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Lecture 15 4

Previous Lecture: 2-d array examples

Today’s Lecture: Working with images

Announcements: Discussion this week in the UP B7 computer lab Prelim 1 to be returned at end of lecture.

Unclaimed papers (and those on which student didn’t indicate the lecture time) can be picked up during consulting hours (Su-R 5-10p) at ACCEL Green Rm (Carpenter Hall) starting at 5pm today

Lecture 14 6

Who Can Fill the Order?

38 5 99 34

82 19 83 12Inv

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42

42

87

1 0 12 529PO

Yes

No

Yes

Lecture 14 7

Wanted: A True/False Function

iCanDoInv

PO

i

DO

DO is “true” if factory i can fill the order.DO is “false” if factory i cannot fill the order.

Lecture 14 8

Example: Check inventory of factory 2

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82 19 83 12Inv

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42

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1 0 12 529PO

Lecture 14 9

Initialization

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82 19 83 12Inv

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1 0 12 529PO

DO 1

Lecture 14 10

Still True…

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82 19 83 12Inv

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1 0 12 529PO

DO 1

DO = DO && ( Inv(2,1) >= PO(1) )

Lecture 14 11

Still True…

38 5 99 34

82 19 83 12Inv

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42

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1 0 12 529PO

DO 1

DO = DO && ( Inv(2,2) >= PO(2) )

Lecture 14 12

Still True…

38 5 99 34

82 19 83 12Inv

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42

42

87

1 0 12 529PO

DO 1

DO = DO && ( Inv(2,3) >= PO(3) )

Lecture 14 13

No Longer True…

38 5 99 34

82 19 83 12Inv

51 29 21 56

42

42

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DO 0

DO = DO && ( Inv(2,4) >= PO(4) )

Lecture 14 14

Stay False…

38 5 99 34

82 19 83 12Inv

51 29 21 56

42

42

87

1 0 12 529PO

DO 0

DO = DO && ( Inv(2,5) >= PO(5) )

Lecture 14 15

function DO = iCanDo(i,Inv,PO)% DO is true if factory i can fill% the purchase order. Otherwise, false

nProd = length(PO);DO = 1;for j = 1:nProd

DO = DO && ( Inv(i,j) >= PO(j) );end

Encapsulate…

Lecture 14 16

function DO = iCanDo(i,Inv,PO)% DO is true if factory i can fill% the purchase order. Otherwise, falsenProd = length(PO);j = 1;while j<=nProd && Inv(i,j)>=PO(j)

j = j+1;endDO = _______;

Encapsulate…

Lecture 14 17


j = j+1;endDO = _________;

Encapsulate…

DO should be true when…• j < nProd• j == nProd• j > nProd

A

CB

Lecture 14 18


j = j+1;endDO = (j>nProd);

Encapsulate…

Lecture 14 19

iBest = 0; minBill = inf;

for i=1:nFactiBill = iCost(i,C,PO);if iBill < minBill

% Found an Improvement iBest = i; minBill = iBill;

endend

Back To Finding the Cheapest

Lecture 14 20

iBest = 0; minBill = inf;for i=1:nFact

if iCanDo(i,Inv,PO)iBill = iCost(i,C,PO);if iBill < minBill% Found an Improvement

iBest = i; minBill = iBill;end

endend

Back To Finding the Cheapest

See Cheapest.mfor alternative implementation

Lecture 15 24

A picture as a matrix

1458-by-2084

150 149 152 153 152 155151 150 153 154 153 156153 151 155 156 155 158154 153 156 157 156 159156 154 158 159 158 161157 156 159 160 159 162

Lecture 15 25

Images can be encoded in different ways

Common formats include JPEG: Joint Photographic Experts Group GIF: Graphics Interchange Format

Data are compressed We will work with jpeg files:

imread: read a .jpg file and convert it to a “normal numeric” array that we can work with

imwrite: write an array into a .jpg file (compressed data)

Lecture 15 26

Grayness: a value in [0..255]

150 149 152 153 152 155151 150 153 154 153 156153 151 155 156 155 158154 153 156 157 156 159156 154 158 159 158 161157 156 159 160 159 162

0 = black255 = white

These are integer valuesType: uint8

Lecture 15 27

Let’s put a picture in a frame

Things to do:1. Read bwduck.jpg from memory and convert it

into an array2. Show the original picture3. Assign a gray value (frame color) to the “edge

pixels”4. Show the manipulated picture

Lecture 15 28

Reading a jpeg file and displaying the image

% Read jpg image and convert to % an array P

P = imread(‘bwduck.jpg');

% Show the data in array P as % an image

imshow(P)

Lecture 15 29

% Frame a grayscale picture

P= imread(’bwduck.jpg’);imshow(P)

% Change the ”frame” color

imshow(P)

Lecture 15 30



% Change the ”frame” colorwidth= 50;frameColor= 200; % light gray

imshow(P)

Lecture 15 31



% Change the ”frame” colorwidth= 50;frameColor= 200; % light gray[nr,nc]= size(P);for r= 1:nr

for c= 1:nc% At pixel (r,c)

endendimshow(P)

Lecture 15 32



% Change the ”frame” colorwidth= 50;frameColor= 200; % light gray[nr,nc]= size(P);for r= 1:nr

for c= 1:nc% At pixel (r,c)if r<=width || r>nr-width || ...

c<=width || c>nc-widthP(r,c)= frameColor;

endend

endimshow(P)

Things to consider…1. What is the type of the values in P?2. Can we be more efficient?

Lecture 15 33

Accessing a submatrix

M refers to the whole matrix M(3,5) refers to one component of M

2 0.5-1 -3

52 7.581 2

5 98.5-3 10

3 768 7M

Lecture 15 34

Accessing a submatrix

M refers to the whole matrix M(3,5) refers to one component of M M(2:3,3:5) refers to a submatrix of M

2 0.5-1 -3

52 7.581 2

5 98.5-3 10

3 768 7M

row indices

column indices

Lecture 15 35

Grayness: a value in [0..255]

150 149 152 153 152 155151 150 153 154 153 156153 151 155 156 155 158154 153 156 157 156 159156 154 158 159 158 161157 156 159 160 159 162

0 = black255 = white

These are integer valuesType: uint8

A color picture is made up of RGB matrices 3-d array114 114 112 112 114 111 114 115 112 113114 113 111 109 113 111 113 115 112 113115 114 112 111 111 112 112 111 112 112116 117 116 114 112 115 113 112 115 114113 112 112 112 112 110 111 113 116 115115 115 115 115 113 111 111 113 116 114112 113 116 117 113 112 112 113 114 113115 116 118 118 113 112 112 113 114 114116 116 117 117 114 114 112 112 114 115

153 153 150 150 154 151 152 153 150 151153 152 149 147 153 151 151 153 150 151154 153 151 150 151 152 150 149 150 150155 156 155 152 152 155 151 150 153 153151 150 150 150 150 148 149 151 152 151153 153 153 153 151 149 149 151 152 150150 151 152 153 151 150 150 151 152 151153 154 154 154 151 150 150 151 152 152154 154 153 153 149 149 150 150 152 153

212 212 212 212 216 213 215 216 213 213212 211 211 209 215 213 214 216 213 213213 212 210 209 212 214 213 212 213 212214 215 214 214 213 216 214 213 215 212213 212 212 212 212 210 211 213 214 211215 215 216 216 213 211 211 213 212 210212 213 214 215 213 212 212 213 214 213215 216 216 216 213 212 212 213 214 214216 216 215 215 213 213 213 213 214 215

0 ≤ A(i,j,1) ≤ 255

0 ≤ A(i,j,3) ≤ 255

0 ≤ A(i,j,2) ≤ 255E.g., color image data is stored in a 3-d array A:

Lecture 15 36

Lecture 15 37

Operations on images amount to operations on matrices!

Color image 3-d Array

0 ≤ A(i,j,1) ≤ 255

0 ≤ A(i,j,3) ≤ 255

0 ≤ A(i,j,2) ≤ 255

A color picture is made up of RGB matrices 3-d array

Lecture 15 38

Example: Mirror Image

LawSchool.jpg LawSchoolMirror.jpg

1. Read LawSchool.jpg from memory and convert it into an array.

2. Manipulate the Array.3. Convert the array to a jpg file and write it to memory.

Lecture 15 39

Reading and writing jpg files

% Read jpg image and convert to % a 3D array A

A = imread('LawSchool.jpg');

% Write 3D array B to memory as % a jpg image

imwrite(B,'LawSchoolMirror.jpg')

Lecture 15 40

A 3-d array as 3 matrices

[nr, nc, np] = size(A) % dimensions of 3-d array A

#rows#columns

#layers (pages)

4-by-6 M1= A(:,:,1)

4-by-6 M3= A(:,:,3)

4-by-6 M2= A(:,:,2)

A(1:nr,1:nc,1)

Lecture 15 41

%Store mirror image of A in array B

[nr,nc,np]= size(A);for r= 1:nr

for c= 1:nc

B(r,c )= A(r,nc-c+1 );

endend

A B

1

5

2

4

3

3

4

2

5

1

Lecture 15 42

%Store mirror image of A in array B

[nr,nc,np]= size(A);for r= 1:nr

for c= 1:ncfor p= 1:np

B(r,c,p)= A(r,nc-c+1,p);end

endend

Lecture 15 45

% Make mirror image of A -- the whole thing

A= imread(’LawSchool.jpg’);[nr,nc,np]= size(A);

for r= 1:nrfor c= 1:ncfor p= 1:npB(r,c,p)= A(r,nc-c+1,p);

endend

endimshow(B) % Show 3-d array data as an imageimwrite(B,’LawSchoolMirror.jpg’)

Lecture 15 46

% Make mirror image of A –- the whole thing

A= imread(’LawSchool.jpg’);[nr,nc,np]= size(A);

B= zeros(nr,nc,np);B= uint8(B); % Type for image color values

for r= 1:nrfor c= 1:ncfor p= 1:npB(r,c,p)= A(r,nc-c+1,p);

endend

endimshow(B) % Show 3-d array data as an imageimwrite(B,’LawSchoolMirror.jpg’)

Lecture 15 47

Vectorized code simplifies things…Work with a whole column at a time

A

Lecture 15 48


A B

Lecture 15 54


A B

16

Lecture 15 55


A B

16 25

Lecture 15 56


A B

16 25 34

Lecture 15 57


A B

16 25 34 6541 2 3

Column c in Bis column nc-c+1 in A

Lecture 15 58

Consider a single matrix (just one layer)

[nr,nc,np] = size(A);for c= 1:nc

B(: ,c ) = A(: ,nc+1-c );

end

all rows all rows

Lecture 15 59



B(1:nr,c ) = A(1:nr,nc+1-c );

end

Lecture 15 60



B( : ,c ) = A( : ,nc+1-c );

end

Lecture 15 61

Now repeat for all layers


B(:,c,1) = A(:,nc+1-c,1)B(:,c,2) = A(:,nc+1-c,2)B(:,c,3) = A(:,nc+1-c,3)

end

Lecture 15 62

Vectorized code to create a mirror image

A = imread(’LawSchool.jpg’)[nr,nc,np] = size(A);for c= 1:nc

B(:,c,1) = A(:,nc+1-c,1)B(:,c,2) = A(:,nc+1-c,2)B(:,c,3) = A(:,nc+1-c,3)

endimwrite(B,'LawSchoolMirror.jpg')

Prelim 1 Q1: Program trace (vectors) & function scope Q2: random numbers, for-loop pattern (for vector) Q3: accumulation pattern (similar to P2 pi sequence) Q4: simulation involving while-loop, rand int, if-construct; function

and function call; building a vector of non-determined length (similar to random walk and P3 simulation)

Q5: nested loops, drawing a 2-d pattern (similar to P2 café wall)

Median 84Mean 78.2; Std. Dev. 18.9Max 100

If your paper isn’t here, pick it up from Matlab consultants in ACCEL Green Rm during consulting hrs (starting today at 5pm)

if score>80celebrate, look up solutions and learn from mistakes

elseif score>60re-do the open questions that you got wrong first; then read solutions

elsesee course staff one-on-one to re-do the questions; avoid the solutions!

end

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