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Midterm Exam Solutions - Digital Image Processing | EE 465, Exams of Electrical and Electronics Engineering

West Virginia University (WVU)Electrical and Electronics Engineering
Prof. Xin Li

Material Type: Exam; Professor: Li; Class: Intro to Digital Image Process; Subject: Electrical Engineering; University: West Virginia University; Term: Spring 2006;

Typology: Exams

Pre 2010

Uploaded on 08/01/2009

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EE465 Introduction to Digital Image Processing
Spring 2006 โ€“ Midterm Exam
Mar 9, 2006 (9:30-10:45AM)
INSTRUCTIONS:
1) Please write your name and G/UG in the front page of your answer sheets.
2) This is a closed-book exam, but you are allowed to use the available computing (not
human) resource.
3) You have 75 minutes to complete five problems. The number of points is given for
each problem and will total 100. The sixth problem is optional โ€“ try it if you have time.
1. (Set and morphological operators, 20 points)
a) (8 points) Given X={(1,2),(1,-1),(0,3)}, B={(-1,0),(0,1),(0,0)} and
z=(-1,1), calculate Xz and
B
ห†;
Xz={(0,3),(0,0),(-1,4)},
B
ห†={(1,0),(0,-1),(0,0)}
b) (12 points) Binary image X and structuring element are given as follows.
X B
Calculate Y1=BXฮ˜, where
ฮ˜
denotes the morphological erosion operator and
Y2=BX cห†
โŠ• where โŠ• denotes the morphological dilation operator;
Y1 Y2
2. (Distance transform, 20 points)
a) (12 points) Calculate the distance transform of the following binary image:
origin
pf3

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Download Midterm Exam Solutions - Digital Image Processing | EE 465 and more Exams Electrical and Electronics Engineering in PDF only on Docsity!

EE465 Introduction to Digital Image Processing Spring 2006 โ€“ Midterm Exam Mar 9, 2006 (9:30-10:45AM)

INSTRUCTIONS:

  1. Please write your name and G/UG in the front page of your answer sheets.
  2. This is a closed-book exam, but you are allowed to use the available computing ( not human ) resource.
  3. You have 75 minutes to complete five problems. The number of points is given for each problem and will total 100. The sixth problem is optional โ€“ try it if you have time.
  1. (Set and morphological operators, 20 points) a) (8 points) Given X={(1,2),(1,-1),(0,3)}, B={(-1,0),(0,1),(0,0)} and

z=(-1,1), calculate Xz and B ห†^ ;

Xz={(0,3),(0,0),(-1,4)}, B ห†^ ={(1,0),(0,-1),(0,0)}

b) (12 points) Binary image X and structuring element are given as follows.

X B

Calculate Y 1 = X ฮ˜ B^ , where ฮ˜^ denotes the morphological erosion operator and

Y 2 = X^ B

c ห†

โŠ• where โŠ• denotes the morphological dilation operator;

Y 1 Y 2

  1. (Distance transform, 20 points) a) (12 points) Calculate the distance transform of the following binary image:

origin

X

Note: the formula of calculating distance transform is given by

X 0 ( m , n )= X ( m , n ), Xk ( m , n )= X 0 ( m , n )+min{ Xk โˆ’ 1 ( i , j )|( i , j ): d ( m , n ; i , j )โ‰ค 1 }

where d(m,n;i,j) denotes the city-block distance between (m,n) and (i,j); 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 2 2 2 0 0 0 0 1 2 3 2 1 0 0 0 0 1 2 2 2 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0

b) (8 points) Use distance transform to find the skeleton of this image. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

  1. (Entropy calculation and Huffman coding, 20 points) a) (8 points) Compute the entropy for the following discrete source: a balanced dice with no face โ€œ5โ€ or โ€œ 6 โ€ but two faces being โ€œ1โ€ and โ€œ 2 โ€, i.e., P(X=5)=P(X=6)=0 , P(X=3)=P(X=4)=1/6 and P(X=1)=P(X=2)=1/3. H(X)=1.918bps

b) (8 points) Design Huffman codes for the above 4-ary source;

c) (4 points) Calculate the code redundancy of the Huffman codes generated in b); r=l (^) avg -H(X)=2-1.918=0.082bps