Isabelle Debled-Rennesson

A linear algorithm for segmentation of digital curves

A new very efficient linear algorithm for the segmentation of 8-connected digital curves is given. The simplicity comes from a definition of digital lines using a linear double diophantine inequality. A complete Pascal source code is given.

A discrete geometry approach for dominant point detection

We propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments [2]. Starting from results of discrete geometry [3,4], the notion of maximal blurred segment of width @n[2] has been proposed, well adapted to possibly noisy curves. The first method uses a fixed parameter that is the width of considered maximal blurred segments. The second method is deduced from the first one based on a multi-width approach to obtain a non-parametric method that uses no threshold for working with noisy curves. Comparisons with other methods in the literature prove the efficiency of our approach. Thanks to a recent result [5] concerning the construction of the sequence of maximal blurred segments, the complexity of the proposed methods is O(nlogn). An application of vectorization is also given in this paper.

Curvature estimation in noisy curves

An algorithm of estimation of the curvature at each point of a general discrete curve in O(n log2 n) is proposed. It uses the notion of blurred segment, extending the definition of segment of arithmetic discrete line to be adapted to noisy curves. The proposed algorithm relies on the decomposition of a discrete curve into maximal blurred segments also presented in this paper.

Segmentation and Length Estimation of 3D Discrete Curves

We propose in this paper an arithmetical definition of 3-D discrete lines as well as an efficient construction algorithm. From this notion, an algorithm of 3-D discrete lines segmentation has been developed. It is then used to calculate the length of a discrete curve. A proof of the multigrid convergence of length estimators is presented.

3D Discrete Normal Vectors

Precise knowledge of normal vectors to discrete objects is mandatory in rendering algorithms. This article introduces a new method for the calculation of normal vectors to a digital object. This technique relies on discrete geometry theories : the recognition of discrete straight lines and tangential lines in dimension 2. Results obtained with synthetic and real objects from medical imagery are presented and commented.

Decomposition of a curve into arcs and line segments based on dominant point detection

A new solution is proposed to decompose a curve into arcs and straight line segments in O(n log n) time. It is a combined solution based on arc detection [1] and dominant point detection [2] to strengthen the quality of the segmentation results. Experimental results show the fastness of the proposed method.

A new method to detect arcs and segments from curvature profiles

In this paper a new method of arc detection based on arithmetic discrete lines is presented. Key points are extracted from such a profile and used for the reconstruction. The used method is fast and easy to implement. Experimental studies on several series of test images show the stability and the robustness of the proposed method

Optimal blurred segments decomposition in linear time

Blurred (previously named fuzzy) segments were introduced by Debled-Rennesson et al [1,2] as an extension of the arithmetical approach of Reveilles [11] on discrete lines, to take into account noise in digital images. An incremental linear-time algorithm was presented to decompose a discrete curve into blurred segments with order bounded by a parameter d. However, that algorithm fails to segment discrete curves into a minimal number of blurred segments. We show in this paper, that this characteristic is intrinsic to the whole class of blurred segments. We thus introduce a subclass of blurred segments, based on a geometric measure of thickness. We provide a new convex hull based incremental linear time algorithm for segmenting discrete curves into a minimal number of thin blurred segments.

Arc segmentation in linear time

A linear algorithm based on a discrete geometry approach is proposed for the detection of digital arcs and digital circles using a new representation of them. It is introduced by inspiring from the work of Latecki [1]. By utilizing this representation, we transform the problem of digital arc detection into a problem of digital straight line recognition. We then develop a linear method for arc segmentation of digital curves.

3D Geometric Analysis of Tubular Objects Based on Surface Normal Accumulation

This paper proposes a simple and efficient method for the reconstruction and extraction of geometric parameters from 3D tubular objects. Our method constructs an image that accumulates surface normal information, then peaks within this image are located by tracking. Finally, the positions of these are optimized to lie precisely on the tubular shape centerline. This method is very versatile, and is able to process various input data types like full or partial mesh acquired from 3D laser scans, 3D height map or discrete volumetric images. The proposed algorithm is simple to implement, contains few parameters and can be computed in linear time with respect to the number of surface faces. Since the extracted tube centerline is accurate, we are able to decompose the tube into rectilinear parts and torus-like parts. This is done with a new linear time 3D torus detection algorithm, which follows the same principle of a previous work on 2D arc circle recognition. Detailed experiments show the versatility, accuracy and robustness of our new method.