Rita Zrour

Discrete bisector function and Euclidean skeleton in 2D and 3D

We propose a new definition and an algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient.

Discrete bisector function and euclidean skeleton

We propose a new definition and an exact algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning method which produces homotopic discrete Euclidean skeletons. Unlike previouly proposed approaches, this method is still valid in 3D.

Optimal Consensus set for digital line and plane fitting

This article presents a new method for fitting a digital line or plane to a given set of points in a 2D or 3D image in the presence of noise by maximizing the number of inliers, namely the consensus set. By using a digital model instead of a continuous one, we show that we can generate all possible consensus sets for model fitting. We present a deterministic algorithm that efficiently searches the optimal solution with time complexity O(Nd log N) for dimension d, where d = 2,3, together with space complexity O(N) where N is the number of points.

Implicit Digital Surfaces in Arbitrary Dimensions

In this paper we introduce a notion of digital implicit surface in arbitrary dimensions. The digital implicit surface is the result of a morphology inspired digitization of an implicit surface {x ∈ ℝn : f(x) = 0} which is the boundary of a given closed subset of ℝ n , {x ∈ ℝn : f(x) ≤ 0}. Under some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness. Furthermore, for a large class of the digital implicit surfaces, there exists a very simple analytical characterization.

Optimal consensus set for annulus fitting

An annulus is defined as a set of points contained between two circles. This paper presents a method for fitting an annulus to a given set of points in a 2D images in the presence of noise by maximizing the number of inliers, namely the consensus set, while fixing the thickness. We present a deterministic algorithm that searches the optimal solution(s) within a time complexity of O(N4), N being the number of points.

O ( n 3 log n ) time complexity for the optimal consensus set computation for 4-Connected Digital Circles

This paper presents a method for fitting 4-connected digital circles to a given set of points in 2D images in the presence of noise by maximizing the number of inliers, namely the optimal consensus set, while fixing the thickness. Our approach has a O(n3log n) time complexity and O(n) space complexity, n being the number of points, which is lower than previous known methods while still guaranteeing optimal solution(s).

Efficient robust digital annulus fitting with bounded error

A digital annulus is defined as a set of grid points lying between two circles sharing an identical center and separated by a given width. This paper deals with the problem of fitting a digital annulus to a given set of points in a 2D bounded grid. More precisely, we tackle the problem of finding a digital annulus that contains the largest number of inliers. As the current best algorithm for exact optimal fitting has a computational complexity in O(N3 logN) where N is the number of grid points, we present an approximation method featuring linear time complexity and bounded error in annulus width, by extending the approximation method previously proposed for digital hyperplane fitting. Experiments show some results and runtime in practice.

Optimal consensus set for digital plane fitting

This paper presents a method for fitting a digital plane to a given set of points in a 3D image in the presence of outliers. We present a new method that uses a digital plane model rather than the conventional continuous model. We show that such a digital model allows us to efficiently examine all possible consensus sets and to guarantee the solution optimality and exactness. Our algorithm has a time complexity O(N3 logN) together with a space complexity O(N) where N is the number of points.

Optimal Consensus Set for nD Fixed Width Annulus Fitting

This paper presents a method for fitting a nD fixed width spherical shell to a given set of nD points in an image in the presence of noise by maximizing the number of inliers, namely the consensus set. We present an algorithm, that provides the optimal solutions within a time complexity