First, consider case where:
This means all gradients in neighborhood are:
(k,0) or
(0, c) or (0, 0)
(or off-diagonals cancel).
What is region like if:
1.l1
= 0?
2.l2
= 0?
3.l1
= 0 and l2 = 0?
4.l1
> 0 and l2 > 0?