Abstract
Digital interpolation is one of the best-kept secrets in medical imaging. Everyone has “kind of” heard about it, but only a few know what it really does. Nonetheless, its effects on diagnostic image quality are profound, and must not be ignored.
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Notes
- 1.
Examples of less-trivial image transformations include nonlinear image registration, 3D rendering, functional maps, etc.
- 2.
This is why you can find the “bi” prefix in the image interpolation algorithm names: “bilinear”, “bicubic”.
- 3.
Note that our definition of “natural” is based entirely on our subjective expectations for normal human imaging and anatomy. The same “staircasing” interpolation would have worked perfectly for a chessboard image.
- 4.
Linear interpolation, as a linear function, cannot have local peaks.
- 5.
For example, DICOM would use 16 bits per pixel to store grayscale medical images, such as X-rays, MRI or CT.
- 6.
Note that we added the requirement of symmetric kernels: h(x) = h(−x).
- 7.
Note how the formula uses the absolute value |x| to satisfy h(x) = h(−x).
- 8.
For example, integer division like 14/3 would produce 4 in virtually all programing languages. This is often referred to as “floor” truncation; for example, floor(2.6) = 2.
References
Keys, R. G., 1981. Cubic Convolution Interpolation for Digital Image Processing. IEEE Transactions on Acoustics, Speech, and Signal Processing, pp. 1153–1160.
Lehmann, T. M., Gönner, C. & Spitzer, K., 1999. Survey: Interpolation Methods in Medical Image Processing. IEEE Transactions on Medical Imaging, pp. 1049–1075.
Pianykh, O. S., 2012. DICOM: A Practical Introduction and Survival Guide. Berlin, New York: Springer.
Pianykh, O. S., 2012. Finitely-supported L2-optimal kernels for digital signal interpolation. IEEE Transactions on Signal Processing, pp. 494–498.
Unser, M., 2000. Sampling-50 years after Shannon. Proceedings of the IEEE, pp. 569–587.
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Pianykh, O.S. (2014). Image Interpolation. In: Digital Image Quality in Medicine. Understanding Medical Informatics. Springer, Cham. https://doi.org/10.1007/978-3-319-01760-0_3
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DOI: https://doi.org/10.1007/978-3-319-01760-0_3
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