The differences between the membranes become most apparent for extremely concave regions. Consider filling an omega-shaped hole(top row). While the Laplace membrane succeeds in eliminating the hole with almost no visible trace, MVC interpolation is less successful.
In a more typical scenario with less extreme gradients and some texture, the results become comparable in quality, even though the same concave region is used(bottom row).
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Input Laplace MVC Input Poisson Cloning MVC Cloning