Topic
Bicubic interpolation
About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.
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TL;DR: A surface interpolation method with local control for meshes of cubic curves is described that gives extra control to the user while preserving first order geometric continuity between the patches.
22 citations
TL;DR: The proposed DnSRGAN method can solve the problem of high noise and artifacts that cause the cardiac image to be reconstructed incorrectly during super-resolution, and is capable of high-quality reconstruction of noisy cardiac images.
22 citations
TL;DR: A short survey on the main methods for the scattered data problem can be found in this article, where the authors present a new triangle-based interpolation method and show its application to a case study.
Abstract: Local numerical methods for scattered data interpolation often require a smart subdivision of the domain in geometrical polyhedral structures. In particular triangulations in the plane (2D) and tetrahedrizations in the space (3D) are widely used to dene interpolation models. In this paper we give a short survey on the main methods for the scattered data problem and we recall preliminaries on triangulations and their related properties. Finally, combining two well-known ideas we present a new triangle-based interpolation method and show its application to a case study.
22 citations
TL;DR: This work presents an optimization of interpolation parameters of the3-D direct Fourier method with Fourier reprojection (3D-FRP) for fully 3-D positron emission tomography data with incomplete oblique projections, and confirms that for the optimal interpolations parameters a very good image accuracy can be achieved even without any extra spectral oversampling.
Abstract: Fourier-based approaches for three-dimensional (3-D) reconstruction are based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The critical step in the Fourier-based methods is the estimation of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for forward-projection (reprojection). The Fourier-based approaches have the potential for very fast reconstruction, but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions. In our previous work, we have investigated optimal interpolation parameters for the Fourier-based forward and back-projectors for iterative image reconstruction. The optimized interpolation kernels were shown to provide excellent quality comparable to the ideal sinc interpolator. This work presents an optimization of interpolation parameters of the 3-D direct Fourier method with Fourier reprojection (3D-FRP) for fully 3-D positron emission tomography (PET) data with incomplete oblique projections. The reprojection step is needed for the estimation (from an initial image) of the missing portions of the oblique data. In the 3D-FRP implementation, we use the gridding interpolation strategy, combined with proper weighting approaches in the transform and image domains. We have found that while the 3-D reprojection step requires similar optimal interpolation parameters as found in our previous studies on Fourier-based iterative approaches, the optimal interpolation parameters for the main 3D-FRP reconstruction stage are quite different. Our experimental results confirm that for the optimal interpolation parameters a very good image accuracy can be achieved even without any extra spectral oversampling, which is a common practice to decrease errors caused by interpolation in Fourier reconstruction
22 citations
TL;DR: In this article, the Hermite interpolation by planar cubic G 1 splines is studied and sufficient conditions for the existence of such a spline are determined that cover most of the cases encountered in practical applications.
Abstract: In this paper, geometric Hermite interpolation by planar cubic G 1 splines is studied. Three data points and three tangent directions are interpolated per polynomial segment. Sufficient conditions for the existence of such a G 1 spline are determined that cover most of the cases encountered in practical applications. The existence requirements are based only upon geometric properties of data and can easily be verified in advance. The optimal approximation order 6 is confirmed, too.
22 citations