UNIT I DIGITAL IMAGE FUNDAMENTALS 9

Steps in Digital Image Processing – Components – Elements of Visual Perception – Image

Sensing and Acquisition – Image Sampling and Quantization – Relationships between pixels -
Color image fundamentals - RGB, HSI models, Two-dimensional mathematical preliminaries,
2D transforms - DFT, DCT

DIGITAL IMAGE FUNDAMENTALS

The field of digital image processing refers to processing digital images by means of digital
computer. Digital image is composed of a finite number of elements, each of which has a
particular location and value. These elements are called picture elements, image elements, pels
and pixels. Pixel is the term used most widely to denote the elements of digital image.
An image is a two-dimensional function that represents a measure of some characteristic such
as brightness or color of a viewed scene. An image is a projection of a 3- D scene into a 2D
projection plane.

An image may be defined as a two-dimensional function f(x,y), where x and y are spatial
(plane) coordinates, and the amplitude to f at any pair of coordinates (x,y) is called the intensity
of the image at that point. The term gray level is used often to refer to the intensity of
monochrome images.
Color images are formed by a combination of individual 2-D images. For example, the RGB
color system, a color image consists of three (red, green and blue) individual component
images. For this reason, many of the techniques developed for monochrome images can be
extended to color images by processing the three component images individually.
An image may be continuous with respect to the x- and y- coordinates and also in amplitude.
Converting such an image to digital form requires that the coordinates, as well as the amplitude,
be digitized.
APPLICATIONS OF DIGITAL IMAGE PROCESSING:
Since digital image processing has very wide applications and almost all of the technical fields
are impacted by DIP. Some of the major applications of DIP.
Digital image processing has a broad spectrum of applications, such as
1. Remote sensing via satellites and other space crafts
2. Image transmission and storage for business applications
3. Medical processing
4. RADAR (Radio Detection and Ranging)
5. SONAR (Sound Navigation and Ranging)
6. Acoustic Image Processing (The study of underwater sound is known as Underwater
Acoustics or Hydro Acoustics)
7. Robotics and automated inspection of industrial parts
Images acquired by satellites are useful in tracking of
1. Earth resources
2. Geographical mapping
3. Prediction of agricultural crops
4. Urban growth and weather monitoring
5. Flood and fire control and many other environmental applications

Space image applications include:

1. Recognition and analysis of objects contained in images obtained from deep space-probe
missions.
2. Image transmission and storage applications occur in broad cast television
3. Teleconferencing
4. Transmission of facsimile images (Printed documents and graphics) for office automation
5. Communication over computer networks
6. Closed-circuit television-based security monitoring systems and
7. In military communications
Medical applications:
1. Processing of chest X-rays
2. Cine angiograms
3. Projection images of trans axial tomography and
4. Medical images that occur in radiology nuclear magnetic resonance (NMR)
5. Ultrasonic scanning

FUNDAMENTAL STEPS IN DIGITAL IMAGE PROCESSING:

There are two categories of the steps involved in the image processing –
1. Methods whose outputs are input are images.
2. Methods whose outputs are attributes extracted from those images.

Fig: Fundamental Steps in Digital Image Processing

Image Acquisition: It could be as simple as being given an image that is already in digital form.
Generally, the image acquisition stage involves processing such scaling.
Image Enhancement: It is among the simplest and most appealing areas of digital image
processing. The idea behind this is to bring out details that are obscured or simply to highlight
certain features of interest in image. Image enhancement is a very subjective area of image
processing.
Image Restoration: It deals with improving the appearance of an image. It is an objective
approach, in the sense that restoration techniques tend to be based on mathematical or
probabilistic models of image processing. Enhancement, on the other hand is based on human
subjective preferences regarding what constitutes a “good” enhancement result.

Color Image Processing: It is an area that is been gaining importance because of the use of
digital images over the internet. Color image processing deals with basically color models and
their implementation in image processing applications.

Wavelets and Multiresolution Processing: These are the foundation for representing image in
various degrees of resolution.
Compression: It deals with techniques reducing the storage required to save an image, or the
bandwidth required to transmit it over the network. It has to major approaches
1. Lossless Compression
2. Lossy Compression
Morphological Processing: It deals with tools for extracting image components that are useful
in the representation and description of shape and boundary of objects. It is majorly used in
automated inspection applications.
Representation and Description: It always follows the output of segmentation step that is, raw
pixel data, constituting either the boundary of an image or points in the region itself. In either
case converting the data to a form suitable for computer processing is necessary.
Recognition: It is the process that assigns label to an object based on its descriptors. It is the
last step of image processing which use artificial intelligence of software.
Knowledge Base: Knowledge about a problem domain is coded into an image processing
system in the form of a knowledge base. This knowledge may be as simple as detailing regions
of an image where the information of the interest in known to be located. Thus, limiting search
that has to be conducted in seeking the information. The knowledge base also can be quite
complex such interrelated list of all major possible defects in a materials inspection problem
or an image database containing high resolution satellite images of a region in connection with
change detection application.

IMAGE PROCESSING TOOLBOX (IPT):

It is a collection of functions that extend the capability of the MATLAB numeric computing
environment. These functions, and the expressiveness of the MATLAB language, make many
image-processing operations easy to write in a compact, clear manner, thus providing an ideal
software prototyping environment for the solution of image processing problem.

COMPONENTS OF IMAGE PROCESSING SYSTEM:

Fig: Components of Image Processing System

Image Sensors: With reference to sensing, two elements are required to acquire digital image.
The first is a physical device that is sensitive to the energy radiated by the object we wish to
image and second is specialized image processing hardware.
Specialize Image Processing Hardware: It consists of the digitizer, plus hardware that performs
other primitive operations such as an arithmetic logic unit, which performs arithmetic such
addition and subtraction and logical operations in parallel on images.

Computer: It is a general-purpose computer and can range from a PC to a supercomputer

depending on the application. In dedicated applications, sometimes specially designed
computer is used to achieve a required level of performance

Software: It consists of specialized modules that perform specific tasks a well-designed

package also includes capability for the user to write code, as a minimum, utilizes the
specialized module. More sophisticated software packages allow the integration of these
modules.

Mass Storage: This capability is a must in image processing applications. An image of size
1024 x1024 pixels, in which the intensity of each pixel is an 8- bit quantity requires one
Megabytes of storage space if the image is not compressed. Image processing applications falls
into three principal categories of storage.
 Short term storage for use during processing
 On line storage for relatively fast retrieval
 Archival storage such as magnetic tapes and disks

Image Display: Image displays in use today are mainly color TV monitors. These monitors are
driven by the outputs of image and graphics displays cards that are an integral part of computer
system.

Hardcopy Devices: The devices for recording image include laser printers, film cameras, heat
sensitive devices inkjet units and digital units such as optical and CD ROM disk. Films provide
the highest possible resolution, but paper is the obvious medium of choice for written
applications.
Networking: It is almost a default function in any computer system in use today because of the
large amount of data inherent in image processing applications. The key consideration in image
transmission bandwidth.

ELEMENTS OF VISUAL PERCEPTION

Structure of the human Eye
The eye is nearly a sphere with average approximately 20 mm diameter. The eye is enclosed
with three membranes
a) The cornea and sclera - it is a tough, transparent tissue that covers the anterior surface of
the eye. Rest of the optic globe is covered by the sclera
b) The choroid –
It contains a network of blood vessels that serve as the major source of nutrition to the eyes.
It helps to reduce extraneous light entering in the eye
It has two parts
(1) Iris Diaphragms- it contracts or expands to control the amount of light that enters the eyes
(2) Ciliary body

(c) Retina – it is innermost membrane of the eye. When the eye is properly focused, light
from an object outside the eye is imaged on the retina. There are various light receptors over
the surface of the retina
The two major classes of the receptors are-
1) cones- it is in the number about 6 to 7 million. These are located in the central portion of
the retina called the fovea. These are highly sensitive to color. Human can resolve fine details
with these cones because each one is connected to its own nerve end. Cone vision is called
photopic or bright light vision
2) Rods – these are very much in number from 75 to 150 million and are distributed over the
entire retinal surface. The large area of distribution and the fact that several roads are
connected to a single nerve give a general overall picture of the field of view. They are not
involved in the color vision and are sensitive to low level of illumination. Rod vision is called is
scotopic or dim light vision.
The absent of reciprocators is called blind spot

Image Formation in the Eye

The major difference between the lens of the eye and an ordinary optical lens in that the
former is flexible.
The shape of the lens of the eye is controlled by tension in the fiber of the ciliary body. To
focus on the distant object the controlling muscles allow the lens to become thicker in order to
focus on object near the eye it becomes relatively flattened.
The distance between the center of the lens and the retina is called the focal length and it
varies from 17mm to 14mm as the refractive power of the lens increases from its minimum to
its maximum.
When the eye focuses on an object farther away than about 3m.the lens exhibits its lowest
refractive power. When the eye focuses on a nearly object. The lens is most strongly refractive.
The retinal image is reflected primarily in the area of the fovea. Perception then takes place
by the relative excitation of light receptors, which transform radiant energy into electrical
impulses that are ultimately decoded by the brain.

Simple Image Model: An image is denoted by a two dimensional function of the form f{x, y}.
The value or amplitude of f at spatial coordinates {x,y} is a positive scalar quantity whose
physical meaning is determined by the source of the image. When an image is generated by a
physical process, its values are proportional to energy radiated by a physical source. As a
consequence, f(x,y) must be nonzero and finite; that is o<f(x,y) <co The function f(x,y) may
be characterized by two components-
 The amount of the source illumination incident on the scene being viewed.
  The amount of the source illumination reflected back by the objects in the scene These
are called illumination and reflectance components and are denoted by i(x,y) and r (x,y)
respectively.

Digital Image Definition: A digital image f(m,n) described in a 2D discrete space is derived
from an analog image f(x,y) in a 2D continuous space through a sampling process that is
frequently referred to as digitization. The mathematics of that sampling process will be
described in subsequent Chapters. For now, we will look at some basic definitions associated
with the digital image. The effect of digitization is shown in figure.

The 2D continuous image f(x,y) is divided into N rows and M columns. The intersection of a
row and a column is termed a pixel. The value assigned to the integer coordinates (m,n) with
m=0,1,2..N-1 and n=0,1,2…N-1 is f(m,n). In fact, in most cases, is actually a function of many
variables including depth, color and time (t).
There are three types of computerized processes in the processing of image
Low level Process: These involve primitive operations such as image processing to reduce
noise, contrast enhancement and image sharpening. These kinds of processes are characterized
by fact the both inputs and output are images.
Mid-level Image Processing: It involves tasks like segmentation, description of those objects
to reduce them to a form suitable for computer processing, and classification of individual
objects. The inputs to the process are generally images but outputs are attributes extracted from
images.
High level Processing: It involves “making sense” of an ensemble of recognized objects, as in
image analysis, and performing the cognitive functions normally associated with vision.
Representing Digital Images: The result of sampling and quantization is matrix of real
numbers. Assume that an image f(x,y) is sampled so that the resulting digital image has M rows
and N Columns. The values of the coordinates (x,y) now become discrete quantities thus the
value of the coordinates at origin become (x,y) = (0,0) The next Coordinates value along the
first signify the image along the first row. it does not mean that these are the actual values of
physical coordinates when the image was sampled.
Thus, the right side of the matrix represents a digital element, pixel or pel. The matrix can be
represented in the following form as well. The sampling process may be viewed as partitioning
the XY plane into a grid with the coordinates of the center of each grid being a pair of elements
from the Cartesian products Z2 which is the set of all ordered pair of elements (Zi, Zj) with Zi
and Zj being integers from Z.

Hence f(x,y) is a digital image if gray level (that is, a real number from the set of real number
R) to each distinct pair of coordinates (x,y). This functional assignment is the quantization
process. If the gray levels are also integers, Z replaces R, the and a digital image become a 2D
function whose coordinates and she amplitude value are integers. Due to processing storage
and hardware consideration, the number gray levels typically are an integer power of 2.
L=2k
Then, the number ‘b’ of bites required to store a digital image is
b=M *N* k
When M=N, the equation become
b=N2*k
When an image can have 2k gray levels, it is referred to as “k- bit”. An image with 256
possible gray levels is called an “8- bit image” (256=28).

Spatial and Gray level Resolution:

Spatial resolution is the smallest discernible details are an image. Suppose a chart can be
constructed with vertical lines of width w with the space between the also having width W, so
a line pair consists of one such line and its adjacent space thus. The width of the line pair is 2w
and there is 1/2w line pair per unit distance resolution is simply the smallest number of
discernible line pair unitdistance.
Gray levels resolution refers to smallest discernible change in gray levels. Measuring
discernible change in gray levels is a highly subjective process reducing the number of bits R
while repairing the spatial resolution constant creates the problem of false contouring. It is
caused by the use of an insufficient number of gray levels on the smooth areas of the digital
image. It is called so because the rides resemble top graphics contours in a map. It is generally
quite visible in image displayed using 16 or less uniformly spaced gray levels.

IMAGE SENSING AND ACQUISITION

The types of images in which we are interested are generated by the combination of an
“Illumination” source and the reflection or absorption of energy from that source by the
elements of the “scene” being imaged. We enclose illumination and scene in quotes to
emphasize the fact that they are considerably more general than the familiar situation in which
a visible light source illuminates a common everyday 3-D (three-dimensional) scene.

For example, the illumination may originate from a source of electromagnetic energy such as
radar, infrared, or X-ray energy. But, as noted earlier, it could originate from less traditional
sources, such as ultrasound or even a computer-generated illumination pattern. Similarly, the
scene elements could be familiar objects, but they can just as easily be molecules, buried rock
formations, or a human brain. We could even image a source, such as acquiring images of the
sun. Depending on the nature of the source, illumination energy is reflected from, or transmitted
through, objects.
An example in the first category is light reflected from a planar surface. An example in the
second category is when X-rays pass through a patient’s body for the purpose of generating a
diagnostic X-ray film. In some applications, the reflected or transmitted energy is focused onto
a photo converter (e.g., a phosphor screen), which converts the energy into visible light.
Electron microscopy and some applications of gamma imaging use this approach. The idea is
simple: Incoming energy is transformed into a voltage by the combination of input electrical
power and sensor material that is responsive to the particular type of energy being detected.
The output voltage waveform is the response of the sensor(s), and a digital quantity is obtained
from each sensor by digitizing its response. In this section, we look at the principal modalities
for image sensing andgeneration.

Fig: Line Sensor

Fig: Single Image Sensor

The components of a single sensor, perhaps the most familiar sensor of this type is the
photodiode, which is constructed of silicon materials and whose output voltage waveform is
proportional to light. The use of a filter in front of a sensor improves selectivity. For example,
a green (pass) filter in front of a light sensor favors light in the green band of the color spectrum.
As a consequence, the sensor output will be stronger for green light than for other components
in the visible spectrum.
Fig: Array sensor Image Acquisition using a Single Sensor

In order to generate a 2-D image using a single sensor, there has to be relative displacements
in both the x- and y-directions between the sensor and the area to be imaged. Figure shows an
arrangement used in high-precision scanning, where a film negative is mounted onto a drum
whose mechanical rotation provides displacement in one dimension. The single sensor is
mounted on a lead screw that provides motion in the perpendicular direction. Since mechanical
motion can be controlled with high precision, this method is an inexpensive (but slow) way to
obtain high-resolution images. Other similar mechanical arrangements use a flat bed, with the
sensor moving in two linear directions. These types of mechanical digitizers sometimes are
referred to as microdensitometers.

Image Acquisition using a Sensor Strips:

A geometry that is used much more frequently than single sensors consists of an in-line
arrangement of sensors in the form of a sensor strip, shows. The strip provides imaging
elements in one direction. Motion perpendicular to the strip provides imaging in the other
direction. This is the type of arrangement used in most flatbed scanners. Sensing devices with
4000 or more in-line sensors are possible. In-line sensors are used routinely in airborne imaging
applications, in which the imaging system is mounted on an aircraft that flies at a constant
altitude and speed over the geographical area to be imaged. One dimensional imaging sensor
strips that respond to various bands of the electromagnetic spectrum are mounted perpendicular
to the direction of flight. The imaging strip gives one line of an image at a time, and the motion
of the strip completes the other dimension of a two-dimensional image. Lenses or other
focusing schemes are used to project area to be scanned onto the sensors. Sensor strips mounted
in a ring configuration are used in medical and industrial imaging to obtain cross-sectional
(“slice”) images of 3-Dobjects.
Fig: Image Acquisition using linear strip and circular strips
Image Acquisition using a Sensor Arrays:

The individual sensors arranged in the form of a 2-D array. Numerous electromagnetic and
some ultrasonic sensing devices frequently are arranged in an array format. This is also the
predominant arrangement found in digital cameras. A typical sensor for these cameras is a CCD
array, which can be manufactured with a broad range of sensing properties and can be packaged
in rugged arrays of elements or more. CCD sensors are used widely in digital cameras and other
light sensing instruments. The response of each sensor is proportional to the integral of the light
energy projected onto the surface of the sensor, a property that is used in astronomical and
other applications requiring low noise images. Noise reduction is achieved by letting the sensor
integrate the input light signal over minutes or even hours. The two dimensional, its key
advantage is that a complete image can be obtained by focusing the energy pattern onto the
surface of the array. Motion obviously is not necessary, as is the case with the sensor
arrangements This figure shows the energy from an illumination source being reflected from a
scene element, but, as mentioned at the beginning of this section, the energy also could be
transmitted through the scene elements. The first function performed by the imaging system is
to collect the incoming energy and focus it onto an image plane. If the illumination is light, the
front end of the imaging system is a lens, which projects the viewed scene onto the lens focal
plane. The sensor array, which is coincident with the focal plane, produces outputs proportional
to the integral of the light received at each sensor. Digital andanalog circuitry sweeps these
outputs and convert them to a video signal, which is then digitized by another section of the
imaging system.
SAMPLING AND QUANTIZATION
To create a digital image, we need to convert the continuous sensed data into digital from. This
involves two processes – sampling and quantization. An image may be continuous with respect
to the x and y coordinates and also in amplitude. To convert it into digital form we have to
sample the function in both coordinates and in amplitudes.
Digitalizing the coordinate values is called Sampling. Digitalizing the amplitude values is
called Quantization. There is a continuous the image along the line segment AB. To simple this
function, we take equally spaced samples along line AB. The location of each samples is given
by a vertical tick back (mark) in the bottom part. The samples are shown as block squares
superimposed on function the set of these discrete locations gives the sampled function.
In order to form a digital, the gray level values must also be converted (quantized) into discrete
quantities. So, we divide the gray level scale into eight discrete levels ranging from eight level
values. The continuous gray levels are quantized simply by assigning one of the eight discrete
gray levels to each sample. The assignment it made depending on the vertical proximity of a
simple to a vertical tick mark. Starting at the top of the image and covering out this procedure
line by line produces a two-dimensional digital image.
Image sampling and Quantization:
To create a digital image, we need to convert the continuous sensed data into digital form.
This involves two processes.
1. Sampling and
2. Quantization

A continuous image, f(x, y), that we want to convert to digital form. An image may be
continuous with respect to the x- and y- coordinates, and also in amplitude. To convert it to
digital form, we have to sample the function in both coordinates and in amplitude.
Digitizing the coordinate values is called Sampling. Digitizing the amplitude values is called
Quantization.

Fig: Sampling

Fig: Quantization
Digital Image Representation:
Digital image is a finite collection of discrete samples (pixels) of any observable object. The
pixels represent a two- or higher dimensional “view” of the object, each pixel having its own
discrete value in a finite range. The pixel values may represent the amount of visible light,
infra-red light, absorption of x-rays, electrons, or any other measurable value such as
ultrasound wave impulses. The image does not need to have any visual sense; it is sufficient
that the samples form a two-dimensional spatial structure that may be illustrated as an image.
The images may be obtained by a digital camera, scanner, electron microscope, ultrasound
stethoscope, or any other optical or non-optical sensor.
Examples of digital image are Digital photographs, Satellite images, Radiological images (x-
rays, mammograms), Binary images, Fax images, Engineering drawings, Computer graphics,
CAD drawings, and vector graphics in general are not considered in this course even though
their reproduction is a possible source of an image. In fact, one goal of intermediate level
image processing may be to reconstruct a model (Eg: Vector Representation) for a given
digital image.

Relationship between Pixels:

We consider several important relationships between pixels in a digital image.
Neighbors of a Pixel:
A pixel p at coordinates (x,y) has four horizontal and vertical neighbors whose coordinates
are given by:
(x+1,y), (x-1, y), (x, y+1), (x,y-1)

This set of pixels, called the 4-neighbors or p, is denoted by N4(p). Each pixel is one unit
distance from (x,y) and some of the neighbors of p lie outside the digital image if (x,y) is on
the border of the image. The four diagonal neighbors of p have coordinates and are denoted by
ND(p).
(x+1, y+1), (x+1, y-1), (x-1, y+1), (x-1, y-1).
These points, together with the 4-neighbors, are called the 8-neighbors of p, denoted by
N8(p).

As before, some of the points in ND(p) and N8(p) fall outside the image if (x,y) is on the
border of the image.

Adjacency and Connectivity:

Let v be the set of gray –level values used to define adjacency, in a binary image, V={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 – 255, V set can be any subset of these 256 values. if we are
reference to adjacency of pixel with value.
Three types of Adjacency:
4- Adjacency – two pixel P and Q with value from V are 4 –adjacency if A is in the set N4(P)
8- Adjacency – two pixel P and Q with value from V are 8 –adjacency if A is in the set N8(P)

M-adjacency –two pixel P and Q with value from V are m – adjacency if (i) Q is in N4(p) or
(ii) Q is in ND(q) and the
(iii) Set N4(p) ∩ N4(q) has no pixel whose values are from V.
Mixed adjacency is a modification of 8-adjacency. It is introduced to eliminate the
ambiguities that often arise when 8-adjacency is used.
For example:
Fig: (a) Arrangement of pixels
(b) pixels that are 8-adjacent (shown dashed) to the center pixel
(c) m-adjacency

Types of Adjacency:
In this example, we can note that to connect between two pixels (finding a path between two
pixels):
In 8-adjacency way, you can find multiple paths between two pixels
While, in m-adjacency, you can find only one path between two pixels
So, m-adjacency has eliminated the multiple path connection that has been generated by the8-
adjacency.
Two subsets S1 and S2 are adjacent, if some pixel in S1 is adjacent to some pixel in S2.
Adjacent means, either 4-, 8- or m-adjacency.

Digital 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)
and (xn, yn) = (s,t) and pixels (xi, yi) and (xi-1, yi-1) are adjacent for 1 ≤ i ≤n, n is the length of
the path.
If (x0,y0) = (xn, yn), the path is closed.
We can specify 4, 8or m-paths depending on the type of adjacency specified.

Return to the previous example

Fig:(a) Arrangement of pixels
(b) pixels that are 8-adjacent (shown dashed) to the center pixel
(c) m-adjacency
In figure (b) the paths between the top right and bottom right pixels are 8-paths. And the path
between the same 2 pixels in figure (c) is m-path
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 consisting entirely of pixels in S.
For any pixel p in S, the set of pixels that are connected to it in S is called a connected
component of S. If it only has one connected component, then set S is called a connected set.
Region and Boundary:
Region: Let R be a subset of pixels in an image, we call R a region of the image if R is a
connected set.
Boundary: The boundary (also called border or contour) of a region R is the set of pixels in
the region that have one or more neighbors that are not in R.
If R happens to be an entire image, then its boundary is defined as the set of pixels in the first
and last rows and columns in the image. This extra definition is required because an image
has no neighbors beyond its borders. Normally, when we refer to a region, we are referring to
subset of an image, and any pixels in the boundary of the region that happen to coincide with
the border of the image are included implicitly as part of the region boundary.
COLOR IMAGE FUNDAMENTALS - RGB, HSI MODELS
According to the theory of the human eye, all colors are seen as variable combinations of the
three so-called primary colors red (R), green (G), and blue (B). The following specific
wavelength values to the primary colors: Blue (B) = 435.8 nm Green (G) = 546.1 nm Red (R)
= 700.0 nm The primary colors can be added to produce the secondary colors Magenta (red +
blue), cyan (green + blue), and yellow (red + green),
Mixing all the three primary colors results in white. Color television reception is based on
this three color system with the additive nature of light.
There are several useful color models: RGB, CMY, YUV, YIQ, and HSI.
RGB color model The colors of the RGB model can be described as a triple (R, G, B), so that
R, G, B .The RGB color space can be considered as a three-dimensional unit cube, in which
each axis represents one of the primary colors, see Figure. Colors are points inside the cube
defined by its coordinates.
The primary colors thus are red=(1,0,0), green=(0,1,0), and blue=(0,0,1). The secondary
colors of RGB are cyan=(0,1,1), magenta=(1,0,1) and yellow=(1,1,0).
The nature of the RGB color system is additive in the sense how adding colors makes the
image brighter. Black is at the origin, and white is at the corner where R=G=B=1. The
gray scale extends from black to white along the line joining these two points. Thus a shade
of gray can be described by (x,x,x) starting from black=(0,0,0) to white=(1,1,1). The colors
are often normalized as given in equation. This normalization guarantees that r+g+b=1

CMY color model The CMY color model is closely related to the RGB model. Its primary
colors are C (cyan), M (magenta), and Y (yellow). I.e. the secondary colors of RGB are the
primary colors of CMY, and vice versa. The RGB to CMY conversion can be performed by
• C= 1-R
• M = 1-G
• Y = 1-B
The scale of C, M and Y also equals to unit: C, M, Y .The CMY color system is used in offset
printing in a subtractive way, contrary to the additive nature of RGB. A pixel of color Cyan,
for example, reflects all the RGB other colors but red. A pixel with the color of magenta, on
the other hand, reflects all other RGB colors but green. Now, if we mix cyan and magenta,
we get blue, rather than white like in the additive color system.

ADDITIVE COLOUR MIXING:

In order to generate suitable colour signals it is necessary to know definite ratios in which
red, green and blue combine form new colours. Since R,G and B can be mixed to create any
colour including white, these are called primary colours.
• R + G + B = White colour
• R – G – B = Black colour
The primary colours R, G and B combine to form new colours
• R+G=Y
• R + B = Magenta (purplish)
• G + B = Cyan (greenish blue)
GRASSMAN’S LAW: Our eye is not able to distinguish each of the colours that mix to
form a new colour but instead perceives only the resultant colour. Based on sensitivity of
human eye to various colours, reference white for colour TV has been chosen to be a mixture
of colour light in the ratio 100% W = 30%R + 59%G + 11%B Similarly yellow can be
produced by mixing 30% of red and 59% of green, magenta by mixing 30% of red and 11%
of blue and cyan by mixing 59% of green to 11% of blue. Base on this it is possible to obtain
white light by mixing 89% of yellow with 11% of blue or 70% of cyan with 30% of red. Thus
the Eye perceives new colours based on the algebraic sum of red, green and blue light fluxes.
This forms the basic of colour signal generation and is known as GRASSMAN’S LAW.
YUV color model
The basic idea in the YUV color model is to separate the color information apart from the
brightness information.
The components of YUV are:
• Y = 0.3 R +0.6 G +.01B
• U= B - Y
• V= R- Y
Y represents the luminance of the image, while U, V consists of the color information, i.e.
chrominance. The luminance component can be considered as a gray-scale version of the RGB
image, The advantages of YUV compared to RGB are:
1. The brightness information is separated from the color information
2. The correlations between the color components are reduced.
3. Most of the information is collected to the Y component, while the information
content in the U and V is less. where the contrast of the Y component is much greater
than that of the U and V components.
The latter two properties are beneficial in image compression. This is because the correlations
between the different color components are reduced, thus each of the components can be
compressed separately. Besides that, more bits can be allocated to the Y component than to U
and V. The YUV color system is adopted in the JPEG image compression standard.
HSI color model
The HSI model consists of hue (H), saturation (S), and intensity (I).
• Intensity corresponds to the luminance component (Y) of the YUV and YIQ models.
• Hue is an attribute associated with the dominant wavelength in a mixture of light
waves, i.e. the dominant color as perceived by an observer.
• Saturation refers to relative purity of the amount of white light mixed with hue.
• The advantages of HSI are: The intensity is separated from the color information (the
same holds for the YUV and YIQ models though). The hue and saturation
components are intimately related to the way in which human beings perceive color.
The RGB to HSI conversion can be summarized as follows: