1
CSE185
Fall 2008
Lecture 13
Digital Image Fundamentals
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
© 1992–2008 R. C. Gonzalez & R. E. Woods
Gonzalez & Woods
Today
• Introduction to the mathematical tools used in
digital image processing (DIP) (Chap. 2)
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
© 1992–2008 R. C. Gonzalez & R. E. Woods
Gonzalez & Woods
Assignments
• Lab #2 due Wed. 10/22 by midnight
• Read chap. 3 except section 3.8 by Mon.
10/20
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
© 1992–2008 R. C. Gonzalez & R. E. Woods
Gonzalez & Woods
Chap 2: Intro. mathematical tools for DIP
• Geometric spatial transformations and image
registration
• Modify the spatial relationships between pixels
• Often called “rubber-sheet” transformations
• Two components:
1. Spatial transformation of coordinates
2. Interpolation to assign intensity values to spatially transformed
pixels
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
© 1992–2008 R. C. Gonzalez & R. E. Woods
Gonzalez & Woods
Chap 2: Intro. mathematical tools for DIP
• Geometric spatial transformations
• Transformation of coordinates
where (v,w) are coordinates in the original image and (x,y) are
the corresponding pixel locations in the transformed image
•Example
– The transformation
shrinks the original image to half it s size in both directions
(, ) {(, )}
x
yTvw=
(, ) {(, )} ,
22
vw
xy T vw
==
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
© 1992–2008 R. C. Gonzalez & R. E. Woods
Gonzalez & Woods
Chap 2: Intro. mathematical tools for DIP
• Geometric spatial transformations
• One of the most commonly used spatial coordinate
transforms is the affine transform:
[][][]
11 12
21 22
31 32
0
11 10
1
tt
xy vw T vw t t
tt
==
