An Algorithm for 3D Curve Smoothing

Santana-Cedrés, Daniel; Monzón, Nelson; Álvarez, Luis

doi:10.5201/ipol.2021.292

Cited by 1 publication

(2 citation statements)

References 13 publications

(31 reference statements)

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“…We use some algorithms proposed in [4] to deal with two technical issues related with this scheme: the first one is that we need to compute g(C n,k ) = d(C n,k , C 0 ) + w and ∇g(C n,k ), which requires the computation of the 3D distance to a curve. The second one is that after each iteration we have to reparametrize the discrete curve to preserve the condition C n,k − C n,k−1 = 1 for all n and k = 2, .., χ(C) − 1.…”

Section: Approximation Of the Local Minima Of E( C) By The Steepest-d...mentioning

confidence: 99%

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3D curve regularization

Álvarez

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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In this paper, we study the regularization of 3D curves connecting two points. We propose an energy-based formulation which is an extension to 3D of the geodesic active contours introduced in 2D by Caselles et al. in 1997. By minimizing this energy we try to minimize the curve length but keeping the curve close to the original one. The energy depends on a regularization parameter which determines the smoothness of the regularized curve. We show the Euler-Lagrange equation of the proposed energy using the arc-length parameterization of the curve. We interpret the Euler-Lagrange equation in terms of the Frenet–Serret frame and we study some qualitative properties of the energy minima. We apply the steepest-descent method to approximate the local minima of the energy using an evolution equation. We propose a numerical scheme to solve the evolution equation and we present some experiments on real data in the context of aortic centerline regularization.

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Section: Approximation Of the Local Minima Of E( C) By The Steepest-d...mentioning

confidence: 99%

“…The second one is that after each iteration we have to reparametrize the discrete curve to preserve the condition C n,k − C n,k−1 = 1 for all n and k = 2, .., χ(C) − 1. In both cases we use algorithms proposed in [4] to deal with these issues.…”

Section: Approximation Of the Local Minima Of E( C) By The Steepest-d...mentioning

confidence: 99%

3D curve regularization

Álvarez

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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An Algorithm for 3D Curve Smoothing

Cited by 1 publication

References 13 publications

3D curve regularization

3D curve regularization

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