'plane of minimal dimensions'

OBJECTIVE

To clarify whether the 'plane of minimal dimensions' of the levator hiatus on three-dimensional (3D) ultrasound accurately represents the minimal anatomical transverse hiatal dimension during a Valsalva maneuver.

METHODS

In this retrospective study of 3D transperineal ultrasound and magnetic resonance (MR) imaging, datasets from 19 female participants were used to measure the transverse diameter of the levator hiatus using the plane of minimal dimensions on maximum Valsalva maneuver. The term 'apparent minimal transverse diameter' (aMTD) was used to define the transverse diameter measured using axial ultrasound and comparable axial or coronal MR images. Coronal MR images, using the plane of the vagina as a reference, were also obtained on maximum Valsalva. The transverse diameter measured between the caudal margin of the pubococcygeus/puborectalis on the MR coronal image is denoted by the term 'true minimal transverse diameter' (tMTD). Statistical comparisons between the aMTD and tMTD were made using Student's t-test.

RESULTS

No significant difference was demonstrated between the aMTD as measured by ultrasonography and MRI. However, there were significant differences found between the aMTD measured by both ultrasound and MRI and the tMTD measured on coronal MR images (both P < 0.01), with mean ( ± SD) values of 4.36 ± 0.85, 4.13 ± 1.09 and 3.23 ± 0.49 cm, respectively.

CONCLUSION

This study highlights the complexity and 3D nature of the levator hiatus and pelvic floor muscles. Investigators have previously assumed that the plane of minimal dimensions of the hiatus can be measured in a flat plane, however, the 3D nature of the hiatus means that the true levator hiatus occupies a warped (non-Euclidean) plane. Hiatal measurements on Valsalva may be subject to systematic error if performed in a single section, i.e. using a flat (Euclidean) plane.

Classification of heterogeneous electron microscopic projections into homogeneous subsets

The co-existence of different states of a macromolecular complex in samples used by three-dimensional electron microscopy (3D-EM) constitutes a serious challenge. The single particle method applied directly to such heterogeneous sets is unable to provide useful information about the encountered conformational diversity and produces reconstructions with severely reduced resolution. One approach to solving this problem is to partition heterogeneous projection set into homogeneous components and apply existing reconstruction techniques to each of them. Due to the nature of the projection images and the high noise level present in them, this classification task is difficult. A method is presented to achieve the desired classification by using a novel image similarity measure and solving the corresponding optimization problem. Unlike the majority of competing approaches, the presented method employs unsupervised classification (it does not require any prior knowledge about the objects being classified) and does not involve a 3D reconstruction procedure. We demonstrate a fast implementation of this method, capable of classifying projection sets that originate from 3D-EM. The method's performance is evaluated on synthetically generated data sets produced by projecting 3D objects that resemble biological structures.

Classification of continuous diffraction patterns: A numerical study

The very intense and short pulses of future X-ray free electron lasers may allow the atomic resolution imaging of small, non-periodic objects. Preliminary estimates show that images obtained from single pulses do not contain statistically enough photons to allow successful reconstruction. Therefore multiple exposures of randomly oriented identical replicas have to be taken and the individual images have to be classified according to the object's orientation. The classification has been analytically treated by Huldt et al. [Huldt, G., Szoke, A., Hajdu, J., 2003. J. Struct. Biol. 144, 219.]. In this paper we extend the analytical results with numerical model calculations. This allows us to simulate realistic situations, which we will face in real experiments. We find significant deviations from the analytical expectations, even in the ideal case of spherical particles with random atomic distributions. We introduce a new norm for the individual scattering patterns and describe a criterion to select images belonging to similar orientation, which makes the classification more reliable in practice. We also discuss the effects of particle shape and size, partial orientational ordering, the measurement's resolution and the charge error caused by the Coulomb explosion.

Applying spatial distribution analysis techniques to classification of 3D medical images

OBJECTIVE

The objective of this paper is to classify 3D medical images by analyzing spatial distributions to model and characterize the arrangement of the regions of interest (ROIs) in 3D space.

METHODS AND MATERIAL

Two methods are proposed for facilitating such classification. The first method uses measures of similarity, such as the Mahalanobis distance and the Kullback-Leibler (KL) divergence, to compute the difference between spatial probability distributions of ROIs in an image of a new subject and each of the considered classes represented by historical data (e.g., normal versus disease class). A new subject is predicted to belong to the class corresponding to the most similar dataset. The second method employs the maximum likelihood (ML) principle to predict the class that most likely produced the dataset of the new subject.

RESULTS

The proposed methods have been experimentally evaluated on three datasets: synthetic data (mixtures of Gaussian distributions), realistic lesion-deficit data (generated by a simulator conforming to a clinical study), and functional MRI activation data obtained from a study designed to explore neuroanatomical correlates of semantic processing in Alzheimer's disease (AD).

CONCLUSION

Performed experiments demonstrated that the approaches based on the KL divergence and the ML method provide superior accuracy compared to the Mahalanobis distance. The later technique could still be a method of choice when the distributions differ significantly, since it is faster and less complex. The obtained classification accuracy with errors smaller than 1% supports that useful diagnosis assistance could be achieved assuming sufficiently informative historic data and sufficient information on the new subject.

Boosting accuracy of automated classification of fluorescence microscope images for location proteomics

BACKGROUND

Detailed knowledge of the subcellular location of each expressed protein is critical to a full understanding of its function. Fluorescence microscopy, in combination with methods for fluorescent tagging, is the most suitable current method for proteome-wide determination of subcellular location. Previous work has shown that neural network classifiers can distinguish all major protein subcellular location patterns in both 2D and 3D fluorescence microscope images. Building on these results, we evaluate here new classifiers and features to improve the recognition of protein subcellular location patterns in both 2D and 3D fluorescence microscope images.

RESULTS

We report here a thorough comparison of the performance on this problem of eight different state-of-the-art classification methods, including neural networks, support vector machines with linear, polynomial, radial basis, and exponential radial basis kernel functions, and ensemble methods such as AdaBoost, Bagging, and Mixtures-of-Experts. Ten-fold cross validation was used to evaluate each classifier with various parameters on different Subcellular Location Feature sets representing both 2D and 3D fluorescence microscope images, including new feature sets incorporating features derived from Gabor and Daubechies wavelet transforms. After optimal parameters were chosen for each of the eight classifiers, optimal majority-voting ensemble classifiers were formed for each feature set. Comparison of results for each image for all eight classifiers permits estimation of the lower bound classification error rate for each subcellular pattern, which we interpret to reflect the fraction of cells whose patterns are distorted by mitosis, cell death or acquisition errors. Overall, we obtained statistically significant improvements in classification accuracy over the best previously published results, with the overall error rate being reduced by one-third to one-half and with the average accuracy for single 2D images being higher than 90% for the first time. In particular, the classification accuracy for the easily confused endomembrane compartments (endoplasmic reticulum, Golgi, endosomes, lysosomes) was improved by 5-15%. We achieved further improvements when classification was conducted on image sets rather than on individual cell images.

CONCLUSIONS

The availability of accurate, fast, automated classification systems for protein location patterns in conjunction with high throughput fluorescence microscope imaging techniques enables a new subfield of proteomics, location proteomics. The accuracy and sensitivity of this approach represents an important alternative to low-resolution assignments by curation or sequence-based prediction.

Three-dimensional tracking of coronary arteries from biplane angiographic sequences using parametrically deformable models

A new method for coronary artery tracking in biplane digital subtraction is presented. The dynamic tracking of nonrigid objects from two views is achieved using a generalization of parametrically deformable models. Three-dimensional (3-D) Fourier descriptors used for shape representation are obtained from the two-dimensional (2-D) descriptors of the projections. A new constraint inferred from epipolar geometry is applied to the contour model. Direct 3-D tracking is compared with the classical approach in two steps: independent 2-D tracking in each of the two projection planes; 3-D reconstruction using the epipolar constraint. Convergence quality and accuracy of the 3-D reconstruction are analyzed for several sequences showing different displacement amplitudes, deformation rates and image contrasts.