GEORGIA INSTITUTE OF TECHNOLOGY
School of Electrical and Computer Engineering
ECE 6258
Digital Image Processing
Fall 2003
Problem Set #2
Issued: Wednesday, September 3, 2003
Due (live): Friday, September 12, 2003
Due (video): Friday, September 26, 2003
Problem 2.1 (Image Resizing): When magnifying an image, the goal is
to produce a digital image ywith support βL×βM pixels(with β>1)
from an image xwith support L×M. Since the pixel locations in the
larger image, y, do not coincide with pixel locations in x, interpolations
between the pixels of xis needed. Two simple techniques that can be
used for this purpose are the following:
Nearest-Neighbor Interpolation: In this method the value of the
new pixel Sin image yis assigned as the value of the spatially closest
pixel of x(when the inverse mapping is applied). Hence, Stakes the
value of one of S1,S2,S3,orS4, whichever is closest.
Bilinear Interpolation: The new pixel Sin image yis computed
from the four closest (inverse mapped) pixels S1,S2,S3,andS4in
image x.
S=(a)(b)S1+(1−a)(b)S2+(a)(1 −b)S3+(1−a)(1 −b)S4
where
a=(S2−S)h
(S2−S1)h
b=(S3−S)v
(S3−S1)v
(a) For both techniques, answer the following: Is it linear? Is it shift-
invariant?
(b) Show that both schemes are separable.
(c) We want to magnify a 4 ×4 image to size 8 ×8. Because of
separability, we can write this as: y=AxB, where xis a 4 ×4
matrix, yis an 8 ×8matrixandAand Bare transposes of each
other. Write Aand Bfor both interpolation schemes.
(d) Implement your own Matlab code for both schemes to magnify
an image by an arbitrary factor β>1. Magnify the cameraman
image by a factor of 1.25. Turn in the magnified images.
(e) Compare the subjective quality of the magnified images and de-
scribe your observations.
