Confusion Related to the Laplacian Filter
The Laplace filter is the sum of the differences of neighbourhood pixels compared to the central pixel. Its output will be zero in regions where the intensity is constant, and non-zero when there is a transition in intensity (i.e. an edge).

For simplicity's sake, consider what happens in one axis only, where the filter kernel would be [1 -2 1]. If we have a sequence of values with a step transition then the input and output will look like this:

input:  10   10   10   10   10  100  100  100  100  100

output:       0    0    0   90  -90    0    0    0