Extraction of visual features from images often involves convolution with filters that are themselves

constructed from combinations of differential operators. One example is the Laplacian $gra{d}^2=\frac{de{l}^2}{del{x}^2}+\frac{de{l}^2}{del{y}^2}$

of a Gaussian $n(x,y,)$ having scale parameter $,$ generating the filter $gra{d}^{2}n(x,y,)$ for convolution with

the image $I(x,y).$ Explain in detail each of the following three operator sequences, where $**$ signifies

two$-$dimensional convolution.

$($a$)gra{d}^2[n(x,y,)**I(x,y)]$

$($b$)n(x,y,)**gra{d}^{2}I(x,y)$

$($c$)[gra{d}^{2}n(x,y,)]**I(x,y)$

What are the differences amongst them in their effects on the image?