# Combining multiple similarity measures in hyperspectral images?

I have a hyperspectral image where the pixels are 21 channels. So each pixel $\in \mathbb{R}^{21}$. I want to perform clustering on the pixels with similarity defined by two different measures, one how close the pixels are, and the other how similar the pixel values are.

Thus if $X_1$ and $X_2$ are the locations of pixels $p_1$ and $p_2$ I have: $$S_X = \|X_1-X_2\|^2_2$$ and $$S_p = \|p_1-p_2\|^2_2$$.

I have seen these measures combined into a single measure like this: $$S= e^{-\frac{S_p}{\sigma^2_p}} \times \,\, e^{-\frac{S_X}{\sigma^2_X}}$$

My question: Is there a right way and a wrong way to combine measures like this, or if it improves my clustering can I combine the measures in any way that suits me?

My question is vaguely related to Combining multiple similarity measures.

• It probably is so highly application and data dependant that we cannot answer this question. Jun 10, 2013 at 21:34
• For reference, this similarity measure is the same as used in bilateral filtering, which is an edge-preserving smoothing filter commonly used in robust image denoising (e.g. for pre-processing in an image-segmentation pipeline). Sep 18, 2016 at 16:01