Bicubic interpolation

About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.

Performing color space conversions with three-dimensional linear interpolation

Abstract: Three-dimensionalinterpolation is suitable for many kinds of color space transformations. We examine and analyze several linear interpolation schemes-some standard, some known, and one novel. An interpolation algorithm design is divided into three parts: packing (filling the space of the input variable with sample points), extraction (selecting from the constellation of sample points those appropriate to the interpolation of a specific input point), and calculation (using the extracted values and the input point to determine the interpolated approximation to the outputpoint). We focus on regular (periodic) packing schemes. Seven principles govern the design of linear interpolation algorithms: 1) Each sample point should be used as a vertex of as many polyhedra as possible; 2) the polyhedra should completely fill the space; 3) polyhedra that share any part of a face must share the entire face; 4) the polyhedra used should have the fewest vertices possible; 5) polyhedra should be small; 6) in the absence of information about cuivature anisotropy, polyhedra should be close to regular in shape; and 7) polyhedra should be of similar size. A test for interpolation algorithm performance in performing actual color space conversions is described, and results are given for an example color space conversion using several linear interpolation methods. The extractions from cubic, body-centered-cubic, and face-centered-cubic lattices are described and analyzed. The results confirm Kanamori's claims for the accuracy of PRISM interpolation; it comes close to the accuracy of trilinear interpolation with roughly three-quarters the computations. The results show that tetrahedral interpolation, with close to half the computational cost of tnlinear interpolation, is capable of providing better accuracy. Of the tetrahedral interpolation techniques, one diagonal extraction from cubic packing is useful as a general-purpose color space interpolator...

Unsupervised Learning for Real-World Super-Resolution

Abstract: Most current super-resolution methods rely on low and high resolution image pairs to train a network in a fully supervised manner. However, such image pairs are not available in real-world applications. Instead of directly addressing this problem, most works employ the popular bicubic downsampling strategy to artificially generate a corresponding low resolution image. Unfortunately, this strategy introduces significant artifacts, removing natural sensor noise and other real-world characteristics. Super-resolution networks trained on such bicubic images therefore struggle to generalize to natural images. In this work, we propose an unsupervised approach for image super-resolution. Given only unpaired data, we learn to invert the effects of bicubic downsampling in order to restore the natural image characteristics present in the data. This allows us to generate realistic image pairs, faithfully reflecting the distribution of real-world images. Our super-resolution network can therefore be trained with direct pixel-wise supervision in the high resolution domain, while robustly generalizing to real input. We demonstrate the effectiveness of our approach in quantitative and qualitative experiments.

The interpolation of rotations and its application to finite element models of geometrically exact rods

Abstract: The finite element formulation of geometrically exact rod models depends crucially on the interpolation of the rotation field from the nodes to the integration points where the internal forces and tangent stiffness are evaluated. Since the rotational group is a nonlinear space, standard (isoparametric) interpolation of these degrees of freedom does not guarantee the orthogonality of the interpolated field hence, more sophisticated interpolation strategies have to be devised. We review and classify the rotation interpolation techniques most commonly used in the context of nonlinear rod models and suggest new ones. All of them are compared and their advantages and disadvantages discussed. In particular, their effect on the frame invariance of the resulting discrete models is analyzed.

Addendum: B-spline interpolation in medical image processing

Abstract: Analyzes B-spline interpolation techniques of degree 2, 4, and 5 with respect to all criteria that have been applied to evaluate various interpolation schemes in a recently published survey on image interpolation in medical imaging (Lehmann et al., 1999). It is shown that high-degree B-spline interpolation has superior Fourier properties, smallest interpolation error, and reasonable computing times. Therefore, high-degree B-splines are preferable interpolators for numerous applications in medical image processing, particularly if high precision is required. If no aliasing occurs, this result neither depends on the geometric transform applied for the tests nor the actual content of images.