The Gateway to Computer Science Excellence
+3 votes
1k views

Given two spatial masks

$S_{1}= \begin{bmatrix}
0&1&0 \\
1&-4&0 \\
0&1&0
\end{bmatrix}$ 

$S_{2} = \begin{bmatrix}
1&1&1 \\
1&-8&1 \\
1&1&1
\end{bmatrix}$

The Laplacian of an image at all points $(x, y)$ can be implemented by convolving the image with spatial mask. Which of the following can be used as the spatial mask ?

  1. only $S_{1}$
  2. only $S_{2}$
  3. Both $S_{1}$ and $S_{2}$ 
  4. None of these 
in Digital Signal Processing by Boss (30.2k points)
recategorized by | 1k views

1 Answer

+5 votes

The ans is S2 only i.e option B

spatial mask  for point (x,y) used to implement the digital  Laplacian of the 2-D is given by

[ f(x+1,y),f(x-1,y),f(x,y+1),f(x,y-1)]-4f(x,y) so possible mask are 

0   1   0              1      1    1

1  -4   1     or      1      8     1  

0   1   0              1      1     1

here in S1  a 1  is missing on the right side of -4  

by Boss (48.8k points)

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,644 questions
56,507 answers
195,558 comments
101,061 users