Genetic Algorithms for Gielis Surface Recovery from 3D Data Sets

Bokhabrine, Youssef; Fougerolle, Yohan; Foufou, Sebti; Truchetet, Frédéric

doi:10.1109/icip.2007.4379214

Cited by 11 publications

(13 citation statements)

References 8 publications

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“…That may explain the preference of numerous authors such as [2][3][4][5][6][7][8][9] for fitting errors based on the inside-outside function. We have also noticed that [17,18] use the insideoutside function for their reconstruction methods based on supershape fitting. However, because real data is noisy and often contains errors from image processing (registration and integration), we have decided to base our fitting error on the pseudo-Euclidean distance, D (P i , S) = I i P i , which is the distance between P i in the point cloud and its corresponding point I i on the surface S. This allows us to integrate a tolerance threshold τ in order to compensate for noise and errors and to make our method more robust.…”

Section: Fitting Error Analysismentioning

confidence: 97%

“…GAs have been already studied for supershapes [18]. However, we found their fitness function based on insideoutside function not suitable to real data where accuracy has to be sacrificed in favor of a tolerance threshold that will handle the presence of noise.…”

Section: Introductionmentioning

confidence: 98%

“…Among those methods, superquadric model [1] have been very well studied [2][3][4][5][6][7][8][9][10][11][12][13][14][15], when methods based on the recent supershape model [16] have been barely investigating [17,18]. Although an analogy between superquadric and supershape models can be made, and that optimization methods to recover the parameters of the best superquadric fitting are usually based on the LevenbergMarquardt (LM) theory [19], LM cannot be applied to retrieve all the parameters for supershape fitting.…”

Section: Introductionmentioning

confidence: 99%

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Genetic algorithms for 3d reconstruction with supershapes

Voisin

Abidi

Foufou

et al. 2009

2009 16th IEEE International Conference on Image Processing (ICIP)

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Supershape model is a recent primitive that represents numerous 3D shapes with several symmetry axes. The main interest of this model is its capability to reconstruct more complex shape than superquadric model with only one implicit equation. In this paper we propose a genetic algorithms to reconstruct a point cloud using those primitives. We used the pseudo-Euclidean distance to introduce a threshold to handle real data imperfection and speed up the process. Simulations using our proposed fitness functions and a fitness function based on inside-outside function show that our fitness function based on the pseudo-Euclidean distance performs better.

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Section: Fitting Error Analysismentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Genetic algorithms for 3d reconstruction with supershapes

Voisin

Abidi

Foufou

et al. 2009

2009 16th IEEE International Conference on Image Processing (ICIP)

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“…This representation has found applications for Gielis surface recovery for mechanical parts (Bokhabrine et al, 2007). Unfortunately, one of its major weakness is that the implicit field equations require the rotational symmetries to be integers.…”

Section: Introductionmentioning

confidence: 99%

“…DNA and proteins in which non-integer symmetries are observed frequently (Janner, 2001;Janner, 2005). Complex objects that are defined as Boolean operations between multiple globally deformed Gielis surfaces can be modeled and reconstructed (Fougerolle et al, 2005;Bokhabrine et al, 2007). To transcribe the Boolean predicates between 3D Gielis surfaces into analytical equations, R-functions have been employed.…”

Section: Introductionmentioning

confidence: 99%

A New Potential Function for Self Intersecting Gielis Curves With Rational Symmetries

2009

Proceedings of the Fourth International Conference on Computer Graphics Theory and Applications

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Abstract: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 this problem by combining the potential values associated with the multiple intersections using R-functions. With this technique, several differentiable potential fields can be defined for RGCs. Especially, by performing N-ary R-conjunction or R-disjunction, two specific potential fields can be generated: one corresponding to the inner curve, that is the curve inscribed within the whole curve, and the outer -or envelope-that is the curve from which self intersections have been removed.

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Towards the evolution of vertical-axis wind turbines using supershapes

Preen

Bull

2014

Evol. Intel.

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We have recently presented an initial study of evolutionary algorithms used to design vertical-axis wind turbines (VAWTs) wherein candidate prototypes are evaluated under fan generated wind conditions after being physically instantiated by a 3D printer. That is, unlike other approaches such as computational fluid dynamics simulations, no mathematical formulations are used and no model assumptions are made. However, the representation used significantly restricted the range of morphologies explored. In this paper, we present initial explorations into the use of a simple generative encoding, known as Gielis superformula, that produces a highly flexible 3D shape representation to design VAWT. First, the target-based evolution of 3D artefacts is investigated and subsequently initial design experiments are performed wherein each VAWT candidate is physically instantiated and evaluated under fan generated wind conditions. It is shown possible to produce very closely matching designs of a number of 3D objects through the evolution of supershapes produced by Gielis superformula. Moreover, it is shown possible to use artificial physical evolution to identify novel and increasingly efficient supershape VAWT designs.

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Genetic Algorithms for Gielis Surface Recovery from 3D Data Sets

Cited by 11 publications

References 8 publications

Genetic algorithms for 3d reconstruction with supershapes

Genetic algorithms for 3d reconstruction with supershapes

A New Potential Function for Self Intersecting Gielis Curves With Rational Symmetries

Towards the evolution of vertical-axis wind turbines using supershapes

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