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

Mathematical Foundations of Machine Learning (hybrid meeting)

Machine learning has achieved remarkable successes in various applications, but there is wide agreement that a mathematical theory for deep learning is missing. Recently, some first mathematical results have been derived in different areas such as mathematical statistics and statistical learning. Any mathematical theory of machine learning will have to combine tools from different fields such as nonparametric statistics, high-dimensional statistics, empirical process theory and approximation theory. The main objective of the workshop was to bring together leading researchers contributing to the mathematics of machine learning. A focus of the workshop was on theory for deep neural networks. Mathematically speaking, neural networks define function classes with a rich mathematical structure that are extremely difficult to analyze because of non-linearity in the parameters. Until very recently, most existing theoretical results could not cope with many of the distinctive characteristics of deep networks such as multiple hidden layers or the ReLU activation function. Other topics of the workshop are procedures for quantifying the uncertainty of machine learning methods and the mathematics of data privacy

Robust object detection under partial occlusion

This thesis focuses on the problem of object detection under partial occlusion in complex scenes through exploring new bottom-up and top-down detection models to cope with object discontinuities and ambiguity caused by partial occlusion and allow for a more robust and adaptive detection of varied objects from different scenes

IMPROVING EFFICIENCY AND SCALABILITY IN VISUAL SURVEILLANCE APPLICATIONS

We present four contributions to visual surveillance: (a) an action recognition method based on the characteristics of human motion in image space; (b) a study of the strengths of five regression techniques for monocular pose estimation that highlights the advantages of kernel PLS; (c) a learning-based method for detecting objects carried by humans requiring minimal annotation; (d) an interactive video segmentation system that reduces supervision by using occlusion and long term spatio-temporal structure information. We propose a representation for human actions that is based solely on motion information and that leverages the characteristics of human movement in the image space. The representation is best suited to visual surveillance settings in which the actions of interest are highly constrained, but also works on more general problems if the actions are ballistic in nature. Our computationally efficient representation achieves good recognition performance on both a commonly used action recognition dataset and on a dataset we collected to simulate a checkout counter. We study discriminative methods for 3D human pose estimation from single images, which build a map from image features to pose. The main difficulty with these methods is the insufficiency of training data due to the high dimensionality of the pose space. However, real datasets can be augmented with data from character animation software, so the scalability of existing approaches becomes important. We argue that Kernel Partial Least Squares approximates Gaussian Process regression robustly, enabling the use of larger datasets, and we show in experiments that kPLS outperforms two state-of-the-art methods based on GP. The high variability in the appearance of carried objects suggests using their relation to the human silhouette to detect them. We adopt a generate-and-test approach that produces candidate regions from protrusion, color contrast and occlusion boundary cues and then filters them with a kernel SVM classifier on context features. Our method exceeds state of the art accuracy and has good generalization capability. We also propose a Multiple Instance Learning framework for the classifier that reduces annotation effort by two orders of magnitude while maintaining comparable accuracy. Finally, we present an interactive video segmentation system that trades off a small amount of segmentation quality for significantly less supervision than necessary in systems in the literature. While applications like video editing could not directly use the output of our system, reasoning about the trajectories of objects in a scene or learning coarse appearance models is still possible. The unsupervised segmentation component at the base of our system effectively employs occlusion boundary cues and achieves competitive results on an unsupervised segmentation dataset. On videos used to evaluate interactive methods, our system requires less interaction time than others, does not rely on appearance information and can extract multiple objects at the same time