A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the Asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.Comment: 17 pages, 8 figures. During preparation of this manuscript the authors became aware of the work of Mileyko at al., concurrently submitted for publicatio

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

The Small World of Osteocytes: Connectomics of the Lacuno-Canalicular Network in Bone

Osteocytes and their cell processes reside in a large, interconnected network of voids pervading the mineralized bone matrix of most vertebrates. This osteocyte lacuno-canalicular network (OLCN) is believed to play important roles in mechanosensing, mineral homeostasis, and for the mechanical properties of bone. While the extracellular matrix structure of bone is extensively studied on ultrastructural and macroscopic scales, there is a lack of quantitative knowledge on how the cellular network is organized. Using a recently introduced imaging and quantification approach, we analyze the OLCN in different bone types from mouse and sheep that exhibit different degrees of structural organization not only of the cell network but also of the fibrous matrix deposited by the cells. We define a number of robust, quantitative measures that are derived from the theory of complex networks. These measures enable us to gain insights into how efficient the network is organized with regard to intercellular transport and communication. Our analysis shows that the cell network in regularly organized, slow-growing bone tissue from sheep is less connected, but more efficiently organized compared to irregular and fast-growing bone tissue from mice. On the level of statistical topological properties (edges per node, edge length and degree distribution), both network types are indistinguishable, highlighting that despite pronounced differences at the tissue level, the topological architecture of the osteocyte canalicular network at the subcellular level may be independent of species and bone type. Our results suggest a universal mechanism underlying the self-organization of individual cells into a large, interconnected network during bone formation and mineralization

Modeling Brain Circuitry over a Wide Range of Scales

If we are ever to unravel the mysteries of brain function at its most fundamental level, we will need a precise understanding of how its component neurons connect to each other. Electron Microscopes (EM) can now provide the nanometer resolution that is needed to image synapses, and therefore connections, while Light Microscopes (LM) see at the micrometer resolution required to model the 3D structure of the dendritic network. Since both the topology and the connection strength are integral parts of the brain's wiring diagram, being able to combine these two modalities is critically important. In fact, these microscopes now routinely produce high-resolution imagery in such large quantities that the bottleneck becomes automated processing and interpretation, which is needed for such data to be exploited to its full potential. In this paper, we briefly review the Computer Vision techniques we have developed at EPFL to address this need. They include delineating dendritic arbors from LM imagery, segmenting organelles from EM, and combining the two into a consistent representation