10.16 One often finds in the literature a derivation of the Laplacian of a Gaussian (LOG)...

  

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10.16 One often finds in the literature a derivation of the Laplacian of a Gaussian (LOG) that starts with the expression G(r) = eno where 2+ y. The LoG is then found by taking the second partial derivative: V2G(r) = aG/ar. Finally, x + y is substituted for 2 to get the (incorrect) result == VG(x, y) = [(x + y - )/04] exp[-(x + y)/20] Derive this result and explain the reason for the difference between this expres- sion and Eq. (10.2-23). - VG(x, y) = (10.2-23) 10.16 One often finds in the literature a derivation of the Laplacian of a Gaussian (LOG) that starts with the expression G(r) = eno where 2+ y. The LoG is then found by taking the second partial derivative: V2G(r) = aG/ar. Finally, x + y is substituted for 2 to get the (incorrect) result == VG(x, y) = [(x + y - )/04] exp[-(x + y)/20] Derive this result and explain the reason for the difference between this expres- sion and Eq. (10.2-23). - VG(x, y) = (10.2-23)