Segmentation and recovery of superquadrics: computational imaging and vision
Segmentation and recovery of superquadrics: computational imaging and vision
Superquadrics with rational and irrational symmetry
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Experimental comparison of superquadric fitting objective functions
Pattern Recognition Letters
Boolean Operations with Implicit and Parametric Representation of Primitives Using R-Functions
IEEE Transactions on Visualization and Computer Graphics
Classification by evolutionary ensembles
Pattern Recognition
Superquadrics and Angle-Preserving Transformations
IEEE Computer Graphics and Applications
Clustering with an N-dimensional extension of Gielis superformula
AIKED'08 Proceedings of the 7th WSEAS International Conference on Artificial intelligence, knowledge engineering and data bases
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Moments of superellipsoids and their application to range image registration
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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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 Lame 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 directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data.