The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website

Constrained Planarity and Augmentation Problems

A clustered graph C=(G,T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G=(V,E). Each vertex m in T corresponds to a subset of the vertices of the graph called ``cluster''. c-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automatic graph drawing. The complexity status of c-planarity testing is unknown. It has been shown by Dahlhaus, Eades, Feng, Cohen that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected. In the first part of the thesis, we provide a polynomial time algorithms for c-planarity testing of specific planar clustered graphs: Graphs for which - all nodes corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T, or graphs in which for each non-connected cluster its super-cluster and all its siblings in T are connected, - for all clusters m G-G(m) is connected. The algorithms are based on the concepts for the subgraph induced planar connectivity augmentation problem, also presented in this thesis. Furthermore, we give some characterizations of c-planar clustered graphs using minors and dual graphs and introduce a c-planar augmentation method. Parts II deals with edge deletion and bimodal crossing minimization. We prove that the maximum planar subgraph problem remains NP-complete even for non-planar graphs without a minor isomorphic to either K(5) or K(3,3), respectively. Further, we investigate the problem of finding a minimum weighted set of edges whose removal results in a graph without minors that are contractible onto a prespecified set of vertices. Finally, we investigate the problem of drawing a directed graph in two dimensions with a minimal number of crossings such that for every node the incoming and outgoing edges are separated consecutively in the cyclic adjacency lists. It turns out that the planarization method can be adapted such that the number of crossings can be expected to grow only slightly for practical instances

SPM: a history.

Karl Friston began the SPM project around 1991. The rest is history

Multigranularity Representations for Human Inter-Actions: Pose, Motion and Intention

Tracking people and their body pose in videos is a central problem in computer vision. Standard tracking representations reason about temporal coherence of detected people and body parts. They have difficulty tracking targets under partial occlusions or rare body poses, where detectors often fail, since the number of training examples is often too small to deal with the exponential variability of such configurations. We propose tracking representations that track and segment people and their body pose in videos by exploiting information at multiple detection and segmentation granularities when available, whole body, parts or point trajectories. Detections and motion estimates provide contradictory information in case of false alarm detections or leaking motion affinities. We consolidate contradictory information via graph steering, an algorithm for simultaneous detection and co-clustering in a two-granularity graph of motion trajectories and detections, that corrects motion leakage between correctly detected objects, while being robust to false alarms or spatially inaccurate detections. We first present a motion segmentation framework that exploits long range motion of point trajectories and large spatial support of image regions. We show resulting video segments adapt to targets under partial occlusions and deformations. Second, we augment motion-based representations with object detection for dealing with motion leakage. We demonstrate how to combine dense optical flow trajectory affinities with repulsions from confident detections to reach a global consensus of detection and tracking in crowded scenes. Third, we study human motion and pose estimation. We segment hard to detect, fast moving body limbs from their surrounding clutter and match them against pose exemplars to detect body pose under fast motion. We employ on-the-fly human body kinematics to improve tracking of body joints under wide deformations. We use motion segmentability of body parts for re-ranking a set of body joint candidate trajectories and jointly infer multi-frame body pose and video segmentation. We show empirically that such multi-granularity tracking representation is worthwhile, obtaining significantly more accurate multi-object tracking and detailed body pose estimation in popular datasets

Wayfinding without Visual Cues: Evaluation of an Interactive Audio Map System

Work completed as part of an MSc by Research project

Ahlfors circle maps and total reality: from Riemann to Rohlin

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known intersection with real algebraic geometry, especially Klein's ortho-symmetric curves via the paradigm of {\it total reality}. This leads to a gallery of pictures quite pleasant to visit of which we have attempted to trace the simplest representatives. This drifted us toward some electrodynamic motions along real circuits of dividing curves perhaps reminiscent of Kepler's planetary motions along ellipses. The ultimate origin of circle maps is of course to be traced back to Riemann's Thesis 1851 as well as his 1857 Nachlass. Apart from an abrupt claim by Teichm\"uller 1941 that everything is to be found in Klein (what we failed to assess on printed evidence), the pivotal contribution belongs to Ahlfors 1950 supplying an existence-proof of circle maps, as well as an analysis of an allied function-theoretic extremal problem. Works by Yamada 1978--2001, Gouma 1998 and Coppens 2011 suggest sharper degree controls than available in Ahlfors' era. Accordingly, our partisan belief is that much remains to be clarified regarding the foundation and optimal control of Ahlfors circle maps. The game of sharp estimation may look narrow-minded "Absch\"atzungsmathematik" alike, yet the philosophical outcome is as usual to contemplate how conformal and algebraic geometry are fighting together for the soul of Riemann surfaces. A second part explores the connection with Hilbert's 16th as envisioned by Rohlin 1978.Comment: 675 pages, 199 figures; extended version of the former text (v.1) by including now Rohlin's theory (v.2

Neurobiological markers for remission and persistence of childhood attention-deficit/hyperactivity disorder

Attention-deficit/hyperactivity disorder (ADHD) is one of the most prevalent neurodevelopmental disorders in children. Symptoms of childhood ADHD persist into adulthood in around 65% of patients, which elevates the risk for a number of adverse outcomes, resulting in substantial individual and societal burden. A neurodevelopmental double dissociation model is proposed based on existing studies in which the early onset of childhood ADHD is suggested to associate with dysfunctional subcortical structures that remain static throughout the lifetime; while diminution of symptoms over development could link to optimal development of prefrontal cortex. Current existing studies only assess basic measures including regional brain activation and connectivity, which have limited capacity to characterize the functional brain as a high performance parallel information processing system, the field lacks systems-level investigations of the structural and functional patterns that significantly contribute to the symptom remission and persistence in adults with childhood ADHD. Furthermore, traditional statistical methods estimate group differences only within a voxel or region of interest (ROI) at a time without having the capacity to explore how ROIs interact in linear and/or non-linear ways, as they quickly become overburdened when attempting to combine predictors and their interactions from high-dimensional imaging data set. This dissertation is the first study to apply ensemble learning techniques (ELT) in multimodal neuroimaging features from a sample of adults with childhood ADHD and controls, who have been clinically followed up since childhood. A total of 36 adult probands who were diagnosed with ADHD combined-type during childhood and 36 matched normal controls (NCs) are involved in this dissertation research. Thirty-six adult probands are further split into 18 remitters (ADHD-R) and 18 persisters (ADHD-P) based on the symptoms in their adulthood from DSM-IV ADHD criteria. Cued attention task-based fMRI, structural MRI, and diffusion tensor imaging data from each individual are analyzed. The high-dimensional neuroimaging features, including pair-wise regional connectivity and global/nodal topological properties of the functional brain network for cue-evoked attention process, regional cortical thickness and surface area, subcortical volume, volume and fractional anisotropy of major white matter fiber tract for each subject are calculated. In addition, all the currently available optimization strategies for ensemble learning techniques (i.e., voting, bagging, boosting and stacking techniques) are tested in a pool of semi-final classification results generated by seven basic classifiers, including K-Nearest Neighbors, support vector machine (SVM), logistic regression, Naïve Bayes, linear discriminant analysis, random forest, and multilayer perceptron. As hypothesized, results indicate that the features of nodal efficiency in right inferior frontal gyrus, right middle frontal (MFG)-inferior parietal (IPL) functional connectivity, and right amygdala volume significantly contributed to accurate discrimination between ADHD probands and controls; higher nodal efficiency of right MFG greatly contributed to inattentive and hyperactive/impulsive symptom remission, while higher right MFG-IPL functional connectivity strongly linked to symptom persistence in adults with childhood ADHD. The utilization of ELTs indicates that the bagging-based ELT with the base model of SVM achieves the best results, with the most significant improvement of the area under the receiver of operating characteristic curve (0.89 for ADHD probands vs. NCs, and 0.9 for ADHD-P vs. ADHD-R). The outcomes of this dissertation research have considerable value for the development of novel interventions that target mechanisms associated with recovery