On Two Algorithms for Multi-Modality Image Registration Based on Gaussian Curvature and Application to Medical Images

Begum, Nasra; Badshah, Noor; Ibrahim, Mazlinda; Ashfaq, Muniba; Minallah, Nasru; Atta, Hadia

doi:10.1109/access.2021.3050651

Cited by 7 publications

(1 citation statement)

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“…The proposed model is discretized using a dedicated scheme introduced in [2] and optimized by gradient descent. The augmented Lagrangian method (ALM) has demonstrated superior performance in image processing [43,10,44,32] and has been applied to optimize Gaussian curvature based models for image denoising [6,38], image registration [3,31], and image inpainting [47]. Although the ALM may converge very quickly, its performances are sensitive to the choice of the augmentation parameters.…”

Section: Introductionmentioning

confidence: 99%

An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging

Líu¹,

Tai²,

Glowinski³

2021

Preprint

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Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon in literature. In this article, we propose an operator-splitting method for a general Gaussian curvature model. In our method, we decouple the full nonlinearity of Gaussian curvature from differential operators by introducing two matrix-and vector-valued functions. The optimization problem is then converted into the search for the steady state solution of a time dependent PDE system. The above PDE system is well-suited to time discretization by operator splitting, the sub-problems encountered at each fractional step having either a closed form solution or being solvable by efficient algorithms. The proposed method is not sensitive to the choice of parameters, its efficiency and performances being demonstrated via systematic experiments on surface smoothing and image denoising.

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