03-Digital Image Fundamentals (5)as.pptx

Instructor: Dr. Ghulam Murtaza Memon

Book title: Digital Image Processing by Gonzales
Digital Image Processing GMM Page 2

Contents
GMM Page 3
Digital Image Processing
2.1 Elements ofVisual Perception
2.1.1 Structure of the Human Eye
2.1.2 Image Formation in the Eye
2.1.3 BrightnessAdaptation and Discrimination
2.2 Light and the Electromagnetic Spectrum
2.3 Image Sensing and Acquisition
2.3.1 Image Acquisition Using a Single Sensor
2.3.2 Image Acquisition Using Sensor Strips
2.3.3 Image Acquisition Using Sensor Arrays
2.3.4A Simple Image Formation Model
2.4 Image Sampling and Quantization
2.4.1 Basic Concepts in Sampling and
Quantization
2.4.2 Representing Digital Images
2.4.3 Spatial and Intensity Resolution
2.4.4 Image Interpolation
2.5 Some Basic Relationships between Pixels
2.5.1 Neighbors of a Pixel
2.5.2 Adjacency, Connectivity, Regions, and Boundaries
2.5.3 Distance Measures
2.6 An Introduction to the MathematicalTools Used in Digital
Image Processing
2.6.1 Array versus Matrix Operations
2.6.2 Linear versus Nonlinear Operations
2.6.3 Arithmetic Operations
2.6.4 Set and Logical Operations
2.6.5 Spatial Operations
2.6.6Vector and Matrix Operations
2.6.7 ImageTransforms
2.6.8 Probabilistic Methods

Elements of Visual Perception
• Digital image processing(DIP) is built on a foundation of
mathematical and probabilistic formulations,
• But human intuition and analysis play a central role in the choice of
one technique versus another.
• Thus choice is subjective and often made on visual judgments.
• A basic understanding of human visual perception is needed for DIP
• The interest is in the mechanics and parameters related to how
images are formed and perceived by humans.
• Here we are learning the physical limitations of human vision to
work with digital images.

Structure of the Human Eye
• Eye is nearly a sphere, average diameter is 20 mm
• Cornea and sclera are outer layer to cover the
choroid layer and retina.
• Choroid contains blood vessels, nutrition to eye
• Choroid coat is heavily pigmented, helps to reduce
the amount of extraneous light entering into eye
• The choroid is divided into ciliary body and iris.
• ciliary body contracts and expands to control the
amount of light entering into eye
• Iris centeral opening i.e., pupil varies in diameter
aprox. 2 to 8 mm.
• The lense is suspended by fibers that attached with
ciliary body.
• It contains 60 to 70% water, about 6% fat, and
more protein than any other tissue in the eye.

• The lens is colored by a slightly yellow
pigmentation that increases with age.
• An excessive clouding of lens causes
cataracts leads to loss of clear vison.
• The Lens absorbs approx. 8% of light
of the visible light spectrum
• Both infrared and ultraviolet light are
absorbed appreciably by proteins
within the lens structure and, in
excessive amounts, can damage the
eye.

•The innermost membrane of the
eye is the retina contain light
receptors.
•When the eye is properly focused,
light from an object outside the eye
is imaged on the retina via light
receptors.
•Two classes of light receptors
• Cones and
• Rods

• The cones in each eye number
between 6 and 7 million. Which are
sensitive to color. Cone vision is
called photopic/bright-light vision
• Rods are 75 to 150 million are
distributed over the retinal surface.
• Rods serve to give a general, overall
picture of the field of view.
• Rods are sensitive to low levels of
illumination. Like object appear color
less in moonlight compare to sunlight
due to rods. Called scotopic or dim-
light vision.

Image Formation in the Eye
•In human eye the distance between lens and retina is fixed,
but shape of length is variable.
•Whereas it is converse in camera.

Brightness Adaptation and Discrimination

Contents
GMM Page 12
Quantization
Image Processing

Light and the Electromagnetic Spectrum
• In 1666, Sir Isaac Newton discovered that
when a beam of sunlight passes through a
glass prism, the emerging beam of light is
not white but consists instead of a
continuous spectrum of colors ranging
from violet at one end to red at the other.
• As Fig. 2.10 shows, the range of colors
we perceive in visible light is a small
portion of the electromagnetic spectrum.
• On one end of the spectrum are radio
waves with wavelengths billions of times
longer than those of visible light.
• On the other end of the spectrum are
gamma rays with wavelengths millions of
times smaller than those of visible light.

• Electromagnetic waves can be
visualized as propagating
sinusoidal waves with wavelength
λ (Fig. 2.11), or they can be
thought of as a stream of massless
particles,
• Each traveling in a wavelike
pattern and moving at the speed of
light.
• Each massless particle contains a
certain amount (or bundle) of
energy, called a photon.

• We see from Eq. (2-2) that energy is
proportional to frequency,
• so the higher-frequency (shorter
wavelength) electromagnetic phenomena
carry more energy per photon.
• Thus,
• radio waves have photons with low energies,
• microwaves have more energy than radio
waves,
• infrared still more, then visible, ultraviolet, X-
rays, and finally gamma rays, the most
energetic of all.
• High-energy electromagnetic radiation,
especially in the X-ray and gamma ray
bands, is particularly harmful to living
organisms.

• Light is a type of electromagnetic radiation that can be sensed
by the eye.
• The visible (color) spectrum is shown expanded in Fig. 2.10
• The visible band of the electromagnetic spectrum spans the
range from approximately 0.43 mm (violet) to about 0.79 mm
(red).
• For convenience, the color spectrum is divided into six broad
regions:
• violet, blue, green, yellow, orange, and red.
• No color ends abruptly; rather, each range blends smoothly into
the next, as Fig. 2.10 shows.

•The colors perceived in an object are determined by the
nature of the light reflected by the object.
•A body that reflects light relatively balanced in all visible
wavelengths appears white to the observer.
•However, a body that favors reflectance in a limited range
of the visible spectrum exhibits some shades of color.
• For example, green objects reflect light with wavelengths primarily
in the 500 to 570 nm range, while absorbing most of the energy at
other wavelengths.

•Light that is void of color is called monochromatic (or
achromatic) light.
•The only attribute of monochromatic light is its intensity.
•Because the intensity of monochromatic light is perceived
to vary from black to grays and finally to white,
•The term gray level is used commonly to denote
monochromatic intensity.
•The range of values of monochromatic light from black to
white is usually called the gray scale, and monochromatic
images are frequently referred to as grayscale images.

• Chromatic (color) light spans the electromagnetic energy spectrum
from approximately 0.43 to 0.79 mm.
• Three other quantities are used to describe a chromatic light source:
radiance, luminance, and brightness.
• Radiance is the total amount of energy that flows from the light
source, and it is usually measured in watts (W).
• Luminance, measured in lumens (lm), gives a measure of the amount
of energy an observer perceives from a light source.
• For example, light emitted from a source operating in the far infrared region of
the spectrum could have significant energy (radiance), but an observer would
hardly perceive it; its luminance would be almost zero.
• Brightness is a subjective descriptor of light perception that is
practically impossible to measure. It embodies the achromatic notion
of intensity and is one of the key factors in describing color sensation.

• In principle, if a sensor can be developed that is capable of detecting
energy radiated in a band of the electromagnetic spectrum, we can image
events of interest in that band.
• Note, however, that the wavelength of an electromagnetic wave required to
“see” an object must be of the same size as, or smaller than, the object.
• For example,
• a water molecule has a diameter on the order of 10-10 m.
• To study these molecules, we would need a source capable of emitting energy in the
far (high energy) ultraviolet band or soft (low-energy) X-ray bands.
• Although imaging is based predominantly on energy from electromagnetic
wave radiation, this is not the only method for generating images.
• But sound reflected from objects can be used to form ultrasonic images.
• Other sources of digital images are electron beams for electron microscopy, and
• software for generating synthetic images used in graphics and visualization.

Contents
GMM Page 22
Quantization
Image Processing

What is image processing?
• The amplitude of f at any pair of coordinates (x, y) is called the intensity or
gray level of the image at that point.
• When x, y, and the intensity values of f are all finite, discrete quantities, we
call the image a digital image.
• The field of digital image processing refers to processing digital images by
means of a digital computer.
• Thus a digital image composed of elements, each element has a location
and an intensity value.
• These elements are called picture elements, image elements, pels, or pixels.
•An image is a 2-D function f(x,y)
• x and y are spatial (plane) coordinates
i.e., location,

ImageAcquisition Using a Single Sensor
ImageAcquisition Using Sensor Strips
ImageAcquisition Using Sensor Arrays
A Simple Image Formation Model

Image Sensing and Acquisition
• The illumination may originate from a source of electromagnetic energy,
• such as a radar, infrared, or X-ray system.
• OR
• 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, like molecules, buried rock
formations, or a human brain.
• 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 image.
• In some applications, the reflected or transmitted energy is focused onto a photo
converter (e.g., a phosphor screen) that converts the energy into visible light.
• Electron microscopy and some applications of gamma imaging use this approach.

Image Sensing and Acquisition: IMAGE ACQUISITION
USING A SINGLE SENSING ELEMENT
• Figure 2.12 shows the three
principal sensor arrangements used
to transform incident energy into
digital images.
• The 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.

Image Sensing and Acquisition: IMAGE ACQUISITION
USING A SINGLE SENSING ELEMENT
• Figure 2.12(a) shows the components of
a single sensing element.
• A familiar sensor of this type is the
photodiode, which is constructed of
silicon materials and whose output is a
voltage proportional to light intensity.
• Using a filter in front of a sensor
improves its selectivity.
• For example, an optical green-transmission
filter favors light in the green band of the
color spectrum.
• As a consequence, the sensor output would
be stronger for green light than for other
visible light components.

•A geometry used more
frequently than single sensors
is an in-line sensor strip, as
in Fig. 2.12(b).
•The strip provides imaging
elements in one direction.
•Motion perpendicular to the
strip provides imaging in the
other direction, as shown in
Fig. 2.14(a).
Image Sensing and Acquisition
IMAGE ACQUISITION USING SENSOR STRIPS

Image Acquisition Using Sensor Arrays
• Figure 2.12(c) shows individual sensing
elements arranged in the form of a 2-D
array.
• Electromagnetic and ultrasonic sensing
devices frequently are arranged in this
manner.
• This is also the predominant
arrangement found in digital cameras.
• A typical sensor for these cameras is a
CCD (charge-coupled device) array,
which can be manufactured with a broad
range of sensing properties and can be
packaged in rugged arrays of
4000X4000 elements or more.

A SIMPLE IMAGE FORMATION MODEL
•As we denoted images by 2D functions of the form f(x,y).
•The value of f at spatial coordinates (x,y) is a scalar quantity
• whose physical meaning is determined by the source of the image,
and
• whose values are proportional to energy radiated by a physical
source (e.g., electromagnetic waves).
• As a consequence, f(x,y) must be nonnegative and finite; that is,

• As a consequence, f(x,y) must be nonnegative and finite; that is,
Function f(x,y) is characterized by two components:
• (1) the amount of source illumination incident on the scene being viewed,
and
• (2) the amount of illumination reflected by the objects in the scene.
• These are called the illumination and reflectance components,
and are denoted by i(x, y) and r(x,y), respectively.
• The two functions combine as a product to form f(x,y):

• The two functions combine as a product to form f(x,y):
• Reflectance is bounded by 0 (total absorption) and 1 (total
reflectance).
• The nature of i(x,y) is determined by the illumination source, and
• r(x,y) is determined by the characteristics of the imaged objects.

• The interval L[min,max] is called
the intensity (or gray) scale.
• Common practice is to shift this
interval numerically to the interval
[0,1] or [0,C]
• where l = 0 is considered black and
• l = 1 (or C) is considered white on
the scale.
• All intermediate values are
shades of gray varying from black
to white.

Contents
GMM Page 35
Quantization
Image Processing

Image Sampling and Quantization
•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.
•To create a digital image, we need to convert the continuous
sensed data into a digital format. This requires two
processes: sampling and quantization.
•Digitizing the coordinate values is called sampling.
•Digitizing the amplitude values is called quantization.

• The 1-D function in Fig. (b) is a
plot of amplitude (intensity level)
values of the continuous image
along the line segment AB in
Fig.(a).
• To sample this function, we take
equally spaced samples along
line AB, as shown in Fig. (c).
• Small dark squares are showing
samples, i.e. sample function
• Discrete spatial location
indicated by ticks in bottom
• Values of samples is vertically,
are continuous range of
intensities required in
quantization (here are 8-gray
shades from 0 to 1).

• Figure 2.17(a) shows a
continuous image projected
onto the plane of a 2-D sensor.
• Figure 2.17(b) shows the
image after sampling and
quantization.
• The quality of a digital image
is determined to
• a large number of samples and
• discrete intensity levels used in
sampling and quantization.
• However, image content also
plays a role in the choice of
these parameters.

Representing Digital Images
•A 2-D array, containing M rows
and N columns,
• where (x,y) are discrete
coordinates.
• For notational clarity and
convenience, we use integer values
for these discrete coordinates:
• x = 0, 1, 2, ...., M - 1
• y = 0, 1, 2, ...., N – 1
• x and y are referred to as spatial
variables or spatial coordinates.

• As Fig. 2.19 shows, we define the origin of an image at the top left corner.
• This is a convention based on the fact that many image displays/screen.
• Choosing the origin of f(x,y) at that point makes sense mathematically because digital
images in reality are matrices.
• Sometimes we use x and y interchangeably in equations with the rows (r) and columns
(c) of a matrix.
• For example, the center of an
image of size 1023X1024 is at
(511,512).
• Some programming languages
(e.g., MATLAB) start indexing at 1
instead of at 0.
• The center of an image in that
case is found at

•An image exhibiting saturation
and noise.
•Saturation is the highest value
beyond which all intensity values
are clipped (note how the entire
saturated area has a high,
constant intensity level).
•Visible noise in this case appears
as a grainy texture pattern.
•The dark background is noisier,
but the noise is difficult to see.

• This digitization process
requires that decisions be
made regarding the values
for M, N, and for the
number, L, of discrete
intensity levels.
• The number of intensity
levels typically is an integer
power of 2: L= 2k
• Where k is an integer.
• We assume that the discrete
levels are equally spaced and
that they are integers in the
range [0,L-1].

• Figure 2.21 shows the number of megabytes required to store square images
for various values of N and k (as usual, one byte equals 8 bits and a
megabyte equals 106 bytes).
• When an image can have 2k possible intensity levels, it is common practice to
refer to it as a “k-bit image,” (e,g., a 256-level image is called an 8-bit image).
• Note that storage requirements for large 8-bit images (e.g., 10,000*10,000
pixels) are not insignificant.

•Resolution:
• Image resolution describes the amount of detail an image holds.
• Higher resolution images are sharp/more detailed.
• In a lower resolution image, the fine differences in color disappear, edges become
blurred, etc.
• There are many kinds of resolution that can apply to film, television, etc., but the two
types we are concerned with here are
• screen resolution and
• print resolution.
•Screen resolution:
• Measured in pixels per inch (PPI). A pixel is a tiny square of color.
• A monitor uses tiny pixels to assemble text and images on screen.
• The optimal resolution for images on screen is 72 DPI.
• Increasing the DPI won’t make the image look any better, it’ll just make the file larger,
which will probably slow down the website when it loads or the file when it opens.

•Print resolution:
• Measured in dots per inch (or “DPI”),
• DPI means the number of dots of ink per inch that a printer deposits on a piece of
paper.
• For 300 DPI, a printer will output 300 tiny dots of ink to fill every inch of the print.
• 300 DPI is the standard print resolution for high resolution output.
• This means that that images should be a minimum of 300 dpi x 300 dpi or 90,000
dots per square inch to produce a high resolution print.
• If the document will stay on the screen (like a website), you just need to worry about
screen resolution, so your images should be 72 PPI.
• An important note: Sometimes the terms DPI (print) and PPI (screen) are used
interchangeably. So, don’t be confused if someone refers to a 300 DPI image that is
on screen, because pixels per inch (PPI) translate equally to dots per inch (DPI).
• If you’re going to print the document, you need to make sure the images are 300
DPI at 100% of the final output size. This sounds more complicated than it really is.
• The bigger we try to print the 300 pixel × 300 pixel image, the more pixellated it
becomes. The eye can start to see the individual pixels, and the edges become very
sharp.

•How can we figure out the DPI of an image?
•if you want to print an image that is 1024 × 768 (listed as
Width=1024px, Height=768px on a PC), you need to divide
each value by 300 to see how many inches you can print at
300 dpi.
•1024 ÷ 300 = 3.4133″ (width)
•768 ÷ 300 = 2.56″ (height)
•So, you could print this 1024px × 768px image at 300 DPI
at a size of 3.4133″ × 2.56″ –
• any bigger than this, and you risk the image becoming pixellated.

Spatial and Intensity Resolution
•Spatial resolution commonly stated in dots (pixels) per
unit distance like
• dots per inch (dpi) for printing or scanning.
• Pixels per inch (ppi) for screen
•In US to give you an idea of quality,
• newspapers are printed with a resolution of 75 dpi,
• magazines at 133 dpi,
• glossy brochures at 175 dpi, and
• the book page at which you are presently looking is printed at
2400 dpi.

• Image size depends on two factors
• Number of samples or spatial locations
(no of pixels)
• Levels of intensity used in
quantization(Intensity resolution),
• the number of intensity levels usually is an
integer power of two
• commonly used 8 or 16 bits, i.e.; 2k where
k=8,16
• Thus intensity levels will be 28 = 256 or 216 =
65536

Gray scale shades

Python with OpenCV
•OpenCV is a popular open source library for processing
images.
•It has API bindings in Python, C++, Java, and Matlab.
•It comes with thousands of functions and implemented many
advanced image processing algorithms.
•If you’re using Python, a common alternative to OpenCV is
PIL (Python Imaging Library, or its successor, Pillow).
•Compared to PIL, OpenCV has a richer set of features and
is often faster because it is implemented in C++.

Read an image
import cv2
img = cv2.imread("path/Messi2018.png", cv2.IMREAD_GRAYSCALE)
cv2.imshow(“Messi 2018", img)
cv2.waitKey(0)
cv2.destroyAllWindows()

Read an image
import cv2
img = cv2.imread('messi2018.png',cv2.IMREAD_COLOR)
cv2.imshow('Messi 2018',img)
R = img.shape[0]
C = img.shape[1]
Channel = img.shape[2]
print("Image rows:",R)
print("Image col:",C)
print("Image rows:",Channel)
cv2.waitKey(0)
cv2.destroyAllWindows()

Convert image 8 to 16 bit

Convert image 8 to 16 bit (MATALB)
%% convert image 8 to 16 bit
pic1=imread('chestxray.jpg');
imwrite(pic1,'chestxray8.png','BitDepth', 8);
%figure,imshow(pic1);
%title('Chest xray unit 8');
%
imwrite(pic1,'chestxray16.png','BitDepth', 16);
img8 = imread('chestxray8.png');
img16 = imread('chestxray16.png');
%to show max pixel intensity
max(img8,[],'all’)
max(img16,[],'all')

Image Interpolation
•Definition: The process of using known data to estimate
values at unknown locations.
•A basic tool used extensively in tasks such as
• zooming,
• shrinking,
• rotating, and
• geometric corrections.
•Here we apply it to image resizing (shrinking and
zooming),
•which are basically image resampling methods.

Image Interpolation
•Nearest neighbor (NN) interpolation
• A simplest approach to interpolation. This method simply determines the “nearest”
neighboring pixel, and assumes the intensity value of it. Rather than calculate an
average value by some weighting criteria or generate an intermediate value based on
complicated rules.
• It has the tendency to produce undesirable artifacts, such as severe distortion of straight
edges.

Image Interpolation
• Bilinear interpolation: in which we use the four nearest
neighbors to estimate the intensity at a given location.
• Let f(x,y) denote the coordinates of the location to which we want to
assign an intensity value (think of it as a point of the grid described
previously), and
• let v(x,y) denote that intensity value. For bilinear interpolation, the
assigned value is obtained using the equation
• v(x, y) = ax + by + cxy + d
• Where the four coefficients are determined from the four equations in
four unknowns that can be written using the four nearest neighbors of
point .
• Bilinear interpolation gives much better results than nearest neighbor
interpolation, with a modest increase in computational burden.
• Detailed solved example:
• https://www.omnicalculator.com/math/bilinear-interpolation

https://www.omnicalculator.com/math/bilinear-interpolation

Image Interpolation
• Bicubic interpolation: involves the sixteen nearest neighbors
of a point. The intensity value assigned to point is obtained
using the equation:
• Generally, bicubic interpolation does a better job of preserving
fine detail than its bilinear counterpart.
• Bicubic interpolation is the standard used in commercial image
editing programs,
• such as Adobe Photoshop and Corel Photo paint.

Image Interpolation

Image Interpolation
• (a) Image reduced to 72 dpi
and zoomed back to its
original size ( pixels) using
nearest neighbor interpolation.
• (b) Image shrunk and zoomed
using bilinear interpolation.
• (c) Same as (b) but using
bicubic interpolation.
• (d)–(f) Same sequence, but
shrinking down to 150 dpi
instead of 72 dpi

Image Interpolation
•Compare Figs. 2.24(e) and
(f), especially the latter, with
the original image in Fig.
2.20(a).

Image Interpolation

All

See difference for size*2

Interpolation Code MATALB

Interpolation Example MATLAB
clear
img = imread('eye.jpg');
nn = imresize(img,0.3,'nearest'); %shrinking by 30%
bl = imresize(img,0.3,'bilinear');
bc = imresize(img,0.3,'bicubic');
%subplot(2,2,1),
figure,imshow(img), title('Original Image');
%subplot(2,2,2),
figure,imshow(nn), title('Nearest neighbor interpolation');
%subplot(2,2,3),
figure, imshow(bl), title('bilinear interpolation');
%subplot(2,2,4),
figure,imshow(bc), title('bicubic interpolation');

Contents
GMM Page 71
Quantization
Image Processing

Some Basic Relationships between Pixels
• A pixel p at coordinates (x,y) has two horizontal and two vertical neighbors with coordinates
• (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1)
• This set of pixels, called the 4-neighbors of p, is denoted N4(p).
• The four diagonal neighbors of p have coordinates
• and are denoted ND(p).
• These neighbors, together with the 4-neighbors(diagonal), are called the 8-neighbors of p,
denoted by N8(p).
• Def: The set of image locations of the neighbors of a point p is called the neighborhood of
p.
• The neighborhood is said to be closed if it contains p. Otherwise, the neighborhood is said to be
open.

Some Basic Relationships between Pixels

Some Basic Relationships between Pixels:
ADJACENCY, CONNECTIVITY, REGIONS, AND BOUNDARIES
•Let V be the set of intensity values used to define adjacency.
•In a binary image,
• V = {1} if we are referring to adjacency of pixels with value 1.
•In a grayscale image, the idea is the same, but set V
typically contains more elements. For example,
• if we are dealing with the adjacency of pixels whose values are in the range
0 to 255, set V could be any subset of these 256 values.
•We consider three types of adjacency:

• We consider three types of adjacency:
• 1. 4-adjacency. Two pixels p and q with values from V are 4-adjacent if q is in the set N4(p).
• 2. 8-adjacency. Two pixels p and q with values from V are 8-adjacent if q is in the set N8(p).
• 3. m-adjacency (also called mixed adjacency). Two pixels p and q with values from V are m-
adjacent if
(a) q is in N4(p), or
(b) q is in ND(p) and the set N4(p)ՈN4(q) has no pixels whose values are from V.
• Mixed adjacency is a modification of 8-adjacency, and is introduced to eliminate the ambiguities
that may result from using 8-adjacency.
• For example, consider the pixel arrangement in Fig. 2.28(a) and let V = {1}.
• The three pixels at the top of Fig. 2.28(b) show multiple (ambiguous) 8-adjacency, as indicated by the
dashed lines.
• This ambiguity is removed by using m-adjacency, as in Fig. 2.28(c).
• In other words, the center and upper-right diagonal pixels are not m-adjacent because they do not satisfy
condition(b).

• Connectivity between pixels
• It is an important concept in digital image processing.
• It is used for establishing boundaries of objects and components of regions in an image.
• Two pixels are said to be connected:
• if they are adjacent in some sense( neighbour pixels,4/8/m-adjacency)
• if their gray levels satisfy a specified criterion of similarity(equal intensity level)
• There are three types of connectivity on the basis of adjacency. They are:
• a) 4-connectivity: Two or more pixels are said to be 4-connected if they are 4-adjacent with each others.
• b) 8-connectivity: Two or more pixels are said to be 8-connected if they are 8-adjacent with each others.
• c) m-connectivity: Two or more pixels are said to be m-connected if they are m-adjacent with each others.

• Let R represent a subset of pixels in an image.
• We call R a region of the image if R is a connected set.
• Two regions, Ri and Rj are said to be adjacent if their union
forms a connected set.
• Regions that are not adjacent are said to be disjoint.
• We consider 4- and 8-adjacency when referring to regions.
• For our definition to make sense, the type of adjacency used
must be specified.
• For example, the two regions of 1’s in Fig. 2.28(d) are adjacent
only if 8-adjacency is used.

• The boundary (also called the border or contour) of a region R is the
set of pixels in R that are adjacent to pixels in the complement of R.
• Also, the border of a region is the set of pixels in the region that have at
least one background neighbor.
• Here again, we must specify the connectivity being used to define
adjacency.
• For example, the point circled in Fig. 2.28(e) is not a member of the border of
the 1-valued region if 4-connectivity is used between the region and its
background, because the only possible connection between that point and the
background is diagonal.
• As a rule, adjacency between points in a region and its background is
defined using 8-connectivity to handle situations such as this.

Distance Measures: Euclidean distance

Distance Measures: City-block distance

Distance Measures: chessboard distance

Contents
GMM Page 85
Quantization
Image Processing

Array versus Matrix Operations
• An array operation involving one or more images is carried out on a pixel-by-
pixel basis.
• However, there are many operation are made on matrix theory
• Following example shows image based array multiplication.
• It is not like matrix theory.

Linear versus Nonlinear Operations

• Above equation indicates that:
• the output of a linear operation due to the sum of two inputs is the same as performing the
operation on the inputs individually and then summing the results. (called additivity
property)
• In addition, the output of a linear operation to a constant times an input is the same as the
output of the operation due to the original input multiplied by that constant. (called
homogeneity property)
• Example:

• Linear operations are
exceptionally important
because they are based on a
large body of theoretical and
practical results that are
applicable to image
processing.
• Nonlinear systems are not
nearly as well understood, so
their scope of application is
more limited.

Arithmetic Operations
• Arithmetic operations are carried out between corresponding pixel pairs.
• The four arithmetic operations are denoted as
• The operations are performed between corresponding pixel pairs
in f and g for and
• x = 0, 1, 2, … , M - 1 and y = 0, 1, 2, …, N – 1.
• where, as usual, M and N are the row and column sizes of the images.
• s, d, p, and v are images of size MxN also.
• Note that image arithmetic in the manner just defined involves
images of the same size.

Add noise (Gaussian and Uniform)
import numpy as np
import matplotlib.pyplot as plt
import cv2 as cv
#%%
#img=cv.imread("car.png",0)
img=cv.imread("car.png",0)
#A=img.shape
print(img.shape)
R=img.shape[0]
C=img.shape[1]
#%%
#Gaussian Noise
noise=np.zeros((R,C),dtype=np.uint8)
cv.randn(noise,128,20)
gauss_noise=(noise*0.5).astype(np.uint8)
#uniform noise
#uni_noise=np.zeros((R,C),dtype=np.uint8)
cv.randu(noise,0,255)
uni_noise=(noise*0.5).astype(np.uint8)
#%%
gn_img=cv.add(img,uni_noise) # 250+10= 260 => 255
#gn_img1=img+gauss_noise # 250+10= 260%256 = 4
#%%
fig=plt.figure(dpi=300)
fig.add_subplot(1,3,1)
plt.imshow(img,cmap='gray')
plt.axis("off")
plt.title("Original")
plt.imshow(gauss_noise,cmap='gray')
plt.axis("off")
plt.title("Uniform Noise")
plt.imshow(gn_img,cmap='gray')
plt.axis("off")
plt.title("Combined")

Remove Noise (Gaussian)
import numpy as np
import matplotlib.pyplot as plt
import cv2 as cv
#%%
#img=cv.imread("car.png",0)
img=cv.imread("car.png",0)
#A=img.shape
print(img.shape)
R=img.shape[0]
C=img.shape[1]
#%%
#Gaussian Noise
noise=np.zeros((R,C),dtype=np.uint8)
cv.randn(noise,128,20)
gauss_noise=(noise*0.5).astype(np.uint8)
#% Add noise
gn_img=cv.add(img,gauss_noise)# 250+10= 260 => 255
#% Remove noise
denoised1=cv.fastNlMeansDenoising(gn_img,None,10,
10)
#%%
fig=plt.figure(dpi=300)
plt.imshow(img,cmap='gray')
plt.axis("off")
plt.title("Original")
plt.imshow(gn_img,cmap='gray')
plt.axis("off")
plt.title("with Gaussian Noise")
plt.imshow(denoised1,cmap='gray')
plt.axis("off")
plt.title("After Denoising")

Add noise
clc
close all
% Read the test Image
img = imread('Flower.jpg');
mygrayimg = rgb2gray(img);
mygrayimg = imresize(mygrayimg,[256 256],'nearest');
subplot(2,3,1); imshow(mygrayimg);
title('Original Image');
% Add Salt and pepper noise with noise density 0.02
salt = imnoise(mygrayimg,'salt & pepper',0.02);
subplot(2,3,2); imshow(salt);
title('Salt & Pepper Image');
% Add Gaussian noise with mean 0 and variance 0.01
gau = imnoise(mygrayimg, 'gaussian', 0, 0.01);
subplot(2,3,3); imshow(gau);
title('Gaussian Image- mean 0 and variance 0.01');
% Generate Gaussian noise with mean 6 and variance 225
mynoise = 6 + sqrt(225) * randn(256,256);
subplot(2,3,4); imshow(mynoise,[]);
title('Generated gaussian noise');
% Original Image and generated Gaussian
mynoiseimg = double(mygrayimg) + mynoise;
subplot(2,3,5); imshow(mynoiseimg,[]);
title('Gaussian image - mean 6 & Var 225');
% Original Image plus sinusoidal noise
[x y] = meshgrid(1:256,1:256);
mysinusoidalnoise = 15 * sin(2*pi/14*x+2*pi/14*y);
mynoiseimg1 = double(mygrayimg) + mysinusoidalnoise;
subplot(2,3,6);imshow(mynoiseimg1,[]);
title('Generated Sinusoidal noise');

Remove Noise
clc
close all
I = imread('eight.tif');
figure, imshow(I),title('orginal image')
J = imnoise(I,'salt & pepper',0.02);
figure, imshow(J),title('Noisy image')
Kmedian = medfilt2(J);
figure, imshow(Kmedian),
title('Noise removed image')

Arithmetic Operations: Example

• Image of Galaxy
Pair, corrupted by
additive Gaussian
noise.
• (b)–(f) Results of
averaging 5, 10, 20,
50, and 100 noisy
images, respectively.

Arithmetic Operations (difference)
• Arithmetic

Arithmetic Operations
• Arithmetic

Arithmetic Operations (Difference)
• Arithmetic

Arithmetic Operations (Product)
• Arithmetic

Arithmetic Operations (Product)
https://www.mathworks.com/help/images/correcting-nonuniform-illumination.html

Arithmetic Operations: (Product)
• Arithmetic

Image Arithmetic (Example Code)
•https://subscription.packtpub.com/book/data/978180020177
4/2/ch02lvl1sec10/image-arithmetic
•We know that images are nothing but matrices. This raises
an important and interesting question. If we can carry out
arithmetic operations on matrices, can we carry them out on
images as well? The answer is a bit tricky. We can carry out
the following operations on images:
• Adding and subtracting two images
• Adding and subtracting a constant value to/from image
• Multiplying a constant value by an image

Image Arithmetic (Example Code)
•https://www.askpython.com/python/examples/arithmetic-
operations-on-images

Set and Logical Operations
• A

• A

Home work
•Using two images find the five set operations like
• Use two image
• Union
• Intersection
• Complement
• Deference

#import numpy as np
#import matplotlib.pyplot as plt
import cv2 as cv
#%%
#img1 = cv2.imread('black_top_right_triangle.png',0)
#img2 = cv2.imread('black_bottom_right_triangle.png',0)
img1 = cv.imread('Box_A.png',0)
img2 = cv.imread('Box_B.png',0)
img_bwa = cv.bitwise_and(img1,img2) #A Union B
img_bwo = cv.bitwise_or(img1,img2) #A intersection B
img_bwx = cv.bitwise_xor(img1,img2) #
img_Comp = cv.bitwise_not(img_bwo) #
cv.imshow("A: Orginal ImageA", img1)
cv.imshow("B: Orginal Image B", img2)
cv.imshow("Bitwise AND: UnionA and B", img_bwa)
cv.imshow("Bitwise OR: Intersection A and B", img_bwo)
cv.imshow("Bitwise XOR: A XOR B", img_bwx)
cv.imshow("Complement of Image not(A or B)", img_Comp)
cv.waitKey(0)
cv.destroyAllWindows()

#import numpy as np
#import matplotlib.pyplot as plt
import cv2 as cv
#%%
#img1 = cv2.imread('black_top_right_triangle.png',0)
#img2 = cv2.imread('black_bottom_right_triangle.png',0)
img1 = cv.imread('Box_A.png',0)
img2 = cv.imread('Box_B.png',0)
img_bwa = cv.bitwise_and(img1,img2) # A U B
img_bwo = cv.bitwise_or(img1,img2) # A intersection B
img_bwx = cv.bitwise_xor(img1,img2) #
cv.imshow("Black_top_right_triangle", img1)
cv.imshow("Black_bottom_right_triangle", img2)
cv.imshow("Bitwise AND of Image 1 and 2", img_bwa)
cv.imshow("Bitwise OR of Image 1 and 2", img_bwo)
cv.imshow("Bitwise XOR of Image 1 and 2", img_bwx)
cv.waitKey(0)
cv.destroyAllWindows()

Convert to B/W, apply AND operator code
%%
clear all
clc
ImgOrg= imread('box.png');
ImgGray= rgb2gray(ImgOrg);
ImgBW= imbinarize(ImgGray); %convert to binary(BW) image
Figure;
subplot(3,3,1),imshow(ImgOrg), title(‘Original Image')
subplot(3,3,2),imshow(ImgGray), title('Grayscale Image')
subplot(3,3,3),imshow(ImgBW), title('Black and White image')
%% NOT operation
ImgNotBW = not(ImgBW);
subplot(3,3,4),imshow(ImgBW), title('Black and White image')
subplot(3,3,5),imshow(ImgNotBW), title('NOT Image')
%% AND operation
ImgOrg2 = imread('box2.png');
ImgGray2= rgb2gray(ImgOrg2);
ImgBW2= imbinarize(ImgGray2);
ImgAND = and(ImgBW,ImgBW2);
subplot(3,3,7),imshow(ImgBW), title('Image 1')
subplot(3,3,8),imshow(ImgBW2), title('Image 2')
subplot(3,3,9),imshow(ImgAND), title('Image 1 AND Image 2')

Spatial Operations
•Spatial operations are performed directly on the pixels of a
given image. We classify spatial operations into three broad
categories:
•(1) single-pixel operations,
•(2) neighborhood operations, and
•(3) geometric spatial transformations.

Single-pixel operations

Geometric spatial transformations and image registration
•We use geometric transformations modify the spatial
arrangement of pixels in an image.
•These transformations are called rubber-sheet
transformations because they may be viewed as analogous
to “printing” an image on a rubber sheet, then stretching or
shrinking the sheet according to a predefined set of rules.
•Geometric transformations of digital images consist of two
basic operations:
• 1. Spatial transformation of coordinates.
• 2. Intensity interpolation that assigns intensity values to the spatially
transformed pixels.

•Our interest is in so-called affine transformations, which
include scaling, translation, rotation, and shearing.
•The key characteristic of an affine transformation in 2-D is
that it preserves points, straight lines, and planes.
•This transformation can scale, rotate, translate, or sheer an
image, depending on the values chosen for the elements of
matrix A.

Affine transform

•https://www.mathworks.com/help/images/ref/affine2d.html
•The preceding transformation moves the coordinates of
pixels in an image to new locations.
•To complete the process, we have to assign intensity
values to those locations.
•This task is accomplished using intensity interpolation.

IMAGE TRANSFORMS
• All the image processing approaches discussed thus far
operate directly on the pixels of an input image; that is, they
work directly in the spatial domain.
• In some cases, image processing tasks are best formulated
by transforming the input images, carrying the specified task
in a transform domain, and applying the inverse transform to
return to the spatial domain.
• You will encounter a number of different transforms as you
proceed. A particularly important class of 2-D linear
transforms, denoted T(u,v), can be expressed in the general
form

IMAGE TRANSFORMS
• where f(x,y) is an input image, r(x,y,u,v) is called a forward
transformation kernel, and Eq. (2-55) is evaluated for u = 0,1,2 , …
M-1 and v = 0,1,2 , … N-1.
• As before, x and y are spatial variables, while M and N are the row
and column dimensions of f.
• Variables u and v are called the transform variables.
• T(u,v) is called the forward transform of f (x,y).
• Given T(u,v), we can recover f(x,y) using the inverse transform of
T(u,v):
• for x=0,1,2 , … M-1 and y= 0,1,2, … N-1, where s(x,y,u,v) is called
an inverse transformation kernel.
• Together, Eqs. (2-55) and (2-56) are called a transform pair.

IMAGE TRANSFORMS
• Figure 2.44 shows the basic steps for performing image
processing in the linear transform domain.
• First, the input image is transformed, the transform is then
modified by a predefined operation and, finally, the output
image is obtained by computing the inverse of the modified
transform.
• Thus, we see that the process goes from the spatial domain to
the transform domain, and then back to the spatial domain.

IMAGE TRANSFORMS

IMAGE TRANSFORMS
•The nature of a transform is determined by its kernel.
•A transform of particular importance in digital image
processing is the Fourier transform, which has the
following forward and inverse kernels respectively:
•where j = −1, so these kernels are complex functions.

IMAGE TRANSFORMS
•Substituting the preceding kernels into the general
transform formulations in Eqs. (2-55) and (2-56) gives us
the discrete Fourier transform pair:

IMAGE TRANSFORMS

IMAGE TRANSFORMS
• It can be shown that the Fourier kernels are separable and
symmetric, and
• that separable and symmetric kernels allow 2-D transforms to
be computed using 1-D transforms.

MATLAB image library
%Default images with matlab
% AT3_1m4_01.tif AT3_1m4_02.tif
% AT3_1m4_03.tif AT3_1m4_04.tif
% AT3_1m4_05.tif AT3_1m4_06.tif
% AT3_1m4_07.tif AT3_1m4_08.tif
% AT3_1m4_09.tif AT3_1m4_10.tif
% autumn.tif bag.png
% blobs.png board.tif
% cameraman.tif canoe.tif
% cell.tif circbw.tif
% circles.png circuit.tif
% coins.png concordaerial.png
% concordorthophoto.png eight.tif
% fabric.png football.jpg
% forest.tif gantrycrane.png
% glass.png greens.jpg
% hestain.png kids.tif
% liftingbody.png logo.tif
% m83.tif mandi.tif
% moon.tif mri.tif
% office_1.jpg office_2.jpg
% onion.png paper1.tif
% pears.png peppers.png
% pillsetc.png pout.tif
% rice.png saturn.png
% shadow.tif snowflakes.png
% spine.tif tape.png
% testpat1.png text.png
% tire.tif tissue.png
% trees.tif westconcordaerial.png

03-Digital Image Fundamentals (5)as.pptx

Recomendados

Recomendados

Más contenido relacionado

Similar a 03-Digital Image Fundamentals (5)as.pptx

Similar a 03-Digital Image Fundamentals (5)as.pptx (20)

Último

Último (20)

03-Digital Image Fundamentals (5)as.pptx

Notas del editor