Thanh Phuong Nguyen

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.

Statistical binary patterns for rotational invariant texture classification

A new texture representation framework called statistical binary patterns (SBPs) is presented. It consists in applying rotation invariant local binary pattern operators ( LBP riu 2 ) to a series of moment images, defined by local statistics uniformly computed using a given spatial support. It can be seen as a generalisation of the commonly used complementation approach (CLBP), since it extends the local description not only to local contrast information, but also to higher order local variations. In short, SBPs aim at expanding LBP self-similarity operator from the local grey level to the regional distribution level. Thanks to a richer local description, the SBPs have better discrimination power than other LBP variants. Furthermore, thanks to the regularisation effect of the statistical moments, the SBP descriptors show better noise robustness than classical CLBPs. The interest of the approach is validated through a large experimental study performed on five texture databases: KTH-TIPS, KTH-TIPS 2b, CUReT, UIUC and DTD. The results show that, for the four first datasets, the SBPs are comparable or outperform the recent state-of-the-art methods, even using small support for the LBP operator, and using limited size spatial support for the computation of the local statistics. HighlightsWe extend the binary patterns from the pixel level to the local distribution level.We exploit moment images calculated from spatial support of the statistics.Statistical moments clearly improve the expressiveness and robustness of descriptor.

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.

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.

Fast and robust dominant points detection on digital curves

A new and fast method for dominant point detection and polygonal representation of a discrete curve is proposed. Starting from results of discrete geometry [1, 2], the notion of maximal blurred segment of width v has been proposed, well adapted to possibly noisy and/or not connected curves [3]. For a given width, the dominant points of a curve C are deduced from the sequence of maximal blurred segments of C in O(n log2 n) time. Comparisons with other methods of the literature prove the efficacity of our approach.

Curvature and Torsion Estimators for 3D Curves

We propose a new torsion estimator for spatial curves based on results of discrete geometry that works in O (n log2 n ) time. We also present a curvature estimator for spatial curves. Our methods use the 3D extension of the 2D blurred segment notion [1]. These estimators can naturally work with disconnected curves.

Ellipse detection through decomposition of circular arcs and line segments

In this work we propose an efficient and original method for ellipse detection which relies on a recent contour representation based on arcs and line segments [1]. The first step of such a detection is to locate ellipse candidate with a grouping process exploiting geometric properties of adjacent arcs and lines. Then, for each ellipse candidate we extract a compact and significant representation defined from the segment and arc extremities together with the arc middle points. This representation allows then a fast ellipse detection by using a simple least square technique. Finally some first comparisons with other robust approaches are proposed.

Circularity Measuring in Linear Time

We propose a new circularity measure inspired from Arkin \cite{Arkin91}, Latecki \cite{Latecki00} tools of shape matching that is constructed in a tangent space. We then introduce a linear algorithm that uses this measure for circularity measuring. This method can also be regarded as a method for circular object recognition. Experimental results show the robustness of this simple method.

Circular arc reconstruction of digital contours with chosen Hausdorff error

We address the problem of constructing an approximate continuous representation of a digital contour with guarantees on the Hausdorff error between the digital shape and its reconstruction. Instead of polygonalizing the contour, we propose to reconstruct the shape with circular arcs. To do so, we exploit the recent curvature estimators. From their curvature field, we introduce a new simple and efficient algorithm to approximate a digital shape with as few arcs as possible at a given scale, specified by a maximal admissible Hausdorff distance. We show the potential of our reconstruction method with numerous experiments and we also compare our results with some recent promising approaches. Last, all these algorithms are available online for comparisons on arbitrary shapes.