Interpolation using surface splines.
01 Feb 1972-Journal of Aircraft (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 9, Iss: 2, pp 189-191
TL;DR: A surface spline is a mathematical tool for interpolating a function of two variables as discussed by the authors, which is based upon the small deflection equation of an infinite plate and requires the use of a digital computer.
Abstract: A surface spline is a mathematical tool for interpolating a function of two variables. It is based upon the small deflection equation of an infinite plate. The surface spline depends upon the solution of a system of linear equations, and thus, will ordinarily require the use of a digital computer. The closed form solution involves no functions more complicated than logarithms, and is easily coded. Several modifications which can be incorporated are discussed.
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TL;DR: A review of recent as well as classic image registration methods to provide a comprehensive reference source for the researchers involved in image registration, regardless of particular application areas.
6,842 citations
Cites methods from "Interpolation using surface splines..."
...Although they had been used in mechanics and engineering for decades [84], they were introduced to image analysis community by Grimson [78] and Bookstein [21]....
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01 Sep 1990
TL;DR: Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks as mentioned in this paper, and two extensions of the regularization approach are presented, along with the approach's corrections to splines, regularization, Bayes formulation, and clustering.
Abstract: The problem of the approximation of nonlinear mapping, (especially continuous mappings) is considered. Regularization theory and a theoretical framework for approximation (based on regularization techniques) that leads to a class of three-layer networks called regularization networks are discussed. Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks. Learning as approximation and learning as hypersurface reconstruction are discussed. Two extensions of the regularization approach are presented, along with the approach's corrections to splines, regularization, Bayes formulation, and clustering. The theory of regularization networks is generalized to a formulation that includes task-dependent clustering and dimensionality reduction. Applications of regularization networks are discussed. >
3,595 citations
TL;DR: Description of mapping methods using spherical splines, both to interpolate scalp potentials (SPs) and to approximate scalp current densities (SCDs) with greater accuracy in areas with few electrodes.
2,343 citations
TL;DR: Applications of image registration include combining images of the same subject from different modalities, aligning temporal sequences of images to compensate for motion of the subject between scans, image guidance during interventions and aligning images from multiple subjects in cohort studies.
Abstract: Radiological images are increasingly being used in healthcare and medical research. There is, consequently, widespread interest in accurately relating information in the different images for diagnosis, treatment and basic science. This article reviews registration techniques used to solve this problem, and describes the wide variety of applications to which these techniques are applied. Applications of image registration include combining images of the same subject from different modalities, aligning temporal sequences of images to compensate for motion of the subject between scans, image guidance during interventions and aligning images from multiple subjects in cohort studies. Current registration algorithms can, in many cases, automatically register images that are related by a rigid body transformation (i.e. where tissue deformation can be ignored). There has also been substantial progress in non-rigid registration algorithms that can compensate for tissue deformation, or align images from different subjects. Nevertheless many registration problems remain unsolved, and this is likely to continue to be an active field of research in the future.
2,166 citations
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.
Abstract: Absract. This paper is concerned with the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods. The process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation. To indicate the flavor of the type of results obtained, we give a summary table and representative perspective plots of several surfaces.
2,087 citations
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24 citations
22 Jan 1968
21 citations
01 Jan 1969
TL;DR: In this article, mixing and combustion of gaseous and particle laden jets in air stream, analyzing turbulent, coaxial and jet mixing flows is discussed. But the authors do not consider the effects of particle-laden jets on the mixing flow.
Abstract: Mixing and combustion of gaseous and particle laden jets in air stream, analyzing turbulent, coaxial and jet mixing flows
9 citations