Search results for " Geometry."

IC‐P‐024: Localization of hippocampal atrophy in Alzheimer's disease

2011

The hippocampus presents the highest rate of atrophy in the early stage of Alzheimer's disease (AD), with more pronounced neuron loss reported in CA1 and subiculum. The aim of this study is to increase the discrimination power of hippocampal shape analysis between AD and normal controls (NC) by focusing on the subregions with atrophy associated with AD and describing the localized shape changes using statistical shape models (SSMs).

Integrable systems and moduli spaces of curves

2016

This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and mirror symmetry. The text contains a short introduction to the main ideas and prerequisites of the subject from geometry and mathematical physics, followed by a synthetic review of some of my papers (listed below) starting from my PhD thesis (October 2008), and with some open questions and future developements. My results include: • the triple mirror symmetry among P 1-orbifolds with positive Euler characteristic , the Landau-Ginzburg model with superpotential −xyz + x p + y q + z r with 1 p + …

Some inequalities involving the euclidean condition of a matrix

1960

G. Herglotz’ Behandlung von Beschleunigungswellen in seiner Vorlesung «Mechanik der Kontinua» angewandt auf die Stosswellen von Christoffel

1981

Following a lecture delivered by Herglotz in 1925/26 we briefly treat acceleration waves in hyperelastic materials. Our main result is a divergence equation for the squared Euclidean norm of the so-called ‘wave vector’. We then apply Herglotz’ method (devised for acceleration waves) to the propagation of such first order discontinuities in elastic bodies as were treated by Christoffel in [1].

noRANSAC for fundamental matrix estimation

2011

The estimation of the fundamental matrix from a set of corresponding points is a relevant topic in epipolar stereo geometry [10]. Due to the high amount of outliers between the matches, RANSAC-based approaches [7, 13, 29] have been used to obtain the fundamental matrix. In this paper two new contributes are presented: a new normalized epipolar error measure which takes into account the shape of the features used as matches [17] and a new strategy to compare fundamental matrices. The proposed error measure gives good results and it does not depend on the image scale. Moreover, the new evaluation strategy describes a valid tool to compare diffe rent RANSAC-based methods because it does not re…

Universal natural shapes: From unifying shape description to simple methods for shape analysis and boundary value problems

2012

Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three …

Une quête d'exactitude : machines, algèbre et géométrie pour la construction traditionnelle des équations différentielles

2015

In La Géométrie, Descartes proposed a “balance” between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In particular, Cartesian tools were polynomial algebra (analysis) and a class of diagrammatic constructions (synthesis). This setting provided a classification of curves, according to which only the algebraic ones were considered “purely geometrical.” This limit was overcome with a general method by Newton and Leibniz introducing the infinity in the analytical part, whereas the synthetic perspective gradually lost importance with respect to the analytical one—geometry became a mean of visualization, no longer of construction. Descartes’s…

Assessing the Robustness of Thermoeconomic Diagnosis of Fouled Evaporators: Sensitivity Analysis of the Exergetic Performance of Direct Expansion Coi…

2016

Thermoeconomic diagnosis of refrigeration systems is a pioneering approach to the diagnosis of malfunctions, which has been recently proven to achieve good performances for the detection of specific faults. Being an exergy-based diagnostic technique, its performance is influenced by the trends of exergy functions in the “design” and “abnormal” conditions. In this paper the sensitivity of performance of thermoeconomic diagnosis in detecting a fouled direct expansion coil and quantifying the additional consumption it induces is investigated; this fault is critical due to the simultaneous air cooling and dehumidification occurring in the coil, that induce variations in both the chemical and th…

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

2013

RootsGLOH2: embedding RootSIFT 'square rooting' in sGLOH2

2020

This study introduces an extension of the shifting gradient local orientation histogram doubled (sGLOH2) local image descriptor inspired by RootSIFT ‘square rooting’ as a way to indirectly alter the matching distance used to compare the descriptor vectors. The extended descriptor, named RootsGLOH2, achieved the best results in terms of matching accuracy and robustness among the latest state-of-the-art non-deep descriptors in recent evaluation contests dealing with both planar and non-planar scenes. RootsGLOH2 also achieves a matching accuracy very close to that obtained by the best deep descriptors to date. Beside confirming that ‘square rooting’ has beneficial effects on sGLOH2 as it happe…