This weekly report outlines a formula to obtain the exact number of each type (A-K) based on the width and height of an image. It explains that the formula calculates the number of pixels by iterating through the width and height, increasing each by a set difference (Dw and Dh) that varies for each type. It provides Dw and Dh values for each type and gives an example of applying the formula to Type A. The report concludes by discussing transposing the image to calculate the integral image by column-major instead of row-major.

1. WEEKLY REPORT
Thur., Jan 09, 2014
Pin Yi Tsai

2. OUTLINE
• How to obtain the exact number of each type
• The formula
• Take type A as example

3. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
• Wimg : width of the image
• Dw : the difference between iterations of width (varies with types)
• Dh : the difference between iterations of height (varies with types)
• {[([(Wimg -3)% Dw] + Wimg -3) * (((Wimg -3 - [(Wimg -3)% Dw])/
Dw )+1 )]/2} *
{[([(Wimg -2)% Dh] + Wimg -2) * (((Wimg -2 - [(Wimg -2)% Dh])/
Dh )+1)]/2}

4. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE type (D , D ) amount
w
h
A
(4, 2)
1568
B
(2, 4)
1568
C
(2, 6)
1008
D
(2, 8)
784
E
(6, 2)
1008
F
(8, 2)
784
G
(4, 4)
784
H
(4, 4)
784
I
(4, 4)
784
J
(4, 4)
784
K
(4, 4)
784

5. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type A :
• Dw : 4 (2*2)
 each iteration computes 2 horizontal pixels
 w increased by 2
• Dh : 2
 h increased by 2
 w, h, x, y = (0,0,0,0)
•
right=(1,2)+(0,1)-(0,2)-(1,1)
•
left=(1,1)+(0,0)-(0,1)-(1,0)
 y increased by 1

6. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type A :
• Dw : 4 (2*2)
• Dh : 2
 w, h, x, y = (0,0,0,0)
•
right=(1,2)+(0,1)-(0,2)-(1,1)
•
left=(1,1)+(0,0)-(0,1)-(1,0)
 x increased by 1

7. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type A :
• Dw : 4 (2*2)
• Dh : 2
•
w, h, x, y =(0,2,0,0)
•
right=(3,2)+(0,1)-(0,2)-(3,1)
•
left=(3,1)+(0,0)-(0,1)-(3,0)
 x increased by 1
 y increased by 1

8. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type B:
• Dw : 2
 w increased by 2
• Dh : 4 (2*2)
 each iteration computes 2 vertical pixels
 h increased by 2

9. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type C:
• Dw : 2
• w increased by 2
• Dh : 6 (2*3)
• each iteration computes 3 vertical pixels
• h increased by 2

10. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type D:
• Dw : 2
• w increased by 2
• Dh : 8 (2*4)
• each iteration computes
4 vertical pixels
• h increased by 2

11. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type E:
• Dw : 6 (2*3)
• each iteration computes
3 vertical pixels
• w increased by 2
• Dh : 2
• h increased by 2

12. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type F:
• Dw : 8 (2*4)
• each iteration computes
4 vertical pixels
• w increased by 2
• Dh : 2
• h increased by 2

13. FORMULA TO OBTAIN THE EXACT NUMBER OF
EACH TYPE
•
Type G:HIJK
• Dw : 4 (2*2)
• w increased by 2
• Dh : 4 (2*2)
• h increased by 2

14. The End

15. DO TRANSPOSE
•
In order to calculate integral image by column-major
•
Make ( i , j ) to ( j , I )
A
B
C
D
E
F
G
H
I
J
K
L
A
D
G
J
B
E
H
K
C
F
I
L