# An integral conservative gridding--algorithm using Hermitian curve interpolation

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K (2008). An integral conservative gridding--algorithm using Hermitian curve interpolation. Physics in medicine and biology, 53(21), pp. 6245-63. Bristol: Institute of Physics Publishing IOP 10.1088/0031-9155/53/21/023

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The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to significantly reduce these interpolation errors. The accuracy of the new algorithm was tested on a series of x-ray CT-images (head and neck, lung, pelvis). The new algorithm significantly improves the accuracy of the sampled images in terms of the mean square error and a quality index introduced by Wang and Bovik (2002 IEEE Signal Process. Lett. 9 81-4).

#### Item Type:

Journal Article (Original Article)

#### Division/Institute:

04 Faculty of Medicine > Department of Haematology, Oncology, Infectious Diseases, Laboratory Medicine and Hospital Pharmacy (DOLS) > Clinic of Radiation Oncology > Medical Radiation Physics

#### UniBE Contributor:

Volken, Werner, Frei, Daniel, Manser, Peter, Mini, Roberto, Born, Ernst Johann, Fix, Michael

0031-9155

18923199

#### Publisher:

Institute of Physics Publishing IOP

English

#### Submitter:

Factscience Import

#### Date Deposited:

04 Oct 2013 15:03

05 Dec 2022 14:19

#### Publisher DOI:

10.1088/0031-9155/53/21/023

18923199

000260133800023

#### URI:

https://boris.unibe.ch/id/eprint/27369 (FactScience: 106828)