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Digital Image Processing

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Digital Image Fundamentals

S. G. Lakhdive,

Head, Dept. of Computer Science,Prof. Ramkrishna More College, Akurdi, Pune

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Structure of the human eye

Image formation in the human eye

Brightness adaptation and discrimination

Outline

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Human and Computer Vision

We cant think of image processing withoutconsidering the human vision system. We observeand evaluate the images that we process with our

visual system.

Without taking this elementary fact into consideration,we may be much misled in the interpretation ofimages.

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The cornea and sclera outer cover

The choroid

Ciliary bodyIris

Lens

The retina (two kinds of receptors)

Cones vision (photopic/bright-light vision) : centered at fovea, highlysensitive to color

Rods (scotopic/dim-light vision) : general view

Blind spot


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Lens & Retina

Lens : both infrared and ultraviolet light are absorbedappreciably by proteins within the lens structure and,in excessive amounts, can cause damage to the eye.

Retina : Innermost membrane of the eye which linesinside of the walls entire posterior portion. When theeye is properly focused, light from an object outside

the eye is imaged on the retina.

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Receptors

Pattern vision is afforded by the distribution of discrete light

receptors over the surface of the retina.

Receptors are divided into 2 classes:

Cones

Rods

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Cones

6-7 million, located primarily in the central portion ofthe retina (the fovea, muscles controlling the eyerotate the eyeball until the image falls on the fovea)

Highly sensitive to color.

Each is connected to its own nerve end thus humancan resolve fine details.

Cone vision is called photopic or bright-light vision.

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Rods

75-150 million, distributed over the retina surface.

Several rods are connected to a single nerve end

reduce the amount of detail discernible.Serve to give a general, overall picture of the field ofview.

Sensitive to low levels of illumination.

Rod vision is called scotopic or dim-light vision.

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Cross Section Right eye

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Image formation in the human eye

LightReceptor

BrainRadiant

Energy

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Dynamic range of human visual system: 10-6~104 mL

(millilambert)

Can not accomplish this range simultaneously

The current sensitivity level of the visual system is called

brightness adaptation level

Brightness adaptation

i i l i

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Brightness adaptation

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Di it l I P i

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Weber ratio (the experiment) :

I: the background illumination

: the increment of illumination

Small Weber ratio indicates good discrimination

Larger Weber ratio indicates poor discrimination

Weber's Law states that the ratio of the increment

threshold to the background intensity is a constant.

So when you are in a noisy environment you must

shout to be heard while a whisper works in a quiet

room. And when you measure increment thresholds

on various intensity backgrounds, the thresholds

increase in proportion to the background.

Brightness discrimination

IIC

/

CI

Di it l I P i

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Brightness discrimination

Di it l I P i

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The perceived brightness is not a simple function of

intensity

Mach band pattern

Simultaneous contrast

Optical illusion

Psycho-visual effects

Di it l I P i

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Mach band pattern

Di it l I P i

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Simultaneous contrast


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Optical illusion


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Optical illusion


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Optical illusion

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Sampling, Quantization and Other SimpleOperations


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Sampling, Quantization, and Operations

Digital image representation

Image formation model

Uniform sampling

Uniform quantization

Relationships between pixels

Outline


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Digital Image Representation

A digital image is an imagef(x,y) that has been digitized

both in spatial coordinates and brightness.

The value of f at any point (x,y) is proportional to thebrightness (or gray level) of the image at that point.

A digital image can be considered a matrix whoserow and column indices identify a point in the image

and the corresponding matrix element value identifiesthe gray level at that point.


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Digital Image Representation

Pixel values in highlighted region

CAMERA => DIGITIZER =>A set of number in 2D grid

Samples the analog data and digitizes it.


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Sampling, Quantization and Other SimpleOperations

0 ,f x y

,f x y

,i x y

may be characterized by two components :

Illumination: Reflectance: ,r x y

, , ,f x y i x y r x y

0 ,i x y 0 , 1r x y

Monochrome image

Typical values of the illumination and reflectance:Illumination: sun on earth: 90,000 lm/m2 on a sunny day; 10,000 lm/m2 on

a cloud day; moon on clear evening: 0.1 lm/m

2

; in a commercial office isabout 1000 lm/m2

Reflectance: 0.01 for black velvet, 0.65 for stainless steel, 0.80 for flat-white

wall paint, 0.90 for silver-plated metal, and 0.93 for snow

Image Formation Model


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Sampling

digitalized in

spatial domain

Quantizationdigitalized in

amplitude

Uniform sampling and quantization


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Uniform sampling and quantization

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Spatial resolution : It is a measure of smallest discernible

details in an image. The more pixels in a fixed range, the

higher the resolution

Gray-level resolution : the more bits, the higher the

resolution

Image resolution

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g g g

Neighbors of a pixel

Neighbors of pixel are the pixels that are adjacent

pixels of an identified pixel.

Each pixel is a unit distance from the particularpixel.

Some of the neighbors of pixel lie outside the

digital image if its position is on the border of the

image.


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g g g

Pixel at coordinate (column x, rowy) can be represented by f(x,y)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0123

456789

101112131415

Pixel at the

7th

columnand 4th rowis yellow color

Zoom 1600%


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g g g

4-neighbors of pixel

4-neighbors of pixel is denoted by N4(p)

It is set of horizontal and vertical neighbors

f(x,y)is a yellow circlef(x,y-1)is top onef(x-1,y)is left one

f(x+1,y)is right onef(x,y+1)is bottom one

(x-1)

(y-1)

(y+1)

(x+1)(x)

(y)


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Diagonal neighbors of pixel

Diagonal neighbors of pixel is denoted by ND(p)

It is set of diagonal neighbors

f(x,y)is a yellow circlef(x-1,y-1)is top-left onef(x+1,y-1)is top-right onef(x-1,y+1)is bottom-left one

f(x+1,y+1)is bottom-right one

(x-1)

(y-1)

(y+1)

(x+1)(x)

(y)


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8-neighbors of pixel

8-neighbors of pixel is denoted by N8(p)

4-neighbors and Diagonal neighbors of pixel

f(x,y)is a yellow circle(x-1,y-1), (x,y-1),(x+1,y-1),(x-1,y), (x,y), (x+1,y),

(x-1,y+1),(x,y+1), (x+1,y+1)

(x-1)

(y-1)

(y+1)

(x+1)(x)

(y)


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Connectivity

Establishing boundaries of objects and components of

regions in an image.

Group the same region by assumption that the pixels beingthe same color or equal intensity will are the same region


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Connectivity

Let C is the set of colors used to define

There are three type of connectivity:

4-Connectivity : 2 pixels (p and q) with value in C are 4-connectivity if

q is in the set N4(p)

8-Connectivity : 2 pixels (p and q) with value in C are 8-connectivity if

q is in the set N8(p)

M-Connectivity : 2 pixels (p and q) with value in C are 8-connectivity

if(i) Q is in N4(p), or

(ii) Q is in ND(p) and the set N4(p) N4(q) has no pixels whose value are from

V


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m-adjacency

Relationships between pixels


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Distance Measure

For pixels p, q, and z, with coordinates (x,y), (s,t) and

(u,v) respectively, D is a distance function or metric if

(a) D(p,q) 0 and

(b) D(p,q) = 0 iff p = q and

(c) D(p,q) = D(q,p) and

(d) D(p,z) D(p,q) + D(q,z)

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The D8 Distance

Also called chessboard distance

Calculate between p and q is defined as

D8(p,q) = max(| x - s |,| y - t |)

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