Directional clustering through matrix factorization

This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

CT diagnosis of early stroke : the initial approach to the new CAD tool based on multiscale estimation of ischemia

Background: Computer aided diagnosis (CAD) becomes one of the most important diagnostic tools for urgent states in cerebral stroke and other life-threatening conditions where time plays a crucial role. Routine CT is still diagnostically insufficient in hyperacute stage of stroke that is in the therapeutic window for thrombolytic therapy. Authors present computer assistant of early ischemic stroke diagnosis that supports the radiologic interpretations. A new semantic-visualization system of ischemic symptoms applied to noncontrast, routine CT examination was based on multiscale image processing and diagnostic content estimation. Material/Methods: Evaluation of 95 sets of examinations in patients admitted to a hospital with symptoms suggesting stroke was undertaken by four radiologists from two medical centers unaware of the final clinical findings. All of the consecutive cases were considered as having no CT direct signs of hyperacute ischemia. At the first test stage only the CTs performed at the admission were evaluated independently by radiologists. Next, the same early scans were evaluated again with additional use of multiscale computer-assistant of stroke (MulCAS). Computerized suggestion with increased sensitivity to the subtle image manifestations of cerebral ischemia was constructed as additional view representing estimated diagnostic content with enhanced stroke symptoms synchronized to routine CT data preview. Follow-up CT examinations and clinical features confirmed or excluded the diagnosis of stroke constituting 'gold standard' to verify stroke detection performance. Results: Higher AUC (area under curve) values were found for MulCAS -aided radiological diagnosis for all readers and the differences were statistically significant for random readers-random cases parametric and non-parametric DBM MRMC analysis. Sensitivity and specificity of acute stroke detection for the readers was increased by 30% and 4%, respectively. Conclusions: Routine CT completed with proposed method of computer assisted diagnosis provided noticeable better diagnosis efficiency of acute stroke according to the rates and opinions of all test readers. Further research includes fully automatic detection of hypodense regions to complete assisted indications and formulate the suggestions of stroke cases more objectively. Planned prospective studies will let evaluate more accurately the impact of this CAD tool on diagnosis and further treatment in patients suffered from stroke. It is necessary to determine whether this method is possible to be applied widely

Real-Time Anisotropic Diffusion using Space-Variant Vision

Many computer and robot vision applications require multi-scale image analysis. Classically, this has been accomplished through the use of a linear scale-space, which is constructed by convolution of visual input with Gaussian kernels of varying size (scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian is the Green's function of such a system (Koenderink, 1984). Recently, much work has been focused on the use of a variable conductance function resulting in anisotropic diffusion described by a nonlinear partial differential equation (PDF). The use of anisotropic diffusion with a conductance coefficient which is a decreasing function of the gradient magnitude has been shown to enhance edges, while decreasing some types of noise (Perona and Malik, 1987). Unfortunately, the solution of the anisotropic diffusion equation requires the numerical integration of a nonlinear PDF which is a costly process when carried out on a fixed mesh such as a typical image. In this paper we show that the complex log transformation, variants of which are universally used in mammalian retino-cortical systems, allows the nonlinear diffusion equation to be integrated at exponentially enhanced rates due to the non-uniform mesh spacing inherent in the log domain. The enhanced integration rates, coupled with the intrinsic compression of the complex log transformation, yields a seed increase of between two and three orders of magnitude, providing a means of performing real-time image enhancement using anisotropic diffusion.Office of Naval Research (N00014-95-I-0409

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio