CSc 59866/59867 Capstone I/II Fall 2016-Spring 2017
CS/CpE/EE Joint Senior Design Program
Smart Living and Assistive Technologies for People in Need

Assignment 2 ( Deadline: November 16 midnight)
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Note: All the writings must be in soft copies (PDF)  Please send the writing report including both the writing and programming assignments (in PDF) to Prof. Zhu <zhu@cs.ccny.cuny.edu> as an email attachment. You are responsible for the loss of your submission if you don’t include  “Capstone 2016 ” (exactly) in the subject of your email.  In your programming report, please specify what programming language you use, and include your experimental results and analysis.


1. Writing Assignments (20x3 = 60 points)
  (1). How does an image change (e.g., objects' sizes in the image, field of view, etc.) if the focal length of a pinhole camera is varied?
  (2). Give an intuitive explanation of the reason why a pinhole camera has an infinite depth of field.
  (3). Prove that, in the pinhole camera model, three collinear points (i.e., they lie on a line)  in 3D space are imaged into three collinear points on the image plane. You may either use geometric reasoning (with line drawings) or algebra proof (using equations).
 

2. Programming  Assignments (Matlab preferred - here is a quick matlab tutorial.  You may use C++ or Java or Python if you like) (40 points in total)

(1) (20 points) Image formation.  In this small project, you are going to use Matlab to read, manipulate and write image data. The purpose of the project is to make you familiar with the basic digital image formations. Your program should do the following things:

1. Read in a color image C1(x,y) = (R(x,y), G(x,y), B(x,y)) in Windows BMP format, and display it.
2. Display the images of the three color components, R(x,y), G(x,y) and B(x,y), separately. You should display three black-white-like images.
3. Generate an intensity image I(x,y) and display it. You should use the equation I = 0.299R + 0.587G + 0.114B (the NTSC standard for luminance).
4. The original intensity image should have 256 gray levels.  Please uniformly quantize this image into K levels ( with K=4, 16, 32, 64).  As an example,  when K=2 ,  pixels whose values are below 128 are turned to 0,  otherwise to 255.  Display the four quantized images with four different K levels  and tell us  how the images still look like the original ones.
   
5. Quantize  the original three-band color image C1(x,y) into K level color images CK(x,y)= (R’(x,y), G’(x,y), B’(x,y)) (with uniform intervals) , and display them. You may choose K=2 and 4 (for each band).  Do they have any advantages in viewing and/or in computer processing (e.g. segmentation)?
6. Quantize  the original three-band color image C1(x,y) into a color image CL(x,y)= (R’(x,y), G’(x,y), B’(x,y)) (with a logarithmic function) , and display it. You may choose  a function  I' =C ln (I+1) ( for each band), where I is the original value (0~255) , I' is the quantized value,  and C is a constant to scale I'  into (0~255), and ln is the natural logarithm.  Please find the best C value so for an input in the range of 0-255, the output range is still 0 - 255. Note that when I = 0, I' = 0 too.

Please for each of the above, provide your observations / conclusions, rather than just show the experimental results.

I have provided a piece of starting code for you to use. Questions a and b have been done.  You only need to work on c to g. You may use Prof. Zhu's old ID picture for testing your algorithm.

(2)(20 points) Generate the histogram of the image you are using, and then perform a number of histogram operations (such as contrast enhancement, thresholding and equalization) to make the image visually better for either viewing or processing (10 points).  If it is a color image,  please first turn it into an intensity image and then generate its histogram.  Try to display your histogram (5 points), and make some observations of the image based on its histogram (5 points). What are the general distributions of the intensity values? How many major peaks and valleys does your histogram have? How could you use the histogram to understand, analyze or segment the image? Please also display the histograms of the processed images and provide a few important observations.