Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output

Multitemporal Fusion for the Detection of Static Spatial Patterns in Multispectral Satellite Images--with Application to Archaeological Survey

We evaluate and further develop a multitemporal fusion strategy that we use to detect the location of ancient settlement sites in the Near East and to map their distribution, a spatial pattern that remains static over time. For each ASTER images that has been acquired in our survey area in north-eastern Syria, we use a pattern classification strategy to map locations with a multispectral signal similar to the one from (few) known archaeological sites nearby. We obtain maps indicating the presence of anthrosol – soils that formed in the location of ancient settlements and that have a distinct spectral pattern under certain environmental conditions – and find that pooling the probability maps from all available time points reduces the variance of the spatial anthrosol pattern significantly. Removing biased classification maps – i.e. those that rank last when comparing the probability maps with the (limited) ground truth we have – reduces the overall prediction error even further, and we estimate optimal weights for each image using a non-negative least squares regression strategy. The ranking and pooling strategy approach we propose in this study shows a significant improvement over the plain averaging of anthrosol probability maps that we used in an earlier attempt to map archaeological sites in a 20,000 km2 area in northern Mesopotamia, and we expect it to work well in other surveying tasks that aim at mapping static surface patterns with limited ground truth in long series of multispectral images.Anthropolog

Robust techniques and applications in fuzzy clustering

This dissertation addresses issues central to frizzy classification. The issue of sensitivity to noise and outliers of least squares minimization based clustering techniques, such as Fuzzy c-Means (FCM) and its variants is addressed. In this work, two novel and robust clustering schemes are presented and analyzed in detail. They approach the problem of robustness from different perspectives. The first scheme scales down the FCM memberships of data points based on the distance of the points from the cluster centers. Scaling done on outliers reduces their membership in true clusters. This scheme, known as the Mega-clustering, defines a conceptual mega-cluster which is a collective cluster of all data points but views outliers and good points differently (as opposed to the concept of Dave\u27s Noise cluster). The scheme is presented and validated with experiments and similarities with Noise Clustering (NC) are also presented. The other scheme is based on the feasible solution algorithm that implements the Least Trimmed Squares (LTS) estimator. The LTS estimator is known to be resistant to noise and has a high breakdown point. The feasible solution approach also guarantees convergence of the solution set to a global optima. Experiments show the practicability of the proposed schemes in terms of computational requirements and in the attractiveness of their simplistic frameworks. The issue of validation of clustering results has often received less attention than clustering itself. Fuzzy and non-fuzzy cluster validation schemes are reviewed and a novel methodology for cluster validity using a test for random position hypothesis is developed. The random position hypothesis is tested against an alternative clustered hypothesis on every cluster produced by the partitioning algorithm. The Hopkins statistic is used as a basis to accept or reject the random position hypothesis, which is also the null hypothesis in this case. The Hopkins statistic is known to be a fair estimator of randomness in a data set. The concept is borrowed from the clustering tendency domain and its applicability to validating clusters is shown here. A unique feature selection procedure for use with large molecular conformational datasets with high dimensionality is also developed. The intelligent feature extraction scheme not only helps in reducing dimensionality of the feature space but also helps in eliminating contentious issues such as the ones associated with labeling of symmetric atoms in the molecule. The feature vector is converted to a proximity matrix, and is used as an input to the relational fuzzy clustering (FRC) algorithm with very promising results. Results are also validated using several cluster validity measures from literature. Another application of fuzzy clustering considered here is image segmentation. Image analysis on extremely noisy images is carried out as a precursor to the development of an automated real time condition state monitoring system for underground pipelines. A two-stage FCM with intelligent feature selection is implemented as the segmentation procedure and results on a test image are presented. A conceptual framework for automated condition state assessment is also developed

Isometry Invariant Shape Priors for Variational Image Segmentation

Variational methods play a fundamental role in mathematical image analysis as a bridge between models and algorithms. A major challenge is to formulate a given model as a feasible optimization problem. There has been a huge leap in that respect concerning local data models in the framework of convex relaxation. But non-local concepts such as the shape of a sought-after object are still difficult to implement. In this thesis we study mathematical representations for shapes and develop shape prior functionals for object segmentation based thereon. A particular focus is set on the isometry invariance of the functionals and the compatibility with existing convex functionals for image labelling. Optimal transport is used as a central modelling and computational tool to compute registrations between different shapes as a basis for a shape similarity measure. This point of view leads to a link between the two somewhat dual representations of a shape by the region it occupies and its outline, allowing to combine their respective strengths. Naively the computational complexity implied by the derived functionals is unfeasible. Therefore suitable hierarchical optimization methods are developed

Machine Learning for Instance Segmentation

Volumetric Electron Microscopy images can be used for connectomics, the study of brain connectivity at the cellular level. A prerequisite for this inquiry is the automatic identification of neural cells, which requires machine learning algorithms and in particular efficient image segmentation algorithms. In this thesis, we develop new algorithms for this task. In the first part we provide, for the first time in this field, a method for training a neural network to predict optimal input data for a watershed algorithm. We demonstrate its superior performance compared to other segmentation methods of its category. In the second part, we develop an efficient watershed-based algorithm for weighted graph partitioning, the \emph{Mutex Watershed}, which uses negative edge-weights for the first time. We show that it is intimately related to the multicut and has a cutting edge performance on a connectomics challenge. Our algorithm is currently used by the leaders of two connectomics challenges. Finally, motivated by inpainting neural networks, we create a method to learn the graph weights without any supervision