What is the effect of changing the order of a Butterworth filter from 3 to 5?

Increasing the order of a Butterworth filter from 3 to 5 has a specific impact on the characteristics of the filtering process applied to an image. A Butterworth filter is designed to create a smooth frequency response, and as the order of the filter increases, the transition band becomes steeper. This results in a more selective filtering process, allowing high-frequency components (which contribute to noise and fine detail) to be attenuated more efficiently.

When the order changes from 3 to 5, the filter produces a greater degree of smoothing in the image. The additional steepness means that while high-frequency noise is reduced more effectively, the overall image quality tends toward a smoother appearance, with less sharp detail. This is particularly useful in nuclear medicine imaging, where the goal is often to enhance diagnostic clarity by reducing noise that may obscure important anatomical or functional information.

Thus, a Butterworth filter of higher order smooths the image more substantially, making the selection that describes this effect accurate.