The approximation of implicit planar curves by line segments is a very classical problem. Many algorithms use interval analysis to approximate this curve, and to handle the topology of the final reconstruction. In this article, we use discrete geometry tools to build an original geometrical and topological representation of the implicit curve. The polygonal approximation contains few segments, ...

Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay an...

In idiopathic scoliotic patients, dynamical intervertebral efforts acting between vertebrae seem to be correlated with the spinal deformity. The quantification of these efforts, which is useful for the orthopedic surgeons to set up their surgical planning is the final objective of the present research. As a first step, we focus in this contribution on the geometrical reconstruction of the spine...

Using rigorous wave-optical formalism, a general expression is obtained for the image intensity distribution in combined analyser-based/propagation-based phase-contrast imaging. This expression takes into account partial coherence of the wave incident on the object as well as the finite resolution of the detector system. Using this general expression, two approaches based on the geometrical opt...

Textual and geometrical algorithms have been considered as two separate fields. This was caused by the fact that textual data are discrete in principal and interpolation is not defined as there is no metric in general, while geometrical data are considered discrete samples of continuous phenomena, geometrical surface etc. In this paper we present a unified approach to textual and geometrical da...

With the aim of providing our structured light sensor with adaptive capabilities, an uncalibrated reconstruction method is presented here. It allows us to simultaneously determine the projection matrices and the co-ordinates of 3-D points in a projective frame by only using pixel correspondences. Then, by translating geometrical knowledge about the scene into mathematical constraints, an Euclid...

Quality control (QC) is of primary importance for computed tomography systems to obtain reliable data for Non Destructive Testing (NDT). A QC protocol is pursued for the AIMEN dual detector CT by a software add-on update on the reconstruction and visualization software. Image quality parameters are considered following standards and other published papers: uniformity, noise, SNR, contrast, pixe...

Detailed investigation on biomechanics of a complex structure such as the human lumbar spine requires the use of advanced computer-based technique for both the geometrical reconstruction and the stress analysis. In the present study, the computer-assisted tomography (CAT) and finite element method (FEM) are merged to perform detailed three dimensional nonlinear analysis of the human ligamentous...

In this paper, we present a generic topological and geometrical framework for the digital reconstruction of complex contours from labeled images. The proposed technique is based on combinatorial map simplifications guided by digital straight segments. We illustrate the genericity of the framework with a parallel contour reconstruction algorithm.