The document discusses basic pixel relationships and connectivity in digital images. It defines three types of pixel adjacency: 4-adjacency, 8-adjacency, and m-adjacency. Pixels are considered connected if they are neighbors based on these adjacency types and have similar gray levels. Connected pixels form regions, while region boundaries are pixels on the edge connecting to other regions. The document also introduces distance measures like Euclidean, D4, and D8 distance that are used to define pixel neighborhoods.

1. Chapter-4
PART-2

2. Basic Pixel Relationships

3. Connectivity
• Two pixels are connected if:
• They are neighbors (i.e. adjacent in some sense -- e.g. N4(p), N8(p), …)
• Their gray levels satisfy a specified criterion of similarity (e.g. equality, …)
• V is the set of gray-level values used to define adjacency (e.g. V={1}
for adjacency of pixels of value 1)

4. Adjacency
• We consider three types of adjacency:
• V is the set of gray-level values used to define adjacency (e.g. V={1}
for adjacency of pixels of value 1)( the matrix considered for binary
image so it has 0 and 1)
• 4-adjacency: two pixels p and q with values from V are 4-adjacent if q is in the
set N4(p)
• 8-adjacency : p & q are 8- adjacent if q is in the set N8(p)
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4-Adjacency 8-Adjacency
p
q

5. Adjacency
• The third type of adjacency:
• m-adjacency: p & q with values from V are m-adjacent if
• q should be in N4(p) or
• q should be in ND(p) and the set N4(p)N4(q) has no pixels with values from V
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m-Adjacency

6. Adjacency
• Mixed adjacency is a modification of 8-adjacency and is used to
eliminate the multiple path connections that often arise when 8-
adjacency is used.
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4-Adjacency 8-Adjacency m-Adjacency
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7. Digital path
• Line connecting the pixel is called digital path
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Digital path

8. Connectivity
• For any pixel p and q in in a set of pixels ,S(subset of pixels) , the set of
pixels in S that are connected to p and q through digital path is called
connectivity.
• If S has only one connected component then S is called a connected
set.
Digital path

9. • Connectivity in a subset S of an image
• – Two pixels are connected if there is a path between them that lies
completely within S
• Connected Component
• – The set of all pixels in S that are connected to a given pixel
• Connected Set
• – If S has only one connected component

10. Region
• The connectivity gives rise to another concept of
region (R ).
• Region is nothing but a subset of pixels which are
connected. Or connected set of pixels is called
region.
• Ri and Rj are two joint sets and they are adjacent
to each other. They are connected by 8-
adjacency marked(both diagonals are 1) in red
(fig-1). The joint set gives rise to back ground of
image.
• Ri and Rj are not connected marked in red arrow
(as there is 0 and 1 in diagonal )are called the
disjoint sets, This disjoint sets gives rise to fore
ground of image.
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11. Boundary
• It is defined as that the boundary will be having at least one set of
pixels from back ground of the image or edge.
• Edge can be the region boundary (in binary images)
• Its boundary (border, contour) is the set of pixels in R that have at
least one neighbor not in R.
Back ground
Foreground
Edge boundary

13. • If a region corresponds to the whole image, 1st and last rows &
columns are treated as boundary
• Difference
• – Edges Intensity Discontinuities
• – Boundaries Closed Path

14. Distance Measures
• For pixels p,q,z with coordinates (x,y), (s,t), (u,v), D is a distance
function or metric if the three conditions satisfies:
• D(p,q) ≥ 0 [D(p,q)=0 iff p=q( if p and q are located at same position)]
• D(p,q) = D(q,p) (if distance between p and q are equal) and
• D(p,z) ≤ D(p,q) + D(q,z)

15. Distance Measures
• Euclidean distance:
• De(p,q) = [(x-s)2 + (y-t)2]1/2
• Points (pixels) having a distance less than or equal to r from (x,y) are
contained in a disk of radius r centered at (x,y).

16. Distance Measures
• D4 distance (city-block distance):
• D4(p,q) = |x-s| + |y-t|
• forms a diamond centered at (x,y)
• e.g. pixels with D4≤2 from p
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D4 = 1 are the 4-neighbors of p

17. Distance Measures
• D8 distance (chessboard distance): ( Like a king moves 8-ways in chess
board)
• D8(p,q) = max(|x-s|,|y-t|)
• Forms a square centered at p
• e.g. pixels with D8≤2 from p
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D8 = 1 are the 8-neighbors of p

18. Distance Measures
• D4 and D8 distances between p and q are independent of any paths
that exist between the points because these distances involve only
the coordinates of the points (regardless of whether a connected path
exists between them).

19. Distance Measures
• However, for m-connectivity the value of the distance (length of path)
between two pixels depends on the values of the pixels along the
path and those of their neighbors.

20. Interpolation
• Required in image resizing such as shrinking
and zooming
• Using known data to estimate data at
unknown points

22. Morphing

23. Images

24. Image formation

26. Electromagnetic (EM) energy spectrum
Weeks 1 & 2
Major uses
Gamma-ray imaging: nuclear medicine and astronomical observations
X-rays: medical diagnostics, industry, and astronomy, etc.
Ultraviolet: lithography, industrial inspection, microscopy, lasers, biological imaging,
and astronomical observations
Visible and infrared bands: light microscopy, astronomy, remote sensing, industry,
and law enforcement
Microwave band: radar
Radio band: medicine (such as MRI) and astronomy

27. First photograph
• First photograph due to Niepce,
• First on record shown - 1822
• Basic abstraction is the pinhole camera
• First successful commercial
photograph due to Eastman in late
19th

28. First digital picture