Create and merge superpixels by color and texture. Can you explain the article?

Question

Image processing

Hello,
I found an interesting article, which, according to the pictures inside, obtained excellent results in segmenting images based on their color and texture.
The article itself, "Texture superpixels merging by color-texture histograms for color image segmentation", can be downloaded from ResearchGate. What is the meaning of the article:
1. First, using Gabor filters, we obtain information about the texture
2. Based on the information about color and texture, we build superpixels. A new distance metric has been invented that allows you to take into account both color and texture at once
3. Combine superpixels by color (criterion - local histograms normalized by area and texture)
Actually, I didn’t understand the most important things (further notation in the article)
equation 2: is the standard deviation constant for all Gabor filters? Usually they make a different
equation 4: what dimension does Tf get: (M,N, n*k) or (M,N)?
Equation 6: ||(L,a,b)|| - Euclidean norm or something else?
equation 8: Looks like a typo: any non-zero Tf(i) results in zero
equation 9: how to calculate R? Is it just a range of values?
equations 11-13: I didn't understand the idea, where can I read about it?
I would be very grateful for the explanations, if the code works, I will post it on github and indicate the link here