Heike Leitte

Rules and Self-Organizing Properties of Post-embryonic Plant Organ Cell Division Patterns

Plants form new organs with patterned tissue organization throughout their lifespan. It is unknown whether this robust post-embryonic organ formation results from stereotypic dynamic processes, in which the arrangement of cells follows rigid rules. Here, we combine modeling with empirical observations of whole-organ development to identify the principles governing lateral root formation in Arabidopsis. Lateral roots derive from a small pool of founder cells in which some take a dominant role as seen by lineage tracing. The first division of the founders is asymmetric, tightly regulated, and determines the formation of a layered structure. Whereas the pattern of subsequent cell divisions is not stereotypic between different samples, it is characterized by a regular switch in division plane orientation. This switch is also necessary for the appearance of patterned layers as a result of the apical growth of the primordium. Our data suggest that lateral root morphogenesis is based on a limited set of rules. They determine cell growth and division orientation. The organ-level coupling of the cell behavior ensures the emergence of the lateral roots characteristic features. We propose that self-organizing, non-deterministic modes of development account for the robustness of plant organ morphogenesis.

A discrete chain graph model for 3d+t cell tracking with high misdetection robustness

Tracking by assignment is well suited for tracking a varying number of divisible cells, but suffers from false positive detections. We reformulate tracking by assignment as a chain graph---a mixed directed-undirected probabilistic graphical model---and obtain a tracking simultaneously over all time steps from the maximum a-posteriori configuration. The model is evaluated on two challenging four-dimensional data sets from developmental biology. Compared to previous work, we obtain improved tracks due to an increased robustness against false positive detections and the incorporation of temporal domain knowledge.

State of the Art Report on Video-Based Graphics and Video Visualization

In recent years, a collection of new techniques which deal with video as input data, emerged in computer graphics and visualization. In this survey, we report the state of the art in video‐based graphics and video visualization. We provide a review of techniques for making photo‐realistic or artistic computer‐generated imagery from videos, as well as methods for creating summary and/or abstract visual representations to reveal important features and events in videos. We provide a new taxonomy to categorize the concepts and techniques in this newly emerged body of knowledge. To support this review, we also give a concise overview of the major advances in automated video analysis, as some techniques in this field (e.g. feature extraction, detection, tracking and so on) have been featured in video‐based modelling and rendering pipelines for graphics and visualization.

Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures

The extraction of significant structures in arbitrary high-dimensional data sets is a challenging task. Moreover, classifying data points as noise in order to reduce a data set bears special relevance for many application domains. Standard methods such as clustering serve to reduce problem complexity by providing the user with classes of similar entities. However, they usually do not highlight relations between different entities and require a stopping criterion, e.g. the number of clusters to be detected. In this paper, we present a visualization pipeline based on recent advancements in algebraic topology. More precisely, we employ methods from persistent homology that enable topological data analysis on high-dimensional data sets. Our pipeline inherently copes with noisy data and data sets of arbitrary dimensions. It extracts central structures of a data set in a hierarchical manner by using a persistence-based filtering algorithm that is theoretically well-founded. We furthermore introduce persistence rings, a novel visualization technique for a class of topological features-the persistence intervals-of large data sets. Persistence rings provide a unique topological signature of a data set, which helps in recognizing similarities. In addition, we provide interactive visualization techniques that assist the user in evaluating the parameter space of our method in order to extract relevant structures. We describe and evaluate our analysis pipeline by means of two very distinct classes of data sets: First, a class of synthetic data sets containing topological objects is employed to highlight the interaction capabilities of our method. Second, in order to affirm the utility of our technique, we analyse a class of high-dimensional real-world data sets arising from current research in cultural heritage.

A Survey of Topology-based Methods in Visualization

This paper presents the state of the art in the area of topology‐based visualization. It describes the process and results of an extensive annotation for generating a definition and terminology for the field. The terminology enabled a typology for topological models which is used to organize research results and the state of the art. Our report discusses relations among topological models and for each model describes research results for the computation, simplification, visualization, and application. The paper identifies themes common to subfields, current frontiers, and unexplored territory in this research area.

Persistent homology for the evaluation of dimensionality reduction schemes

High‐dimensional data sets are a prevalent occurrence in many application domains. This data is commonly visualized using dimensionality reduction (DR) methods. DR methods provide e.g. a two‐dimensional embedding of the abstract data that retains relevant high‐dimensional characteristics such as local distances between data points. Since the amount of DR algorithms from which users may choose is steadily increasing, assessing their quality becomes more and more important. We present a novel technique to quantify and compare the quality of DR algorithms that is based on persistent homology. An inherent beneficial property of persistent homology is its robustness against noise which makes it well suited for real world data. Our pipeline informs about the best DR technique for a given data set and chosen metric (e.g. preservation of local distances) and provides knowledge about the local quality of an embedding, thereby helping users understand the shortcomings of the selected DR method. The utility of our method is demonstrated using application data from multiple domains and a variety of commonly used DR methods.

Structural Analysis of Multivariate Point Clouds Using Simplicial Chains

Topological and geometrical methods constitute common tools for the analysis of high‐dimensional scientific data sets. Geometrical methods such as projection algorithms focus on preserving distances in the data set. Topological methods such as contour trees, by contrast, focus on preserving structural and connectivity information. By combining both types of methods, we want to benefit from their individual advantages. To this end, we describe an algorithm that uses persistent homology to analyse the topology of a data set. Persistent homology identifies high‐dimensional holes in data sets, describing them as simplicial chains. We localize these chains using geometrical information of the data set, which we obtain from geodesic distances on a neighbourhood graph. The localized chains describe the structure of point clouds. We represent them using an interactive graph, in which each node describes a single chain and its geometrical properties. This graph yields a more intuitive understanding of multivariate point clouds and simplifies comparisons of time‐varying data. Our method focuses on detecting and analysing inhomogeneous regions, i.e. holes, in a data set because these regions characterize data in a different manner, thereby leading to new insights. We demonstrate the potential of our method on data sets from particle physics, political science and meteorology.

Exploring and comparing clusterings of multivariate data sets using persistent homology

Clustering algorithms support exploratory data analysis by grouping inputs that share similar features. Especially the clustering of unlabelled data is said to be a fiendishly difficult problem, because users not only have to choose a suitable clustering algorithm but also a suitable number of clusters. The known issues of existing clustering validity measures comprise instabilities in the presence of noise and restrictive assumptions about cluster shapes. In addition, they cannot evaluate individual clusters locally. We present a new measure for assessing and comparing different clusterings both on a global and on a local level. Our measure is based on the topological method of persistent homology, which is stable and unbiased towards cluster shapes. Based on our measure, we also describe a new visualization that displays similarities between different clusterings (using a global graph view) and supports their comparison on the individual cluster level (using a local glyph view). We demonstrate how our visualization helps detect different—but equally valid—clusterings of data sets from multiple application domains.

Similarity analysis of cell movements in video microscopy

Modern 3D+T video microscopy techniques enable biologists to acquire data of living organisms with unprecedented resolution in time and space. These datasets contain a wealth of biologically relevant and quantifiable information, e.g. the movements of all individual cells in a complex organism. However, extraction, validation, and analysis of this information are both challenging and time-consuming. In this paper, we present a computational technique that classifies and validates similar patterns of cell movements and cell divisions in organisms that consist of up to thousands of cells. Our algorithm determines tracking paths of traced cells that exhibit similar features and shape structures. These similarity values are assigned to our cluster algorithm that clusters paths into groups of coherent behavior. The data can be interactively explored in 2D projections and a 3D cell movement representation. For the first time, this visualization allows biologists to exhaustively assess similarities and differences in division patterns and cell migration on the scale of an entire organism. For validation, we applied our method on a synthetic dataset and two real datasets including zebrafish periods from blastula stage to early epiboly and growing zebrafish tail. We show that our method succeeds in detecting similarities based on shape and cell-movement based features.

Nested Tracking Graphs

Tracking graphs are a well established tool in topological analysis to visualize the evolution of components and their properties over time, i.e., when components appear, disappear, merge, and split. However, tracking graphs are limited to a single level threshold and the graphs may vary substantially even under small changes to the threshold. To examine the evolution of features for varying levels, users have to compare multiple tracking graphs without a direct visual link between them. We propose a novel, interactive, nested graph visualization based on the fact that the tracked superlevel set components for different levels are related to each other through their nesting hierarchy. This approach allows us to set multiple tracking graphs in context to each other and enables users to effectively follow the evolution of components for different levels simultaneously. We demonstrate the effectiveness of our approach on datasets from finite pointset methods, computational fluid dynamics, and cosmology simulations.