Short basis functions for constant-variance interpolation

Philippe Thévenaz; Thierry Blu; Michael Unser

doi:10.1117/12.770234

26 March 2008 Short basis functions for constant-variance interpolation

Philippe Thévenaz, Thierry Blu, Michael Unser

Proceedings Volume 6914, Medical Imaging 2008: Image Processing; 69142L (2008) https://doi.org/10.1117/12.770234
Event: Medical Imaging, 2008, San Diego, California, United States

Abstract

An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and its support. However, as has been recently shown, these features are blind to the amount of registration bias created by the interpolation process alone; an additional requirement that has been named constant-variance interpolation is needed to remove this bias. In this paper, we present a theoretical investigation of the role of the interpolation basis in a registration context. Contrarily to published analyses, ours is deterministic; it nevertheless leads to the same conclusion, which is that constant-variance interpolation is beneficial to image registration. In addition, we propose a novel family of interpolation bases that can have any desired order of approximation while maintaining the constant-variance property. Our family includes every constant-variance basis we know of. It is described by an explicit formula that contains two free functional terms: an arbitrary 1-periodic binary function that takes values from {-1, 1}, and another arbitrary function that must satisfy the partition of unity. These degrees of freedom can be harnessed to build many family members for a given order of approximation and a fixed support. We provide the example of a symmetric basis with two orders of approximation that is supported over [-3/2, 3/2] this support is one unit shorter than a basis of identical order that had been previously

Citation Download Citation

Philippe Thévenaz, Thierry Blu, and Michael Unser "Short basis functions for constant-variance interpolation", Proc. SPIE 6914, Medical Imaging 2008: Image Processing, 69142L (26 March 2008); https://doi.org/10.1117/12.770234

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