ECE-S490 Digital Image Processing
Homework 2
1. Let h(m,n), m=1,..,M, n=1,..,N be a 2D-FIR filter kernel.
Let
∑
=
NM,
nm,
1n)h(m,
,
Let X and Y be images and Y=h*X
Show that the average brightness of Y is equal to the average brightness of X.
2. Let
|
ws s
Xθ|Argminθ
ˆ∑
∈
−=
be a location estimate of {Xs, s∈ w}. Show
that
θ
ˆ
is the median of {Xs, s∈ w}.
3. Is median filter homogeneous?
Is median filter linear?
Explain.
4. There are different discrete approximations for the Laplacian operator.
One form of discrete approximation and the resulting Laplace mask for this
approximation is given in class as:
−
−−
−
0210
21221
0210
/
//
/
Determine the underlying discrete approximation for the Laplace mask given
below:
−−−
−−
−−−
111
181
111
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