Clustering is the preferred choice of method in many applications, and support vector clustering (SVC) has proven efficient for clustering noisy and high-dimensional data sets. A method for multiscale support vector clustering is demonstrated, using the recently emerged method for fast calculation of the entire regularization path of the support vector domain description. The method is illustrated on artificially generated examples, and applied for detecting blood vessels from high resolution time series of magnetic resonance imaging data. The obtained results are robust while the need for parameter estimation is reduced, compared to support vector clustering.
Whole-brain morphometry denotes a group of methods with the aim of relating clinical and cognitive measurements
to regions of the brain. Typically, such methods require the statistical analysis of a data set with
many variables (voxels and exogenous variables) paired with few observations (subjects). A common approach
to this ill-posed problem is to analyze each spatial variable separately, dividing the analysis into manageable
subproblems. A disadvantage of this method is that the correlation structure of the spatial variables is not taken
into account. This paper investigates the use of ridge regression to address this issue, allowing for a gradual
introduction of correlation information into the model. We make the connections between ridge regression and
voxel-wise procedures explicit and discuss relations to other statistical methods. Results are given on an in-vivo
data set of deformation based morphometry from a study of cognitive decline in an elderly population.
Myocardial perfusion Magnetic Resonance (MR) imaging has proven to be a powerful method to assess coronary artery diseases. The current work presents a novel approach to the analysis of registered sequences of myocardial perfusion MR images. A previously reported active appearance model (AAM) based segmentation and registration of the myocardium provided pixel-wise signal intensity curves that were analyzed using the Support Vector Domain Description (SVDD). In contrast to normal SVDD, the entire regularization path was calculated and used to calculate a generalized distance, which is used to discriminate between ischemic and healthy tissue. The results corresponded well to the ischemic segments found by assessment of the three common perfusion parameters; maximum upslope, peak and time-to-peak obtained pixel-wise.
Principal component analysis (PCA) is a widely used tool in medical image analysis for data reduction, model building, and data understanding and exploration. While PCA is a holistic approach where each new variable is a linear combination of all original variables, sparse PCA (SPCA) aims at producing easily interpreted models through sparse loadings, i.e. each new variable is a linear combination of a subset of the original variables. One of the aims of using SPCA is the possible separation of the results into isolated and easily identifiable effects. This article introduces SPCA for shape analysis in medicine. Results for three different data sets are given in relation to standard PCA and sparse PCA by simple thresholding of small loadings. Focus is on a recent algorithm for computing sparse principal components, but a review of other approaches is supplied as well. The SPCA algorithm has been implemented using Matlab and is available for download.
The general behavior of the algorithm is investigated, and strengths and weaknesses are discussed. The original report on the SPCA algorithm argues that the ordering of modes is not an issue. We disagree on this point and propose several approaches to establish sensible orderings. A method that orders modes by decreasing variance and maximizes the sum of variances for all modes is presented and investigated in detail.
In the past decade, statistical shape modeling has been widely popularized in the medical image analysis community. Predominantly, principal component analysis (PCA) has been employed to model biological shape variability. Here, a reparameterization with orthogonal basis vectors is obtained such that the variance of the input data is maximized. This property drives models toward global shape deformations and has been highly successful in fitting shape models to new images. However, recent literature has indicated that this uncorrelated basis may be suboptimal for exploratory analyses and disease characterization. This paper explores the orthomax class of statistical methods for transforming variable loadings into a simple structure which is more easily interpreted by favoring sparsity. Further, we introduce these transformations into a particular framework traditionally based on PCA; the Active Appearance Models (AAMs). We note that the orthomax transformations are independent of domain dimensionality (2D/3D etc.) and spatial structure. Decompositions of both shape and texture models are carried out. Further, the issue of component ordering is treated by establishing a set of relevant criteria. Experimental results are given on chest radiographs, magnetic resonance images of the brain, and face images. Since pathologies are typically spatially localized, either with respect to shape or texture, we anticipate many medical applications where sparse parameterizations are preferable to the conventional global PCA approach.
The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has its benefits and is suitable for describing a range of medical structures in two dimensions. Delineations in medical applications often consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss a Euclidean alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding starting points, the alignment of one shape onto another consists of a single expression. If the starting points are arbitrary, we present a simple algorithm to bring a set of shapes into correspondence.
Results are given for three different data sets; 62 outlines of the corpus callosum brain structure, 61 outlines of the brain ventricles, and 50 outlines of the right lung. The results show that even though starting points, translations, rotations and scales have been randomized, the alignment succeeds in all cases.
As an application of the proposed method, we show how high-quality shape models represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects using the minimum description length criterion, producing ample correspondences. Results on this are also presented for all three data sets.
This paper describes methods for automatic localization of the mid-sagittal plane (MSP) and mid-sagittal surface (MSS). The data used is a subset of the Leukoaraiosis And DISability (LADIS) study consisting of three-dimensional magnetic resonance brain data from 62 elderly subjects (age 66 to 84 years). Traditionally, the mid-sagittal plane is localized by global measures. However, this approach fails when the partitioning plane between the brain hemispheres does not coincide with the symmetry plane of the head. We instead propose to use a sparse set of profiles in the plane normal direction and maximize the local symmetry around these using a general-purpose optimizer. The plane is parameterized by azimuth and elevation angles along with the distance to the origin in the normal direction. This approach leads to solutions confirmed as the optimal MSP in 98 percent of the subjects. Despite the name, the mid-sagittal plane is not always planar, but a curved surface resulting in poor partitioning of the brain hemispheres. To account for this, this paper also investigates an optimization strategy which fits a thin-plate spline surface to the brain data using a robust least median of squares estimator. Albeit computationally more expensive, mid-sagittal surface fitting demonstrated convincingly better partitioning of curved brains into cerebral hemispheres.