Computer Science - The City College of New York
CSC I6716 - Spring 2015 3D Computer Vision
Assignment 1 ( Deadline: March 03 before class)
======================================================================
Note: All the writings must be hard copies in print - you may hand
them in during class, or put them in Prof. Zhigang Zhu's mailbox in
the CS main office. . You also need to turn in your “soft” copies of
your assignment by sending Prof. Zhu by email attachments. You are
responsible for the lose of your submissions if you don’t
include “CSC I6716 ”
(exactly) in the subject of
your email. Send your source code ONLY – please don’t send in your
images and executable. Do write your names and IDs (last four
digits) in both your hard copy and soft copy submissions.
1. Writing Assignments (10x4 = 40 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). In the thin lens model, 1/o + 1/i =
1/f, there are three variables, the focal length f, the object
distance o and the image distance i (please refer to Slide # 18 of
the Image Formation lecture). If we define Z = o-f, and z
= i-f, please
write
two a few words to describe the physical meanings of Z and z, and
prove that Z*z = f*f given 1/o
+ 1/i = 1/f.
(4). 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 if you like, but you will need to bring
your own machine to me in my office hours to run
your programs. ) (10x6 = 60 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:
- Read in a color image C1(x,y) = (R(x,y), G(x,y), B(x,y)) in
Windows BMP format, and display it.
- 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.
- 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).
- 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.
- 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)?
- 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.