Sébastien Fourey

Binomial convolutions and derivatives estimation from noisy discretizations

We present a new method to estimate derivatives of digitized functions. Even with noisy data, this approach is convergent and can be computed by using only the arithmetic operations. Moreover, higher order derivatives can also be estimated. To deal with parametrized curves, we introduce a new notion which solves the problem of correspondence between the parametrization of a continuous curve and the pixels numbering of a discrete object.

Intersection number and topology preservation within digital surfaces

In this paper, we prove a new result of digital topology which states that the digital fundamental groupa notion previously introduced by Kong (Comput. Graphics 13 (1989) 159-166)is sufficient to characterize topology preservation within digital surfaces. This proof involves a new tool for proving theorems in this field: the intersection number which counts the number of real intersections between two surfels loops lying on a digital surface. The main property of the intersection number and the reason why it is useful is the following: the intersection number between two paths does not change after any continuous deformation applied to the paths.

A DIGITAL LINKING NUMBER FOR DISCRETE CURVES

A topological invariant, analogous to the linking number as defined in knot theory, is defined for pairs of digital closed paths of ℤ3. This kind of invariant is very useful for proofs which involve homotopy classes of digital paths. Indeed, it can be used, for example, in order to state the connection between the tunnels in an object and the ones in its complement. Even if its definition is not as immediate as in the continuous case it has the good property that it is immediately computable from the coordinates of the voxels of the paths with no need of a regular projection. The aim of this paper is to state and prove that the linking number has the same property as its continuous analogue: it is invariant under any homotopic deformation of one of the two paths in the complement of the other.

Strong surfaces, surface skeletons, and image superimposition

After having recalled the definition and some local properties of strong surfaces, we present a related new thinning algorithm with surface skeleton and a specific application of these notions to superimposition of images of brains obtained by Magnetic Resonance Image.

Technical Section: Normals estimation for digital surfaces based on convolutions

In this paper, we present a method that we call on-surface convolution which extends the classical notion of a 2D digital filter to the case of digital surfaces (following the cuberille model). We also define an averaging mask with local support which, when applied with the iterated convolution operator, behaves like an averaging with large support. The interesting property of the latter averaging is the way the resulting weights are distributed: given a digital surface obtained by discretization of a differentiable surface of R^3, the masks isocurves are close to the Riemannian isodistance curves from the center of the mask. We eventually use the iterated averaging followed by convolutions with differentiation masks to estimate partial derivatives and then normal vectors over a surface. The number of iterations required to achieve a good estimate is determined experimentally on digitized spheres and tori. The precision of the normal estimation is also investigated according to the digitization step.

Generic Axiomatized Digital Surface-Structures

Abstract In digital topology, Euclidean n-space R n is usually modeled either by the set of points of a discrete grid, or by the set of n-cells in a convex cell complex whose union is R n. For commonly used grids and complexes in the cases n = 2 and 3, certain pairs of adjacency relations (κ, λ) on the grid points or n-cells (such as (4,8) and (8,4) on Z 2 are known to be “good pairs”. For these pairs of relations (κ, λ), many results of digital topology concerning a set of grid points or n-cells and its complement (such as Rosenfelds digital Jordan curve theorem) have versions in which κ-adjacency is used to define connectedness on the set and λ-adjacency is used to define connectedness on its complement. At present, results of 2D and 3D digital topology are usually proved for one good pair of adjacency relations at a time — so for each result there are different (but analogous) theorems for different good pairs of adjacency relations. In this paper we take the first steps in developing an alternative approach to digital topology based on very general axiomatic definitions of “well-behaved digital spaces”. This approach gives the possibility of stating and proving results of digital topology as single theorems which apply to all spaces of the appropriate dimensionality that satisfy our axioms. Specifically, this paper introduces the notion of a generic axiomatized digital surface-structure (GADS) — a general, axiomatically defined, type of discrete structure that models subsets of the Euclidean plane and of other surfaces. Instances of this notion include GADS corresponding to all of the good pairs of adjacency relations that have previously been used (by ourselves or others) in digital topology on planar grids and boundary surfaces. We define basic concepts for a GADS (such as homotopy of paths and the intersection number of two paths), give a discrete definition of planar GADS (which are GADS that model subsets of the Euclidean plane) and present some fundamental results including a Jordan curve theorem for planar GADS.

Simple points and generic axiomatized digital surface-structures

We present a characterization of topology preservation within digital axiomatized digital surface structures (gads), a generic theoretical framework for digital topology introduced in [2]. This characterization is based on the digital fundamental group that has been classically used for that purpose. More briefly, we define here simple points within gads and give the meaning of the words: preserving the topology within gads.

Preface: Volume 46

This book offers a collection of peer-review front-end research articles related to Location-Based Services (LBS). The contributed articles document research activities from various fields. Therefore, this book is divided into five parts. Part I contemplates contributions on Positioning and Indoor Positioning. Yang Cao, Haosheng Huang, and Georg Gartner develop ‘‘A Signal-Loss-Based Clustering Method for Segmenting and Analyzing Mixed Indoor/Outdoor Pedestrian GPS Trajectories’’. They segment and analyze mixed indoor/outdoor pedestrian GPS trajectories and identify the specific pattern of either environment. Keqiang Liu, Yunjia Wang, and Jian Wang contribute a paper on ‘‘Differential Barometric Altimetry Assists Floor Identification in WLAN Location Fingerprinting Study’’, which presents a differential barometric altimetry method to identify floor in consideration of features of WLAN location fingerprinting system. Yuyang Geng, Shuhang Zhang, Hangbin Wu, and Chaoyang Hu document ‘‘Improved Indoor Positioning System Based on Wi-Fi RSSI: Design and Deployment’’, in which a new method added in linear fitting and least square adjustment is used to achieve better positioning results. Chenchen Zhang, Haiyong Luo, Zhaohui Li, Fang Zhao, and Li Deng provide ‘‘A Robust Fingerprinting Localization Algorithm Against Signal Strength Attacks’’, in which they achieve robust wireless indoor localization when signal strength attack present on access points. Feng Wang, Haiyong Luo, Zhaohui Li, Fang Zhao, and Deng Li develop ‘‘Activity-Based Smartphone-Oriented Landmark Identification for Localization’’, in which they propose an activity recognition method to identify the specific landmarks in indoor area. Wolfgang Kainz and Kristin Müllan propose the ‘‘Navigation of Elderly People in Towns: The ASSISTANT Project’’ in order to safeguard elder’s social and economic participation in an increasingly ageing society. Dongjin Wu, Linyuan Xia, and Esmond Mok investigate the ‘‘Hybrid Location Estimation by Fusing WLAN Signals and Inertial Data’’ in which they propose a hybrid location estimation method that fuses WLAN signals and inertial data to maintain the localization accuracy. Part II investigates progress in Spatiotemporal Data Acquisition, Processing, and Analysis. This part includes a contribution from Yunlong Wu and Hui Li on ‘‘Improved Pre-processing Algorithm for Satellite Gravimetry Data Using Wavelet Method’’. In this work, they introduced an improved pre-processing algorithm for satellite gravimetry data by calibrate the scale-factors of observations based on