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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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CSE185
Fall 2008
Lecture 11
Digital Image Fundamentals
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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

-^

Distance measures

are used to calculate the

spatial distance between pixel locations