Search results for " Geometry"

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…

Combinatorial proofs of two theorems of Lutz and Stull

2021

Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…

Topological Logics with Connectedness over Euclidean Spaces

2013

We consider the quantifier-free languages, Bc and Bc °, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of R n ( n ≥ 2) and, additionally, over the regular closed semilinear sets of R n . The resulting logics are examples of formalisms that have recently been proposed in the Artificial Intelligence literature under the rubric Qualitative Spatial Reasoning. We prove that the satisfiability problem for Bc is undecidable over the regular closed semilinear sets in all dimensions greater than 1,…

REDUCTION OF CONSTRAINT SYSTEMS

1993

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into well constrained, over-, and underconstrained subsystems. This paper also gives an efficient method to decompose well constrained systems into irreducible ones. These decompositions greatly speed up the resolution in case of reducible systems. They also allow debugging systems of constraints.

On the Structure of Bispecial Sturmian Words

2013

A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended to the left and to the right with both letters remaining a Sturmian word. There is a deep relation between bispecial Sturmian words and Christoffel words, that are the digital approximations of Euclidean segments in the plane. In 1997, J. Berstel and A. de Luca proved that \emph{palindromic} bispecial Sturmian words are precisely the maximal internal factors of \emph{primitive} Christoffel words. We extend this result by showing that bispecial Sturmian wo…