CSE185
Fall 2008
Lecture 11
Digital Image Fundamentals
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Digital Image Fundamentals: Sampling, Quantization, and Interpolation - Prof. Shawn Newsam, Assignments of Computer Science
A lecture note from the computer science and engineering (cse) 185 course at the university of california, berkeley, taught by r. C. Gonzalez and r. E. Woods. The lecture focuses on the fundamentals of digital images, including image sampling, quantization, and interpolation techniques such as nearest neighbor, bilinear, and bicubic interpolation. The document also covers advanced interpolation methods like splines and wavelets, as well as basic relationships between pixels, adjacency, paths, connectedness, regions, and boundaries.
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CSE185Fall 2008Lecture 11
Digital Image Fundamentals
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Today
•^
Digital Image Fundamentals (Chap. 2)
-^
Basic relationships between pixels (Chap. 2)
-^
[Introduction to the mathematical tools used indigital image processing (DIP) (Chap. 2)]
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Image sampling and quantization
•^
Nearest neighbor interpolation– Uses intensity value of just the nearest pixel
-^
Bilinear interpolation– Uses intensity values from 4 nearest neighboring pixels– Assumes image intensity is linear along axis directions and
quadratic in any other direction
•^
Bicubic interpolation– Uses intensity values from 16 nearest neighboring pixels– Standard interpolation used in image editing applications
such as Photoshop
- Fits a higher-order polynomial function to image surface
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Image sampling and quantization
Original:3692x
213x162 443x
213x162 443x
213x162 443x
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
- Neighbors of a pixel
– N
(p) = 4-neighbors of p 4
- N
(p) = 8-neighbors of p 8
- Used in defining sets of pixels
- Adjacency, connectivity, regions, boundaries
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
-^
Adjacency –^
Two pixels p and q are
4-adjacent
if q
N
(p) 4
and their values satisfy a given constraint
Two pixels p and q are
8-adjacent
if q
N
(p) 8
and their values satisfy a given constraint
Two pixels are
m-adjacent
if their values satisfy
a given constraint and1.^
q∈
N
(p), or 4
q∈
N
(p) and the set N 8
(p) 4
∩
N
(q) has no pixels that 4
satisfy the constraint
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
- Paths
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
•^
Connectedness
-^
Let S be a set of pixels in an image– p and q are
connected
in S if
∃
a path between them
consisting entirely of pixels in S
- For any pixel p
∈
S, the set of pixels that are connected
to it in S is called a
connected component
of S
- If S has only one connected component then S is called
a^
connected set
•^
S is typically the entire image
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
- Regions
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
•^
Region boundaries
-^
The
boundary
of a region R is the set of points (in R)
which are adjacent to points in the complement of R
-^
A boundary is defined in terms of 4- or 8-adjacency
Digital Image Processing, 3rd ed.Digital Image Processing, 3rd ed.
www.ImageProcessingPlace.com
Gonzalez & Woods
Chap 2: Some basic relationships between pixels
-^