digital image fundamentals and pixels relationships

2. The eye is nearly a sphere, with an average dia. Of approximately 20mm.
Three membranes enclose the eye: the cornea and sclera outer cover; the
choroid; and the retina.
The cornea is a tough, transparent tissue that covers the anterior surface of
the eye. Continuous with cornea, the sclera is an opaque membrane that
encloses the remainder of optical globe.
The choroid is a membrane contains a network of blood vessels that serve
as a major source of nutrition to the eye.
The lens is made up of concentric layers of fibrous cells . It contains 60-
70% of water, about 6% fat, and more protein than any other tissue in the
eye.
The innermost membrane of the eye is the retina, which lines the inside of
the wall’s entire posterior portion.
When eye is properly focussed, light from an object outside the eye is
imaged on the retina. Pattern vision is afforded by the distribution of
discrete light receptors over the surface of the retina.
There are two classes of receptors: cones and rods

3. Cones:
The cones in each eye number between 6 and 7 million.
They are located primarily in the central portion of retina, called the
fovea , and are highly sensitive to colour.
Humans can resolve fine details with these cones largely because each
one is connected to its own nerve end.
Cone vision is called photopic or bright-light vision.
Rods:
The number of rods is much larger: some 75 to 150 million are
distributed over the retinal surface.
Rods serve to give overall picture of the field of view. They are not
involved in colour vision and are sensitive to low levels of illumination
Rod vision is known as scotopic or dim-light vision.

8. DIGITAL IMAGE FORMATION MODEL

9.  We denote image by 2 dimensional functions of the form f(x,y).
f(x,y) must be nonzero and finite; 0< f(x,y)< ∞.
f(x,y) may be characterised by two components.
1) the amount of source illumination incident on the scene being viewed
2) the amount of reflected by the objects in the scene.
These are called the illumination and reflectance components are denoted by
i(x,y) and r(x,y), respectively.
f(x,y) = i(x,y)r(x,y )
where 0< i(x,y)< ∞ and 0< r(x,y)< 1
reflection is bounded by 0(total absorption) and 1(total reflection).
r(x,y) is determined by the characteristics of the imaged objects.

10. Sampling and quantization

13. Representing a Digital Image

18. Contouring
a) 256 gray levels b)32 gray levels c) 16 gray levels
The lines, that start appearing on this image (c) are known as contouring that
are very much visible in the image(c) compared to (a) & (b).
The effect of contouring increase as we reduce the number of gray levels and
the effect decrease as we increase the number of gray levels. They are both
vice versa

19. Relationship between pixels
 Neighbourhood
 Adjacency
 Connectivity
 Paths
 Distance Measures

20. Neighbours of a Pixel
1) N4(p) : 4- vertical and horizontal neighbours of p.
• Any pixel p(x, y) has two vertical and two horizontal neighbours, given by
coordinates (x+1,y), (x-1, y), (x, y+1), (x, y-1)
• This set of pixels are called the 4-neighbors of P, and is denoted by N4(P)
2) ND(p) : 4- diagonal neighbours of p
• This set of pixels, called 4- diagonal neighbours and denoted by ND (p)
• ND (p) : Any pixel p(x, y) has 4- diagonal neighbours, given by coordinates,
(x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1)
3) N8(p): 8-neighbors of p.
• N4(P)and ND(p) together are called 8-neighbors of p, denoted by N8(p).
• N8(p) = N4(P) ᴜ ND(p)

21. ND(p N4(p) ND(p
N4(p) p ( x, y ) N4(p)
ND(p N4(p) ND(p
• N8(p) = N4(P) ᴜ ND(p)

22. Adjacency:
1) Two pixels are connected if they are neighbors and their gray levels satisfy some
specified criterion of similarity.
• For example, in a binary image two pixels are connected if they are 4-neighbors
and have same value (0/1)
• Let v: a set of intensity values used to define adjacency and connectivity.
• In a binary Image v={1}, if we are referring to adjacency of pixels with value 1.
• In a Gray scale image, the idea is the same, but v typically contains more elements,
for example v= {180, 181, 182,....,200}.
• If the possible intensity values 0 to 255, v set could be any subset of these 256
values.

23. Types of Adjacency:
• 4-adjacency: Two pixels p and q with values from v are 4-adjacent if q is in the
set N4(p).
• 8-adjacency: Two pixels p and q with values from v are 8-adjacent if q is in the
set N8(p).
• m-adjacency (mixed): two pixels p and q with values from v are m-adjacent if:
 q is in N4(p) or
 q is in ND(p) and
 The set N4(p) ∩ N4(q) has no pixel whose values are from v (No intersection).
• Mixed adjacency is a modification of 8-adjacency ''introduced to eliminate the
ambiguities that often arise when 8- adjacency is used. (eliminate multiple path
connection)

24. Connectivity
• Let V be the set of gray-level values
used to define connectivity; then Two
pixels p, q that have values from the
set V are:
a) 4-connected, if q is in set N4 (p)
b) 8-connected, if q is in set N8 (p)
c) m-connected, if
• q is in N4(p) or
• q is in ND(p) and N4(p) ∩ N4(q) = null
V={1,2}
0 1 1
0 2 0
0 0 1
0 1 1
0 2 0
0 0 1
0 1 1
0 2 0
0 0 1

25. Path :
• A digital path (or curve) from pixel p with coordinate (x,y) to pixel q with
coordinate (s,t) is a sequence of distinct pixels with coordinates (x0 , y0 ), (x1 , y1 ),
..., (xn , yn ), where (x0 , y0 )= (x,y), (xn , yn )= (s,t)
• (xi , yi ) is adjacent pixel (xi-1, yi-1) for 1≤j≤n ,
• n- The length of the path.
• If (x0 , y0 ) = (xn , yn ), the path is closed path.
• We can define 4- ,8- , or m-paths depending on the type of adjacency specified.

26. Connectivity :
• Let S represent a subset of pixels in an image, two pixels p and q are said to be
connected in S if there exists a path between them.
• Two image subsets S1 and S2 are adjacent if some pixel in S1 is adjacent to
some pixel in S2
S1
S2