The document discusses the relationship between pixels in an image, including pixel neighborhoods and connectivity. It defines different types of pixel neighborhoods - the 4 nearest neighbors, 8 nearest neighbors including diagonals, and boundary pixels that have fewer than 8 neighbors. Connectivity refers to whether two pixels are adjacent or connected based on their intensity values and neighborhood relationships. Specifically, it describes 4-connectivity, 8-connectivity, and m-connectivity. Regions in an image are sets of connected pixels, while boundaries separate adjacent regions.

1. Relationship between Pixels
Subject: Image Procesing & Computer Vision
Dr. Varun Kumar
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 1 / 11

2. Outlines
1 Types of Image
2 Pixels neighborhood and their types
3 What is meant by connectivity ?
4 What is adjacency and its types ?
5 Learning of distance measure
6 References
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 2 / 11

3. Types of Image:
Types of Image
Binary image (1 bit quantized image) {0,1}
Gray scale image (8 bit quantized image) {0,255}
Color image : Made with the help of primary color
1 Red (8 bit)
2 Blue (8 bit)
3 Green (8 bit)
Total 24 bit scale is used for representing the color image.
Note:
Color image consumes more bandwidth.
By 24 bit quantizer level, 224 → 16 M colors can be formed.
Most of the camera claim 16 M color.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 3 / 11

4. Pixels Neighborhood
Pixels Neighborhood
A pixels p(x, y) has two horizontal and two vertical neighbor.
p(x + 1, y) and p(x − 1, y) → Horizontal neighbors. p(x, y + 1) and
p(x, y − 1) → Vertical neighbors. Denoted as N4(p)
p(x − 1, y + 1), p(x − 1, y − 1) →, p(x + 1, y − 1) and
p(x + 1, y + 1) → Diagonal neighbors. Denoted as ND(p)
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 4 / 11

5. Continued–
The points of N4(p) and ND(p) is combined, then this pixel has 8
neighbors.
N8(p) = N4(p) ∪ ND(p)
If pixel p(x, y) is a boundary pixel then number of neighbors is less
than 8.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 5 / 11

6. Connectivity of the pixels
Key Features
Finding object boundary
Address the image component/regions etc
Address the shape, size and other important information to the object.
If g(x, y) > Th ⇒ (x, y) ∈ Object and g(x, y) < Th ⇒ (x, y) ∈
Background
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 6 / 11

7. Continued–
Object but not connected
Connectivity:
Two pixels are said to be connected, if they are adjacent in some
sense
(a) If they are neighbors (N8(p), N4(p) or ND(p)).
(b) In gray scale, the intensity level is similar.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 7 / 11

8. Continued–
Let V is the set of gray level to define connectivity between two pixel p
and q then three types of connectivity is used
1 4-connectivity ⇒ p, q ∈ v & p ∈ N4(q)
2 8-connectivity ⇒ p, q ∈ v & p ∈ N8(q)
3 m-connectivity
i. q ∈ N4(p) or
ii. q ∈ N4(p) and N4(p) ∩ N4(q) = φ
4 Mixed connectivity is a special case of 8-connectivity that eliminates
the multiple path.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 8 / 11

9. Adjacency and Paths
Two pixels are p and q are adjacent if they are connected
4-adjacency
8-adjacency
m-adjacency
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 9 / 11

10. Regions and Boundary
Region:
Let R be a subset of pixels in an image.
Two regions Ri and Rj are said to be adjacent if their union form a
connected set.
Regions that are not adjacent are said to be disjoint.
We consider 4- and 8- adjacency when referring to regions.
Example
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 10 / 11

11. References
M. Sonka, V. Hlavac, and R. Boyle, Image processing, analysis, and machine vision.
Cengage Learning, 2014.
D. A. Forsyth and J. Ponce, “A modern approach,” Computer vision: a modern
approach, vol. 17, pp. 21–48, 2003.
L. Shapiro and G. Stockman, “Computer vision prentice hall,” Inc., New Jersey,
2001.
R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital image processing using
MATLAB. Pearson Education India, 2004.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 4 11 / 11