Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 1: Due Feb. 11.
1.1 Determine if y[n]=3x[n]+7 is linear? time-invariant?
1.2 Prove that convolution is

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
Lossy Still Image Coding
DPCM approach:
pp
earliest and simplest
p
non-PCM method.
Transformation-Qu

Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 4: Due Mar. 3.
4.1 2-D DFT and DCT are separable, and can be implemented through 1-D DFT or DCT
along

Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 8: Due Apr. 28.
8.1 Quantization and Huffman coding
8.1.1 Use a 5-level uniform scalar quantizer as sh

511
200
511
Vertical edge
Apply R1 ﬁlter
output 0
jout ut-150
I: P
zoozoozoo so so
zoozoolzoo: o so so
zoo zoo zoo so so so
zoo zoo zoo _s_o_ so so
zoo zoo zoo so so so
zoo zoo zoo so so so
Horizontal edge
Apply R1 filter
output 0
P3 output 150
II
so

Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 2: Due Feb. 18.
2.1 (1A) Prove the multiplication property of DTFT
DTFT
x[ n] y[ n]
1
X ( e j )Y ( e

n2
1
1
2
1
2
1
2
0
n2
x[n1,n2]
1
h[n1,n2]
3
1
2
n1
1
Step 1: flip h[n1,n2] twice to form a mask,
0
4
n1
1
indicates the origin
mask
4
2
1
3
4
2
1
3
Step 2: slide the mask from left to right and from bottom to top on the x[n1,n2] plane,
and generate one ou

DFT Example
N 1
X [ k ] = x[ n] e
j
2
kn
N
0 k N 1
,
n =0
If N = 4, Then we have
X [ k = 0] = x[ n = 0]e
X [ k = 1] = x[ n = 0]e
j
j
2
( k =1)( n =0)
4
j
2
( k = 2)( n =0)
4
j
2
( k =3)( n =0)
4
X [ k = 2] = x[ n = 0]e
X [ k = 3] = x[ n = 0]e
2
( k =0)( n

x[k]
2
h[k]
2
1
1
1
1
0
0
k
1
0
1
Step 1: flip h[k] to form a filter mask,
indicates the origin of the mask
mask
h[-k]
1
1
1
0
1
0
0
-1
k
-1
-1
k
1
-1
Step 2: slide the mask from left to right on the x[k] plane, and generate one output
sample at a time on

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
Geometric Processing
Simple
p image
g ggeometric pprocessingg includes
Scaling
Rotation
Translatio

Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 3: Due Feb. 25.
3.1 (1A) Given:
x 1[n] [n] 2[n 1]
x 2 [n] 2[n] [n 1] [n 2]
3.1.1 Compute the linear co

In a DPCM system:
1. Assume the prediction function used by the encoder and decoder is
x%
[n] x[ n 1] ,
which means the previous sample is used as the prediction of the current sample;
2. We assume there is no quantization error, i.e. all samples are alre

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
Announcements
Project
j report
p (2~5
(
pages)
p g ) and presentation
p
(10
( min.):
)
Clearly state

Stevens Institute of Technology
Department of Electrical and Computer Engineering
CpE 462 Introduction to Image Processing
Homework 8:
8.1 Quantization and Huffman coding
8.1.1 Use a 5-level uniform scalar quantizer as shown to quantize the sample sequenc

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
Image Analysis
Common image
g analysis
y operators
p
Feature detection
Feature extraction, segmenta

Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 7: Due Apr. 21.
7.1 Assume that a bi-level input image x[n1, n2] of 512512 as shown below, where the
d

Stevens Institute of Technology
Department of Electrical and Computer Engineering
Spring Semester 2016
CpE 462 Introduction to Image Processing
Homework 5: Due Mar. 31.
5.1 Follow the steps carefully:
o Unzip the file matlab_files.zip and save all files i

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
Area Processing
Area pprocessingg usuallyy
are 2-D filtering operation.
Two major tasks:
Smoothing:

Given:
Reference frame
Current frame
1. Partition the current frame to macro blocks, no partitioning on
the reference frame
Note that the coordinate system for motion vectors is usually
defined as the following, and the motion vector is pointing from
the

HW7.3
Iterative thresholding:
new_T = 200.0; /* initial threshold */
delta_T = 100.0; /* any big number to get into the loop */
while (delta_T > 5.0 | delta_T < -5.0)
cfw_
count1 = 0; count2 = 0;
sum1 = 0.0; sum2 = 0.0;
for (j=0; j<height; j+)
for (k=0; k

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
2-D Signals
A 2-D signal
g
x[n
[ 1 ,n2] is a function of two independent
p
variables
Elementary 2-D

CpE
p 462 Introduction to Image
g
Processing and Coding
Prof. Hong Man
Department of Electrical and
Computer Engineering
Stevens Institute of Technology
Image Perception
Image
g pperception
p
involves three components:
p
Light source
i( x, y, )
Illumin

5.1 Follow the steps carefully: o Unzip thefile "matlab_files.zip" and save all files in your working directory with images. o Use your camera to take a color picture and save it in JPEG format. o Then open the picture in Matlab use the "readjpg" fun