An elementary algorithm for digital arc segmentation

International audienceThis paper concerns the digital circle recognition problem, especially in the form of the circular separation problem. General fundamentals, based on classical tools, as well as algorithmic details are given (the latter by providing pseudo-code for major steps of the algorithm). After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arcs

A robust coregistration method for in vivo studies using a first generation simultaneous PET/MR scanner

Purpose: Hybrid positron emission tomography (PET)/magnetic resonance (MR) imaging systems have recently been built that allow functional and anatomical information obtained from PET and MR to be acquired simultaneously. The authors have developed a robust coregistration scheme for a first generation small animal PET/MR imaging system and illustrated the potential of this system to study intratumoral heterogeneity in a mouse model. Methods: An alignment strategy to fuse simultaneously acquired PET and MR data, using the MR imaging gradient coordinate system as the reference basis, was developed. The fidelity of the alignment was evaluated over multiple study sessions. In order to explore its robustness in vivo, the alignment strategy was applied to explore the heterogeneity of glucose metabolism in a xenograft tumor model, using ^(18)F-FDG-PET to guide the acquisition of localized ^1H MR spectra within a single imaging session. Results: The alignment method consistently fused the PET/MR data sets with subvoxel accuracy (registration error mean=0.55 voxels, <0.28 mm); this was independent of location within the field of view. When the system was used to study intratumoral heterogeneity within xenograft tumors, a correlation of high ^(18)F-FDG-PET signal with high choline/creatine ratio was observed. Conclusions: The authors present an implementation of an efficient and robust coregistration scheme for multimodal noninvasive imaging using PET and MR. This setup allows time-sensitive, multimodal studies of physiology to be conducted in an efficient manner

The Geometry of the Intersection of Voxel Spaces

AbstractViews rendered by the numerous current digital medical facilities and 3D technologies (Positron Emission Tomography, Magnetic Resonance Imaging, Synchrotron Radiation, Radars, Stereography, etc.) of a 3D object may often be assimilated to tilings of R 3 space by identical cubes (or voxels). Relating two such views of a single object obtained by two distinct processes, in order to fusion their information on a new image, requires a processing of these two tilings specially for objects whose size is close to the resolution of the employed technology

New results about 3D digital lines

The current definition of 3D digital lines 3 , which uses the 2D digital lines of closest integer points (Bresenham&apos;s lines) of two projections, has several drawbacks: ffl the discrete topology of this 3D digital line notion is not clear, ffl its third projection is, generally, not the closest set of points of the third euclidean projection, ffl if we consider a family of parallel euclidean lines, we do not know how many combinatorially distinct digital structures will be built by this process, ffl and mainly the set of voxels defined in this way is not the set of closest points of the given euclidean line. And these questions are the simplest ones; many others could be asked: dependence on the choice of the projections, intersections with digital planes, intersections between 3D digital lines,... This paper gives a new definition of 3D digital lines relying on subgroups of Z 3 , whose main advantage over the former one is its ability to convert any practical question into rigo..

Géométrie discrète, calcul en nombres entiers et algorithmique

Les numérisations variées conduisent souvent à des cohabitations difficiles sinon des conflits entre discret et continu. Les analyses de nombreuses situations de ce type montrent la plupart du temps que l'origine des problèmes réside dans l'emploi simultané de nombres réels et de nombres entiers, aux propriétés bien distinctes. Contrairement à l'approche traditionnelle de ces questions, qui traite "individuellement", ob jet par ob jet, les relations discret-continu, nous adoptons un point de vue "global", pour une théorie complète. Nous proposons dans la première partie une solution possible de ces conflits par l'usage de Théories où les nombres réels sont remplacés par des entiers; les notions continues (ou topologiques) sont retrouvées simplement en utilisant la notion d'entier infiniment grand de l'Analyse Non Standard. Bien qu'un très grand nombres de domaines, tant en Mathématique qu'en Physique, soient concernés il nous a semblé clair que l'informatique, autre source de problèmes discret-continu importants, pouvait offrir un champ d'expérimentation à ces idées. Nous donnons en particulier les fondements d'une Géométrie Discrète Arithmétique, pendant discret de la Géométrie Euclidienne; elle occupe la deuxième partie. C'est une mathématisation immédiate de la pratique du discret-continu géométrique, domaine qui va de l'Algorithmique Graphique à la Conception des Circuits en passant par la Géométrie Algorithmique, la Synthèse d'images etc.; elle permet de résoudre de nombreuses questions concrètes posées dans ces domaines. L'émergence de cette théorie est certainement le résultat le plus significatif de ce travail. Nous nous contentons dans ce descriptif de mentionner quelques résultats pouvant donner une idée de l'intérêt de cette Géométrie

An elementary algorithm for digital arc segmentation

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Multiresolution images fusion for the quantification of neuronal activity: a discrete approach

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