Search results for "Gielis Curves"
showing 4 items of 4 documents
Universal natural shapes: From unifying shape description to simple methods for shape analysis and boundary value problems
2012
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three …
A robust evolutionary algorithm for the recovery of rational Gielis curves
2013
International audience; Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot…
Road Signs Detection and Reconstruction using Gielis Curves
2012
International audience; Road signs are among the most important navigation tools in transportation systems. The identification of road signs in images is usually based on first detecting road signs location using color and shape information. In this paper, we introduce such a two-stage detection method. Road signs are located in images based on color segmentation, and their corresponding shape is retrieved using a unified shape representation based on Gielis curves. The contribution of our approach is the shape reconstruction method which permits to detect any common road sign shape, i.e. circle, triangle, rectangle and octagon, by a single algorithm without any training phase. Experimental…
A NEW POTENTIAL FUNCTION FOR SELF INTERSECTING GIELIS CURVES WITH RATIONAL SYMMETRIES
2009
International audience; We present a new potential field equation for self-intersecting Gielis curves with rational rotational symmetries. In the literature, potential field equations for these curves, and their extensions to surfaces, impose the rotational symmetries to be integers in order to guarantee the unicity of the intersection between the curve/surface and any ray starting from its center. Although the representation with natural symmetries has been applied to mechanical parts modeling and reconstruction, the lack of a potential function for Rational symmetry Gielis Curves (RGC) remains a major problem for natural object representation, such as flowers and phyllotaxis. We overcome thi…