I will pay $20 to whoever can help me figure out this fucking paper
https://openaccess.thecvf.com/content_CVPR_2020/html/Hou_Learning_to_Structure_an_Image_With_Few_Colors_CVPR_2020_paper.html

I'm a fucking brainlet, please help.
The topic is convolutional neural network and color quantization
I'm can understand the first 3 equations (the third one kind of) , but after that, I can't manage.

I'm confused on T(x) speficially (why its shape is C x 3), which depends on M(x), but I don't know what a color index map exactly is (although I have some idea).