Image Processing Lecture 3 Digital Image Fundamentals

Visual Perception •How images are formed in the eye ? •Eye’s physical limitation ? •Human visual interpretation of images ?

1. Introduction



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In many image processing applications, the objective is to h elp a human observer perceive the visual information in an image. Therefore, it is important to understand the human visual system. The human visual system consists Eye (image sensor or camera) Optic nerve (transmission path) Brain (image information processing unit or computer) It is one of the most sophisticated image processing and a nalysis systems.

Prof Bhavin Mehta

Structure of human eyes

Structure of human eyes Three membranes enclose the eye: – Cornea and sclera • Cornea is a tough, transparent tissue cover the anterior surface of the eye. •Sclera is a opaque membrane enclose the remainder of the optic globe. –Choroid • A network of blood vessels for eye nutrition • At its anterior extreme, it is divided into the ciliary body and iris diaphragm. • The central opening (the pupil) varies in diameter from 2 to 8 mm.

–Retina Retina lines the insides of the wall’s interior portion with two classes of receptors:

Structure of human eyes – Cones: (Red 65%, Green 33%,Blue 2%) • 6 – 7 millions located primarily in the central portion of the retina • Highly sensitive to color • Photopic or bright-light vision – Rods

• 75- 150 millions distributed over the retinal surface. • Not involved in color vision and sensitive to low illumination • Scoptopic or dim vision

Structure of human eyes   

The cones are most dense in the center of retina. Density of cones in the area of fovea is 150,000 element/mm2 The number of cones in fovea is 337,000 elements.

Image Formation in the Eyes





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Photographic Camera  lens has fixed focal length.  focusing  achieved by varying the distance between lens & imaging plane, where the film is located. Human Eye – Distance between lens & imaging region ( Retina) is fixed . (Approx. 17 mm)( Focal Length)  focal length needed to achieve proper focus is obtained by varying the shape of lens. The range of focal length varies from 14mm to 17mm . The shape of lens ( flatter or thicker) is controlled by the ten sion of fibers of the ciliary body. The retinal image is reflected primarily in the area of fovea. Perception = excitation of light receptors, which transform radiant energy into impulses that are ultimately decoded by the brain.

Image Formation in the Eyes h= height of that object in the retinal image. H = 15m (actual height of object) Length = 100m ( between object and lens) D = 17mm ( distance between lens & retina) 15/100 = h/17 h= 2.55mm

Brightness Adaptation & Discrimination The range of light intensity levels to which the human visual system can adapt is enormous - on the order of 10^10 between S to G.

Brightness Adaptation & Discrimination

• The subjective brightness is a logarithmic function of light intensity incident on the eye. • Brightness adaptation.

– The current sensitivity level it can discriminate simultaneously is rather small compared with the total adaptation range – Brightness adaptation level: the current sensitive level of the visual system. Example (Ba)

Brightness Adaptation & Discrimination Ability of eye to discriminate between changes in light intensity at any specific adaption level is also of considerable interest.  Example – Diffuser ( Opaque glass) ..illuminated by light source ..I ( varied intensity) ∆I – less or no bright – Response No. ∆I- brighter enough – Response Yes

Brightness Adaptation & Discrimination •The ∆Ic is the increment of illumination discriminable 50% of the time with the background illumination I. • The quantity ∆Ic/I is called the Weber ratio. • The smaller ∆Ic/I means that a small percentage change in intensity is discriminable – good brightness discrimination

• The larger ∆Ic/I means that a large percentage change in intensity is discriminable – poor brightness discrimination

Brightness Adaptation & Discrimination Perceived brightness is not a simple function of intensity, rather it is log of intensity



The first is based on the fact that the visual system tends to undershoot or overshoot around the boundary of regions of different intensities.( MACH BANDS)

Brightness Adaptation & Discrimination – A region’s perceived brightness does not simply depend on its intensity (fig. 2.8) – Simultaneous contrast.

Light and EM Spectrum

Light and EM Spectrum •Light is a particular type of EM radiation that can be seen by human eye. •EM waves are massless particles each traveling in a wavelike pattern and moving at a speed of light.(2.998*10^8) •We can specify waves through frequency and wavelength.

•The colors that human perceive in an object are determined by the nature of the light reflected from the object. For example green objects reflect light with wavelengths primarily in the 500 to 570nm range while absorbing most of the energy at other wavelengths. Here h = Planck’s constant

 

c



E  hv

Light and EM Spectrum •

Achromatic Light

Light that is void of color is called achromatic or monochromatic light. The only attribute of such light is its intensity. The term gray level generally is used to describe monochromatic intensity because it ranges from black to grays and finally to white



Chromatic light spans EM spectrum from 0.43 um (violet) ( red).

to 0.79 um

Three basic quantities are used to describe the quality of a chromatic light source – Radiance – Luminance – Brightness

Light and EM Spectrum •

Radiance

The total amount of energy that flows from the light source

Measured in Watts(W)

• Luminance Gives a measure of the amount of energy an observer perceives from the a light source. Measured in Lumens(lm) For example light emitted from a source operating in a far infrared region of the spectrum could have significant energy (radiance) but an observer would hardly perceive it; its luminance would be hardly zero •

Brightness Subjective descriptor of light perception that is practically impossible to measure

Image Sensing and Acquisition • Electromagnetic energy source and sensor that can detect the energy of the electromagnetic source are needed to generate an image. EM source will illuminate the objects that need to be imaged and then a sensor will detect the reflected energy from the objects. • Different objects will have different degree of reflections and absorption of the electromagnetic energy. • These differences in reflections and absorption are the reasons for objects to appear distinct in the images.

Image Acquisition Photodiode – form of silicon material & out put waveform is prop ortional to light.

Image Acquisition using point sensor Specify the location of vertical and horizontal motors Sense the light reflection Voltage waveform will be received (Analog signal) Convert this analog signal into digital signal through sampling and quantization - Apply Sampling to digitize coordinate values - Apply Quantization to digitize amplitude values

Store the digitized value in memory

Image Acquisition using Line sensor Specify the location of vertical motor Sense the light reflection Voltage waveform will be received (Analog signal) Convert this analog signal into digital signal through sampling and quantization

- Apply Sampling to digitize coordinate values - Apply Quantization to digitize amplitude values Store the digitized value in memory

Image Acquisition using Array sensor  Application  ultrasonic sensing device ( Array Format)  Digital Camera --CCD array  4000 * 4000 element  low noise images. Response of each sensor is proportional to the integral of light en ergy projected onto the surface of the sensor. Formed 2 D image by focusing the energy pattern onto the surface of the array.

Digital Image Digital image = a multidimensional array of numbers (such as intensity image) or vectors (such as color image)

Each component in the image called pixel associates with the pixel value (a single number in the case of intensity images or a vector in the case of color images).

10 10 16 28 56  43  9 656 70 26 37  78  32 99  67  54 70 96 56  15 256013 902296   67   21  54 47  42  32  158587 853943  92 54  65 65 39  32 65 87 99

3.4. A Simple Image Formation Model

Mathematical representation of monochromatic images. • Two dimensional function f(x,y), where f is the gray level of a pixel at location x and y. • The values of the function f at different locations are proportional to the energy radiated from the imaged object.

Fundamentals of Digital Images

x Origin

y

Image “After snow storm”

f(x,y)

w An image: a multidimensional function of spatial coordinates. w Spatial coordinate: (x,y) for 2D case such as photograph, (x,y,z) for 3D case such as CT scan images (x,y,t) for movies w The function f may represent intensity (for monochrome images) or color (for color images) or other associated values.

Digital Image Types : Intensity Image

Intensity image or monochrome image each pixel corresponds to light intensity normally represented in gray scale (gray level).

Gray scale values 10 10 16 28  9 6 26 37   15 25 13 22     32 15 87 39

Digital Image Types : RGB Image

Color image or RGB image: each pixel contains a vector representing red, green and blue components.

RGB components 10 10 16 28 56  43  9 656 70 26 3756  78 70  32 99 54 96  67  15  256013 902296   67 21 54 47     42  32 15 87 39   85 85 43  92 54  65 65 39  32 65 87 99

Image Types : Binary Image Binary image or black and white image Each pixel contains one bit : 1 represent white 0 represents black

Binary data 0 0  1  1

0 0 0 0 0 0  1 1 1  1 1 1

Image Types : Index Image Index image Each pixel contains index number pointing to a color in a color table Color Table Index No.

1 4 9 6 4 7    6 5 2

Index value



Red

Green

Blue

component

component

component

1

0.1

0.5

0.3

2

1.0

0.0

0.0

3

0.0

1.0

0.0

4

0.5

0.5

0.5

5

0.2

0.8

0.9







Digital Image Acquisition Process

(Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image Processing, 2nd Edition.

3.4. A Simple Image Formation Model

0< f(x,y) <

Nonzero and Finite

f(x,y)=i(x,y)*r(x,y) f(x,y)=i(x,y)*t(x,y)

Reflectivity Transmissivity

0< i(x,y) < 0  r(x,y) and t(x,y)  1 H.R. Pourreza

Image Formation Model

0 = total absorption 1= total reflectance

   After Acquiring image ??   To create Digital Image   convert the continuous sensed data into digital form.  1) sampling  2) Quantization  Objective

Sampling and Quantization

Original contin uous image X & y coordinates and amplitude Digitizing (X,Y) Digitizing (amplitude)

Sampling and Quantization

Sampling:

Digitization of the spatial coordinates (x,y)

Quantization: Digitization in amplitude (also called gray-level quantization) 8 bit quantization: 28 =256 gray levels (0: black, 255: white) Binary (1 bit quantization):2 gray levels (0: black, 1: white) Commonly used number of samples (resolution) Digital still cameras: 640x480, 1024x1024, up to 4064 x 2704 Digital video cameras: 640x480 at 30 frames/second

Representing Digital Images Digital image is expressed as

Spatial and Gray level Resolution

Spatial and Gray level Resolution

Spatial and Gray level Resolution

Spatial and Gray level Resolution

Aliasing and Moire Patterns •Aliasing:

– If a function is under-sampled then a phenomena called aliasing corrupts the sampled image. – A signal sampled too slowly is misrepresented by the samples, “ high spatial frequency components of the original signal appear as low spatial frequency components in the sampled signal (an effect known as aliasing. –The corruption is in the form of additional frequency components being introduced into the sampled function. These are called Aliased frequencies. –The principal approach for reducing the aliasing effects on an ima ge is to reduce its high frequency components by blurring the ima ge •Moire Patterns –Moire Pattern is caused by a break-up of the periodicity, i.e., images are scanned from a printed page, which consists of periodic ink dots.

Zooming and Shrinking Zooming:

–Create a new pixel locations –Assign a gray-levels to those new locations •Nearest neighbor interpolation –Pixel replication –Bilinear interpolation using four nearest neighbors –Higher-order non-linear interpolation: using more neighbors for interpolation •Shrinking: –Direct shrinking causes aliasing –Expansion then Shrinking: blurring the image before shrinking it and reduce aliasing.

Zooming and Shrinking

Relationships Between Pixels • Pixel Neighbourhood Types of Neighbourhood  What is meant by connectivity?

 Adjacency and its components  Distance measure

Basic Relationship of Pixels column 1

(x-1,y-1)

1 row

2

(x,y-1)

3

(x+1,y-1)

2

3

(x-1,y)

(x-1,y+1)

(x,y)

(x,y+1)

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

Conventional indexing method

Neighbors of a Pixel

Neighborhood relation is used to tell adjacent pixels. It is useful for analyzing regions.

4-neighbors of p:

(x-1,y)

(x,y-1)

(x,y)

(x,y+1)

N4(p) = (x+1,y)

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

4-neighborhood relation considers only vertical and horizontal neighbors. Note: q N4(p) implies p N4(q)

Neighbors of a Pixel (cont.) (x-1,y-1)

(x-1,y)

(x-1,y+1)

8-neighbors of p: (x,y-1)

(x+1,y-1)

(x,y)

(x,y+1)

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

N8(p) =

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

8-neighborhood relation considers all neighbor pixels.

Neighbors of a Pixel (cont.) (x-1,y-1)

(x-1,y+1)

Diagonal neighbors of p: (x,y)

(x+1,y-1)

(x+1,y+1)

ND(p) =

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

Diagonal -neighborhood relation considers only diagonal neighbor pixels.

Basic Relationships between Pixels

Connectivity Connectivity is adapted from neighborhood relation. Two pixels are connected if they are in the same class (i.e. the same color or the same range of intensity) and they are neighbors of one another. It is useful concept Establish boundary object Defining image component/regions (Thresholding)  Identify the pixels belongs to object or background For p and q from the same class w 4-connectivity: p and q are 4-connected if q N4(p)

w 8-connectivity: p and q are 8-connected if q N8(p) w mixed-connectivity (m-connectivity): p and q are m-connected if q N4(p) or q ND(p) and N4(p) N4(q) = 

Is used to avoid multiple connection path

Adjacency A pixel p is adjacent to pixel q is they are connected. Two image subsets S1 and S2 are adjacent if some pixel in S1 is adjacent to some pixel in S2

S1

S2 Type of adjacency: 4-adjacency 8-adjacency m-adjacency depending on type of connectivity.

Path

A path from pixel p at (x,y) to pixel q at (s,t) is a sequence of distinct pixels: (x0,y0), (x1,y1), (x2,y2),…, (xn,yn) such that (x0,y0) = (x,y) and (xn,yn) = (s,t) and (xi,yi) is adjacent to (xi-1,yi-1), i = 1,…,n p

q

We can define type of path: 4-path, 8-path or m-path depending on type of adjacency.

Path (cont.)

8-path p

q

8-path from p to q results in some ambiguity

m-path p

q

p

q m-path from p to q solves this ambiguity

Distance For pixel p, q, and z with coordinates (x,y), (s,t) and (u,v), D is a distance function or metric if

w D(p,q) 0 (D(p,q) = 0 if and only if p = q) w D(p,q) = D(q,p) Symmetric Properties

w D(p,z) D(p,q) + D(q,z) Inequality Properties Example: Euclidean distance

De ( p, q)  ( x - s)2 + ( y - t )2

Distance (cont.)

D4-distance (city-block distance) is defined as

D4 ( p, q)  x - s + y - t 2 2

2 1 2 1 P 1 2 1 2 2

2

Pixels with D4(p) = 1 is 4-neighbors of p.

Distance (cont.)

D8-distance (chessboard distance) is defined as

D8 ( p, q)  max( x - s , y - t ) 2

2

2

2

2

2 2 2 2

1 1 1 2

1 p 1 2

1 1 1 2

2 2 2 2

Pixels with D8(p) = 1 is 8-neighbors of p.

Any question

Digital Image Processing

Eye (image sensor or camera). ➢ Optic nerve ... –Choroid. • A network of blood vessels for eye nutrition .... Digital Camera --CCD array → 4000 * 4000 element.

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