Homework Assignment 1 - Problems Due Jan 24.

Read Chapter 1.

Software preparation.
Download and install Image/J on your computer (http://rsb.info.nih.gov/ij/index.html).  You will also want to download the image folder and the documentation.  Other programs can be downloaded if you wish (URLs are on Protocols page).

Problem Set 1:
1.  Estimate the smallest dot that can be seen from 20 cm.  Assume that the dot cannot be seen if its image stimulates only a single cone in the fovea, and that the fovea is 1.5 mm in diameter and that the effective lens center of the eye is 14 mm from the retina.  

2.  About how long will it take to transmit a 256 level (8 bits) grayscale image of size 512 x 512 at a baud rate (bits/s) of 9600? 

3.  A 4 x 4 image has values {{3,1,2,1(q)},{2,2,0,2},{1,2,1,1},{1(p),0,1,2}}.  Compute the D₄,  D₈, and D_m distances between p and q subject to V{0,1} [i.e., considering only pixels with values of 0 or 1].

Homework Assignment 2 - Problems Due Jan 31.

Read Chapter 2 (pp. 40 - 71).

Problem Set 2:
1.  Show that the discrete Fourier transform and its inverse are periodic functions.  Assume 1-dimensional  functions.

2.  Show the validity of the translation properties of the discrete 2-dimensional Fourier transform pair.  Show the translation properties for the special case of a square image when w_o = z_o = N/2.

3.  A one-dimensional function f(x) is sampled at four points: x_o = 0.5, x₁ = 0.75, x₂ = 1.0, and x₃ = 1.25, producing data values f(x) at those points of 2, 3, 4, 4, respectively. Calculate the Fourier transform, and determine the Fourier spectrum.

Solutions are here.

Homework Assignment 3 - Problems Due Feb 7.

Read Chapter 3.

Problem Set 3:
1.  An image has the gray level PDF p_r(r) shown in the image shown below on the left.  Assume continuous quantities and find the transformation (in terms of r and z) that will map p_r(r) to the p_z(z) shown below on the right.  

z

Solution is here.

2.  Do Lab 1.

Homework Assignment 4  -  Problems Due Feb 14.

. Read Chapter 4, sections 4.1 to 4.3, inclusive.

Problem Set 4.
1.  Form a low-pass spatial filter that averages the 4-neighbors of a point but excludes the point itself.  (a) Find the equivalent filter H(n,m) in the frequency domain. (b) Show that this is a low-pass filter.

2.  Using the image shown below (icextl.tif), use sharpening to enhance the pictures.  What can you do about the uneven illumination?  Can you improve the picture?

Solutions are here.

Homework Assignment 5 - Problems Due Feb 21.

Read Chapter 4, section 4.4, on image restoration.
Read Chapter 5, sections 5.1 to 5.2, inclusive, on rank or statistic filters.

Homework Assignment 6 - Problems Due Mar 28.

Read Chapter 5, section 4, on homomorphic filters.
Read Chapter 6 on color models and filtering of color images.

Homework Assignment 7 - Problems Due Apr 9.

Read Chapter 7, sections 7.3 to 7.4, on morphological filters.
Read Chapter 8, section 1, on image thresholding.

Homework Assignment 8 - Problems Due Apr 18.

Read Chapter 8, sections 8.2 to 8.4, on edge detection, region based segmentation, and image representation.

Homework Assignment 9 - Problems Due Apr 30.

Read Chapter 9. Error-free and lossy compression methods.