How to get the values for C1 and C2 in Chan-Vese Model? This question will consider the widely accepted segmentation algorithm of Chan-Vese, given in the following publications:


  T.F. Chan, L.A. Vese, An active contour model without edges, Lecture
  Notes in Computer Science, vol. 1682, pp. 141–151, 1999.
  
  T.F. Chan, L.A. Vese, Active Contours Without Edges, IEEE
  Transactions on Image Processing, vol. 10, no. 1, pp. 266–277, 2001


The main publication is accessible here:
http://www.math.ucla.edu/~lvese/PAPERS/IEEEIP2001.pdf

Equation 6 and 7 of this paper mentions $c_1$ and $c_2$ values. The energy function is also parameterized by these variables. My question involves the algorithm / method to compute these values. How can I do that?
The actual formulas are given on the publication, which I linked by editing your question. Besides, there are many publicly available implementations of Chan-Vese algorithm, including, but not limited to:

https://www.mathworks.com/matlabcentral/fileexchange/23445-chan-vese-active-contours-without-edges

https://github.com/kevin-keraudren/chanvese

http://www.ipol.im/pub/art/2012/g-cv/

https://www.mathworks.com/matlabcentral/fileexchange/19567-active-contour-segmentation

http://math.arizona.edu/~rcrandall/code.html

I think you could find all the details in those generously shared source codes.