Elastic Registration of Geodesic Vascular Graphs

Vascular graphs can embed a number of high-level features, from morphological parameters, to functional biomarkers, and represent an invaluable tool for longitudinal and cross-sectional clinical inference. This, however, is only feasible when graphs are co-registered together, allowing coherent multiple comparisons. The robust registration of vascular topologies stands therefore as key enabling technology for group-wise analyses. In this work, we present an end-to-end vascular graph registration approach, that aligns networks with non-linear geometries and topological deformations, by introducing a novel overconnected geodesic vascular graph formulation, and without enforcing any anatomical prior constraint. The 3D elastic graph registration is then performed with state-of-the-art graph matching methods used in computer vision. Promising results of vascular matching are found using graphs from synthetic and real angiographies. Observations and future designs are discussed towards potential clinical applications

Perceiving environmental structure from optical motion

Generally speaking, one of the most important sources of optical information about environmental structure is known to be the deforming optical patterns produced by the movements of the observer (pilot) or environmental objects. As an observer moves through a rigid environment, the projected optical patterns of environmental objects are systematically transformed according to their orientations and positions in 3D space relative to those of the observer. The detailed characteristics of these deforming optical patterns carry information about the 3D structure of the objects and about their locations and orientations relative to those of the observer. The specific geometrical properties of moving images that may constitute visually detected information about the shapes and locations of environmental objects is examined

From buildings to cities: techniques for the multi-scale analysis of urban form and function

The built environment is a significant factor in many urban processes, yet direct measures of built form are seldom used in geographical studies. Representation and analysis of urban form and function could provide new insights and improve the evidence base for research. So far progress has been slow due to limited data availability, computational demands, and a lack of methods to integrate built environment data with aggregate geographical analysis. Spatial data and computational improvements are overcoming some of these problems, but there remains a need for techniques to process and aggregate urban form data. Here we develop a Built Environment Model of urban function and dwelling type classifications for Greater London, based on detailed topographic and address-based data (sourced from Ordnance Survey MasterMap). The multi-scale approach allows the Built Environment Model to be viewed at fine-scales for local planning contexts, and at city-wide scales for aggregate geographical analysis, allowing an improved understanding of urban processes. This flexibility is illustrated in the two examples, that of urban function and residential type analysis, where both local-scale urban clustering and city-wide trends in density and agglomeration are shown. While we demonstrate the multi-scale Built Environment Model to be a viable approach, a number of accuracy issues are identified, including the limitations of 2D data, inaccuracies in commercial function data and problems with temporal attribution. These limitations currently restrict the more advanced applications of the Built Environment Model

New evidence of visual space anisotropy with autostereograms

Postprint (published version

There are 174 Subdivisions of the Hexahedron into Tetrahedra

This article answers an important theoretical question: How many different subdivisions of the hexahedron into tetrahedra are there? It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5 tetrahedra. However, all hexahedra are not cubes and moving the vertex positions increases the number of subdivisions. Recent hexahedral dominant meshing methods try to take these configurations into account for combining tetrahedra into hexahedra, but fail to enumerate them all: they use only a set of 10 subdivisions among the 174 we found in this article. The enumeration of these 174 subdivisions of the hexahedron into tetrahedra is our combinatorial result. Each of the 174 subdivisions has between 5 and 15 tetrahedra and is actually a class of 2 to 48 equivalent instances which are identical up to vertex relabeling. We further show that exactly 171 of these subdivisions have a geometrical realization, i.e. there exist coordinates of the eight hexahedron vertices in a three-dimensional space such that the geometrical tetrahedral mesh is valid. We exhibit the tetrahedral meshes for these configurations and show in particular subdivisions of hexahedra with 15 tetrahedra that have a strictly positive Jacobian

On the origin of Phase Transitions in the absence of Symmetry-Breaking

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model. The system so obtained undergoes a thermodynamic phase transition in the absence of symmetry-breaking. Besides the well known use of quantities like the Wilson loop we show how else the phase transition in such a kind of models can be detected. It is found that the first order phase transition undergone by this model is characterised according to an Ehrenfest-like classification of phase transitions applied to the configurational entropy. On the basis of the topological theory of phase transitions, it is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy can be considered as the "shadow" of some suitable topological transition of certain submanifolds of configuration space.Comment: 31 pages, 9 figure

A flexible sensor technology for the distributed measurement of interaction pressure

We present a sensor technology for the measure of the physical human-robot interaction pressure developed in the last years at Scuola Superiore Sant'Anna. The system is composed of flexible matrices of opto-electronic sensors covered by a soft silicone cover. This sensory system is completely modular and scalable, allowing one to cover areas of any sizes and shapes, and to measure different pressure ranges. In this work we present the main application areas for this technology. A first generation of the system was used to monitor human-robot interaction in upper- (NEUROExos; Scuola Superiore Sant'Anna) and lower-limb (LOPES; University of Twente) exoskeletons for rehabilitation. A second generation, with increased resolution and wireless connection, was used to develop a pressure-sensitive foot insole and an improved human-robot interaction measurement systems. The experimental characterization of the latter system along with its validation on three healthy subjects is presented here for the first time. A perspective on future uses and development of the technology is finally drafted