Considering a minimization of the Mumford and Shah energy functional for purposes of image segmentation, I understand why we'd want to enforce the first two terms of the energy. I don't understand the benefit of minimizing the final term, which represents border length of an image segment:
If the idea is to find an "ideal" boundary to segment the image, why should the boundary be constrained by length? What if the image is naturally segmented into a very large partition? Wouldn't minimizing this term then have an adverse affect on the convergence to the "ideal" partition?
To summarize into a single question:
What is the intuition behind minimizing boundary length for segmentation?