International audienceWe 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 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

Abstract. 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 ∈ R n : f (x) = 0} which is the boundary of a given closed subset ofUnder some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness, and can be analytically characterized.

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.

Given a digital straight line D of known characteristics (a, b, c), and given two arbitrary discrete points A(x a , y a ) and B(x b , y b ) of it, we are interested in computing the characteristics of the digital straight segment (DSS) of D delimited by the endpoints A and B. Our method is based entirely on the remainder subsequence S = {ax − c mod b; x a ≤ x ≤ x b }. We show that minimum and maximum remainders correspond to the three leaning points of the subsegment needed to determine its characteristics. One of the key aspects of the method is that we show that computing such a minimum and maximum of a remainder sequence can be done in logarithmic time with an algorithm akin to the Euclidean algorithm. Experiments show that our algorithm is faster than the previous ones proposed by Said and Lachaud in [11] and Sivignon in [16].

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(N d log N) for dimension d, where d 5 2,3, together with space complexity O(N) where N is the number of points.

International audienceAn 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(N 4), N being the number of points

In this paper, a new bijective reflection algorithm in two dimensions is proposed along with an associated rotation. The reflection line is defined by an arbitrary Euclidean point and a straight line passing through this point. The reflection line is digitized and the 2D space is paved by digital perpendicular (to the reflection line) straight lines. For each perpendicular line, digital points are reflected by central symmetry with respect to the reflection line. Two consecutive digital reflections are combined to define a digital bijective rotation about arbitrary center (i.e. bijective digital rigid motion).

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(n 3 log 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).