GEORGIA INSTITUTE OF TECHNOLOGY
School of Electrical and Computer Engineering
ECE 6258
Digital Image Processing
Fall 2003
Problem Set #1
Issued: Friday, August 22, 2003
Due: Monday, September 1, 2003
Problem 1.1 (Quantization): On the class webpage
http://www.ee.gatech.edu/users/rmm/fall2003/ece6258/ece6258fall03.html
you will find a file containing a copy of the Cameraman image,
cameraman.tif. (It is also available in the Image Processing Tool-
box in Matlab.)
(a) Read the image into Matlab and quantize it uniformly to ten
levels. Turn in both the original image and the quantized image.
Evaluate the mean squared error between the original image and
the quantized image. Be careful to select the representative levels
to make the mean squared error as small as possible.
(b) Generate random noise uniformly distributed over [−d/2,d/2],
where dis the step size for the quantization in part (a), and add
this noise to the original image. Quantize this dithered image
uniformly to 10 levels. Turn in this dithered and quantized im-
age. Also, evaluate the mean squared error between the original
and the dithered and quantized image.
(c) In which case ((a) or (b)) do you get a higher mean squared error?
In which case do you get a higher subjective quality. Explain
your answers briefly.
Problem 1.2 (Image Segmentation): Download the (color) aerial im-
age of the Island of Jersey (jersey.jpg) from the class webpage.
(a) Write an image processing algorithm in Matlab that measures
the area of the island in pixels. If each pixel corresponds to a
square surface patch that is 30m on a side, estimate the area of
the island in square kilometers.
(b) Turn in a mask image in which the island pixels are colored white
and the remainder of the image is black.
(c) (optional) Think about how you might derive an automatic pro-
cedure that will clean up the mask image in (b) so that the white
pixels are confined to the main island.
Problem 1.3 (2-D Convolution): Consider the sequence xdefined by
x[n1, n2] = (1,0≤n1≤n2
0,otherwise.
Determine the convolution of xwith itself.