Fingerprint Matching UsingHough Transform and Latent Prints
ABSTRACTFingerprint is considered as the greater part robust
biometric in the intellect that it could even be obtained without
keen participation of the subjects. Fingerprints are single in the
sense of location and direction of minutiae points present. Latents
are partial fingerprints that are usually smudgy, with small area
and containing large distortion. Due to these characteristics,
latents have a significantly smaller number of minutiae points
compared to full (rolled or plain) fingerprints. The small number
of minutiae and the noise characteristic of latents make it
extremely difficult to automatically match latents to their mated
full prints that are stored in law enforcement databases. Further,
they often rely on features that are not easy to extract from poor
quality latents. In this paper, we propose a new fingerprint
matching algorithm which is especially designed for matching
latents. The proposed algorithm uses a robust alignment algorithm
(descriptor-based Hough transform) to align fingerprints and
measures similarity between fingerprints by considering both
minutiae and orientation field information.
1. INTRODUCTIONFingerprint is a widely used form of biometric
identification. It is a dynamic means of person identification.
Fingerprint recognition has forensic applications like Criminal
investigation, missing children etc., government applications like
social safety, border control, passport control, driving license
etc., and commercial applications like e-commerce, internet access,
ATM, credit card etc [1]. Because of their uniqueness and
reliability over the time, fingerprints have been used for
identification and verification over a century.There are
essentially three types of fingerprints in law enforcement
applications (see Fig. 1): Binarization using Rough set Theory ,(i)
rolled, which is obtained by rolling the finger nail-to-nail either
on a paper (in this case ink is first applied to the finger
surface) or the platen of a scanner; (ii) plain, which is obtained
by placing the finger flat on a paper or the platen of a scanner
without rolling; and (iii) latents, which are lifted from surfaces
of objects that are unconsciously touched or handled by a person
typically at crime scenes. Lifting of latents may involve a
complicated process, and it can range from simply photographing the
print to more complex dusting or chemical processing [2].A
fingerprint is believed to be unique to each person (and each
finger). Even the fingerprints of identical twins are different.
The pattern is quite stable trough out our lifetime, in case of a
cut, the same pattern will grow back. The features of a fingerprint
depend on the nerve growth in the skins surface. This growth is
determined by genetic factors and environmental factors such as
nutrients, oxygen levels and blood flow which are unique for every
individual. [19] Fingerprints are one of the most full-grown
biometric technologies and are used as proofs of evidence in courts
of law all over the world. Fingerprints are, therefore, used in
forensic divisions worldwide for criminal investigation.The
performance of matching techniques relies partly on the quality of
the input fingerprint. In practice, due to skin conditions, sensor
noise, incorrect finger pressure and bad quality fingers like from
elderly people and manual workers, a significant percentage of
fingerprint images is of poor quality. This makes it quite
difficult to compare fingerprints.
The central question that will be answered in this report,
is:
How are fingerprints compared to each other?
Based on this, the following questions can be set up: Which
steps are to be taken before the actual matching can take place?
Which techniques are there to match fingerprints and which one is
most used in practice? How this most does used matching technique
work?
In chapter 2 the whole process of fingerprint matching is
globally described. It contains five steps, all further explained
in the succeeding chapters. Chapter 3 contains the first step of
that process: preprocessing the image. A few enhancement techniques
are discussed. After that, there is a classification step,
described in chapter 4. In chapter 5 the actual matching is
explained. The method specified is minutiae-based matching, a
method that is well known and widely used. Finally the conclusions
are to find in chapter 6.Law enforcement agencies have started
using fingerprint recognition technology to identify suspects since
the early 20th century [2]. Nowadays, automated fingerprint
identificationsystem (AFIS) has become an indispensable tool for
law enforcement agencies.There are essentially three types of
fingerprints in law enforcement applications (see Fig. 1): (i)
rolled, which is obtained by rolling the finger nail-to-nail either
on a paper (in this case ink is first applied to the finger
surface) or the platen of a scanner; (ii) plain, which is obtained
by placing the finger flat on a paper or the platen of a scanner
without rolling; and(iii) latents, which are lifted from surfaces
of objects that are inadvertently touched or handled by a person
typically at crime scenes. Lifting of latents may involve a
complicated process, and it can range from simply photographing the
print to more complex dusting or chemical processing Rolled prints
contain the largest amount of information about the ridge structure
on a fingerprint since they capture the largest finger surface
area; latents usually contain the least amount of information for
matching or identification because of their size and inherent
noise. Compared to rolled or plain fingerprints, latents are smudgy
and blurred, capture only a small finger area, and have large
nonlinear distortion due to pressure variations.Due to their poor
quality and small area, latents have a significantly smaller number
of minutiae compared to rolled or plain prints (the average number
of minutiae in NIST Special Database 27 (NIST SD27) [3] images is
21 for latents versus 106 for their mated rolled prints). These
characteristics make the latent fingerprint matching problem very
challenging.Fingerprint examiners who perform manual latent
fingerprint identification follow a procedure referred to as ACE-V
(analysis, comparison, evaluation and verification) [4]. Because
the ACE-V procedure is quite tedious and time consuming for latent
examiners, latents are usually matched against full prints of a
small number of suspects identified by other means, such as eye
witness description or M.O. (mode of operation).With the
availability of AFIS, fingerprint examiners are able to match
latents against a large fingerprint database using a semiautomatic
procedure that consists of following stages: (i) manually mark the
features (minutiae and singular points) in the latent, (ii) launch
an AFIS search, and (iii) visually verify the top- ( is
typically50) candidate fingerprints returned by AFIS. The accuracy
and speed of this latent matching procedure is still not
satisfactory. It certainly does not meet the lights-out mode of
operationdesired by the FBI and included in the Next Generation
Identification.For fingerprint matching, there are two major
problems which need to be solved. The first is to align the two
fingerprints to be compared and the second is to compute a match
score between the two fingerprints. Alignment between a latent and
a rolled print is a challenging problem because latents often
contain a small number of minutiae and undergo large skin
distortion. To deal with these two problems, we propose the
descriptor-basedHough transform (DBHT), which is a combination of
the generalized Hough transform and a local minutiae descriptor,
called Minutia Cylinder Code (MCC) [6]. The MCC descriptor improves
the distinctiveness of minutiae while the Hough transform method
can accumulate evidence as well as improve the robustness against
distortion. Match score computation between a latent and a rolled
print is also challenging because the number Of mated minutiae is
usually small. To address this issue, we further consider
orientation field as a factor in computing match score. Since we
only have manually marked minutiae for latents, a reconstruction
algorithm is used to obtain orientation field from minutiae.
PREVIOUS METHODS:IMAGE BINARIZATIONThe problem of image
binarization has been widely studied in the field of Image
processing. Otsu (1979) [3] proposed an optimum global thresholding
method based on an idea of minimizing the between class variance.
Moayer and Fu (1986) [6] proposed a binarization technique based on
an iterative application of laplacian operator and a pair of
dynamic thresholds. During this phase the gray scale image is
transformed into a binary image by computing the global adaptive
thresholding. This thresholding approach gives a particular
threshold value for each image which we are consider for our
simulation and testing phase. In this way each pixel of the core
region is transferred to two different intensity levels as compared
to gray scale image of 256 intensity levels. So the processing of
binary image is easy.Figure 5 shows the binarized image of
corresponding original fingerprint image. The disadvantage of
binarization is that the ridges termination near the boundary is
considered as minutia even though it is not actual minutia. The
problem of binarization is eliminated in thinning process.A similar
method proposed by Xiao and Raafat (1991) [7] in which a local
threshold is used after the convolution step to deal with regions
with different contrast. Verma, Majumdar, and Chatterjee (1987) [8]
proposed a fuzzy approach that uses adaptive threshold to preserve
the same number of 1 and 0 valued pixels for each neighbourhood.
Ratha, Chen, and Jain (1995) [9] introduced a binarization approach
based on peak detection in the gray-level profiles along sections
orthogonal to the ridge orientation. Among all these approaches
Otsus thresholding has been widely used. The reason of its
popularity is that it works directly on gray scale histogram and
hence it is very fast method once histogram is computed. Otsus
thresholding works on the assumption that the image has only two
ranges of intensities i.e., the image histogram is mostly bi-modal
and selects the threshold in between two peaks. But it may not
always true as in case of fingerprint. Figure 5: A fingerprint
Image and its histogram (X-axis shows the image intensity values.
Y-axis shows the frequency).
Fingerprint Image Enhancement
Fingerprint Image enhancement is to make the image clearer for
easy further operations. Since the fingerprint images acquired from
sensors or other medias are not assured with perfect quality, those
enhancement methods, for increasing the contrast between ridges and
furrows and for connecting the false broken points of ridges due to
insufficient amount of ink,are very useful for keep a higher
accuracy to fingerprint recognition.
Histogram Equalization:
Histogram equalization is to expand the pixel value distribution
of an image so as toincrease the perceptional information. The
original histogram of a fingerprint image has thebimodal type the
histogram after the histogram equalization occupies all the range
from 0 to 255 and the visualization effect is enhanced.
Figure 6.1 The Original Histogram of a Figure 6.2 Histogram
after fingerprint image histogram equalization
Figure 6.3. Original Image Figure 6.4 Enhanced Image
afterHistogram Equalization
Fingerprint Image BinarizationFingerprint Image Binarization is
to transform the 8-bit Gray fingerprint image to a 1-bit image with
0-value for ridges and 1-value for furrows. After the operation,
ridges in thefingerprint are highlighted with black color while
furrows are white.A locally adaptive binarization method is
performed to binarize the fingerprint image.Such a named method
comes from the mechanism of transforming a pixel value to 1 if the
valueis larger than the mean intensity value of the current block
(16x16) to which the pixel belongs[Figure 6.1and Figure 6.2].
Figure 7.1 Enhanced Image Figure 7.2 Image after Adaptive
BinarizationTHINNING:It is the process of reducing the thickness of
each line of fingerprint patterns to a single pixel width.Here we
are considered templates of (3x3) windows for thinning and trimming
of unwanted pixels. In previous thinning process, the applied
algorithm takes the image as an object and processes its operation.
So that it maynt be possible to get the exact thinned image i.e.
the line image into single pixel strength. But in our process we
have considered each pixel as our object space and applied rules on
its pixel level and try to remove the singular pixel as well as the
unwanted pixels from fingerprint. These rules are purely
observational and we consider all possibility to eliminate the
unnecessary pixel from image and convert the image into single
pixel strength. This thinning process acts iteratively on
fingerprint. Exact thinning is ensured when the pixel level of the
ridge having only one pixel width. However, this is not always
true. There some locations, where the ridge has two-pixel width at
some erroneous pixels. An erroneous pixel is defined as the one
with more than two 4-connected neighbors. Hence, before minutiae
extraction, there is a need to develop an algorithm to eliminate
the erroneous pixels while preserving the pattern connectivity. For
this purpose an enhanced thinning algorithm is followed after
thinning process.Enhanced thinning algorithmStep 1: Scanning the
pattern of fingerprint image row wise from top to bottom. Check if
the pixel is 1.Step 2: Count its four connected neighbors.Step 3:
If the sum is greater that two, mark it as an erroneous pixel.Step
4: Remove the erroneous pixel.Step 5: Repeat steps 1 4 until whole
of the image is scanned and the erroneous pixels are removed.
FEATURE EXTRACTION:Minutia is characteristics of a fingerprint
which is used for identification purpose. These are the points in
the normal direction of the ridges such as ridge endings,
bifurcations, and short ridges. Many automatic recognition systems
only consider ridge endings and bifurcations as minutia. A reason
for this is that all other structure like bridge and island
structures are considered as false minutia. The advantage of using
this assumption that, it does not differentiate between these
minutiae. This is due to, when a real bifurcation is mistakenly
separated, or if an end point mistakenly joins a ridge, it forms a
bifurcation.Image Binarization based on Rough Set Before the
proposed rough set based binarization process is described, it
would be good for the readers to have some idea about the rough
set. For this purpose a short note on rough set is presented. Note
that detail of the rough set can be obtained from [4] Rough Set
Theory The concept of Rough-set Theory was given by Pawlak [4].
Rough-set theory has become a popular tool for generating logical
rules for classification and prediction. It is a mathematical tool
to deal with vagueness and uncertainty. The focus of the rough-set
theory is on the ambiguity of objects. A Rough-set is a set with
uncertainties in it i.e. some elements may or may not be the part
of the set. Rough-set theory uses approximation for these
rough-sets. A rough-set can be defined in terms of lower and upper
approximations.The uncertainties at object boundaries can be
handled by describing different objects as Rough-sets with lower
(inner) and upper (outer) approximations. Figure 4 shows the object
present along with its lower and upper approximation. Consider an
image as a collection of pixels. This collection can be partitioned
in to different blocks (granules) which are used to find out the
object and background regions. From the roughness of these regions
rough entropy is computed to obtain the threshold. The detail of
these concepts is now discussed. Figure 8: An example of object
Lower and Upper approximations and background lower and upper
approximations.
A. Granulation:
Granulation involves decomposition of whole into parts. In this
step image is divided into blocks of different sizes. These blocks
are termed as Granules. For this decomposition quad-tree
representation of the image is used. Quad-trees are most often used
to partition a two dimensional space by recursively subdividing it
into four quadrants or regions. Each region is subdivided on the
basis of some conditions. In this case following condition has been
used for the decomposition.For a block B if 90 % or more of pixels
are either greater than or less than some predefined threshold, the
block is not split. Let xi, i = 1, 2 n be pixel values belonging to
block B. The block B is not split if, 90% of xi T or xi T, where T
is a pre-specified threshold. The block B is otherwise split.
Figure 5 shows the quad-tree granules obtained from a fingerprint
image. The above condition is used because 90% of the pixels are of
same range implies the block as homogeneous otherwise the variation
in intensity values compelled to split the block unless only
homogeneous blocks are left. Figure 9: Fingerprint Image and
granules obtained by quad tree decomposition.
B. Object-Background Approximation Once the image is split in
granules, next task is to identify each granule as either object or
background. The image is divided into granules based on some
criteria (see Section A). Let G be the total number of granules
then problem is to classify each granule as either object or
background. At this point we also need to know the dynamic range of
the image. Let [0, L] be the dynamic range of the image. Our final
aim is to find a threshold T, 0TL-1, so that the image could be
binarized based on threshold T. Granules with pixel values less
than T characterize object while granules with values greater than
T characterize background. After getting this separation, object
and background can be approximated by two sets as follows. The
lower approximation of the object or background: For all blocks
belonging to object (background), the blocks having pixels with
same intensity values are called lower (inner) approximations of
object (background). The upper approximation of the object or
background: All blocks belonging to object (background) also belong
to upper approximation of the object (background). Once we have the
two above mentioned approximation, the roughness of each granule
needs to be computed.C. Roughness of Object and background
Roughness of object and background is computed as described in [5].
We are only defining the term here; the detail explanation can be
obtained from [5]. The roughness of object is Here | | and | | are
cardinality of object upper approximation and lower approximation
respectively. Similarly roughness of background can be defined as
Where, || and || are cardinality of Background upper approximation
and lower approximation respectively.Roughness is a measure of
uncertainty in object or background. It can be obtained as the
number of granules out of total number of granules that are
certainly not the members of the object or background. Thus the
value of the roughness depends on the threshold value (T) used to
obtained the lower and upper approximation (see Section B) of the
object or background. The rough entropy is now measured on the
basis of above two roughnesses.
D. Rough Entropy Measure A measure called Rough entropy based on
the concept of image granules is used as described in [5]. Rough
entropy is computed from object and background roughness as Here,
Ro is the object roughness and Rb is the background roughness.
Maximization of this Rough-entropy measure minimizes the
uncertainty i.e., roughness of object and background. The optimum
threshold is obtained as that maximizing the rough entropy.
E. Algorithm for binarization Images are then processed
stepwise, as described in Section A D, to get their binarized form.
Following are the steps for the binarization of image as proposed
in this article.
Represent the image in the form of quad-tree decomposition. For
a threshold value T, 0>) and where the output of those commands
is displayed. MATLAB defines the workspace as the set of variables
that the user creates in a work session. The workspace browser
shows these variables and some information about them. Double
clicking on a variable in the workspace browser launches the Array
Editor, which can be used to obtain information and income
instances edit certain properties of the variable. The current
Directory tab above the workspace tab shows the contents of the
current directory, whose path is shown in the current directory
window. For example, in the windows operating system the path might
be as follows: C:\MATLAB\Work, indicating that directory work is a
subdirectory of the main directory MATLAB; WHICH IS INSTALLED IN
DRIVE C. clicking on the arrow in the current directory window
shows a list of recently used paths. Clicking on the button to the
right of the window allows the user to change the current
directory. MATLAB uses a search path to find M-files and other
MATLAB related files, which are organize in directories in the
computer file system. Any file run in MATLAB must reside in the
current directory or in a directory that is on search path. By
default, the files supplied with MATLAB and math works toolboxes
are included in the search path. The easiest way to see which
directories are on the search path. The easiest way to see which
directories are soon the search path, or to add or modify a search
path, is to select set path from the File menu the desktop, and
then use the set path dialog box. It is good practice to add any
commonly used directories to the search path to avoid repeatedly
having the change the current directory. The Command History Window
contains a record of the commands a user has entered in the command
window, including both current and previous MATLAB sessions.
Previously entered MATLAB commands can be selected and re-executed
from the command history window by right clicking on a command or
sequence of commands. This action launches a menu from which to
select various options in addition to executing the commands. This
is useful to select various options in addition to executing the
commands. This is a useful feature when experimenting with various
commands in a work session.Using the MATLAB Editor to create
M-Files: The MATLAB editor is both a text editor specialized for
creating M-files and a graphical MATLAB debugger. The editor can
appear in a window by itself, or it can be a sub window in the
desktop. M-files are denoted by the extension .m, as in pixelup.m.
The MATLAB editor window has numerous pull-down menus for tasks
such as saving, viewing, and debugging files. Because it performs
some simple checks and also uses color to differentiate between
various elements of code, this text editor is recommended as the
tool of choice for writing and editing M-functions. To open the
editor , type edit at the prompt opens the M-file filename.m in an
editor window, ready for editing. As noted earlier, the file must
be in the current directory, or in a directory in the search
path.Getting Help: The principal way to get help online is to use
the MATLAB help browser, opened as a separate window either by
clicking on the question mark symbol (?) on the desktop toolbar, or
by typing help browser at the prompt in the command window. The
help Browser is a web browser integrated into the MATLAB desktop
that displays a Hypertext Markup Language(HTML) documents. The Help
Browser consists of two panes, the help navigator pane, used to
find information, and the display pane, used to view the
information. Self-explanatory tabs other than navigator pane are
used to perform a search.
DIGITAL IMAGE PROCESSING
Digital image processingBackground:Digital image processing is
an area characterized by the need for extensive experimental work
to establish the viability of proposed solutions to a given
problem. An important characteristic underlying the design of image
processing systems is the significant level of testing &
experimentation that normally is required before arriving at an
acceptable solution. This characteristic implies that the ability
to formulate approaches &quickly prototype candidate solutions
generally plays a major role in reducing the cost & time
required to arrive at a viable system implementation. What is DIP
An image may be defined as a two-dimensional function f(x, y),
where x & y are spatial coordinates, & 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 & the amplitude
values of f are all finite discrete quantities, we call the image a
digital image. The field of DIP refers to processing digital image
by means of digital computer. Digital image is composed of a finite
number of elements, each of which has a particular location &
value. The elements are called pixels.Vision is the most advanced
of our sensor, so it is not surprising that image play the single
most important role in human perception. However, unlike humans,
who are limited to the visual band of the EM spectrum imaging
machines cover almost the entire EM spectrum, ranging from gamma to
radio waves. They can operate also on images generated by sources
that humans are not accustomed to associating with image. There is
no general agreement among authors regarding where image processing
stops & other related areas such as image analysis&
computer vision start. Sometimes a distinction is made by defining
image processing as a discipline in which both the input &
output at a process are images. This is limiting & somewhat
artificial boundary. The area of image analysis (image
understanding) is in between image processing & computer
vision. There are no clear-cut boundaries in the continuum from
image processing at one end to complete vision at the other.
However, one useful paradigm is to consider three types of
computerized processes in this continuum: low-, mid-, &
high-level processes. Low-level process involves primitive
operations such as image processing to reduce noise, contrast
enhancement & image sharpening. A low- level process is
characterized by the fact that both its inputs & outputs are
images.
Mid-level process on images involves tasks such as segmentation,
description of that object to reduce them to a form suitable for
computer processing & classification of individual objects. A
mid-level process is characterized by the fact that its inputs
generally are images but its outputs are attributes extracted from
those images. Finally higher- level processing involves Making
sense of an ensemble of recognized objects, as in image analysis
& at the far end of the continuum performing the cognitive
functions normally associated with human vision.Digital image
processing, as already defined is used successfully in a broad
range of areas of exceptional social & economic value.What is
an image? An image is represented as a two dimensional function
f(x, y) where x and y are spatial co-ordinates and the amplitude of
f at any pair of coordinates (x, y) is called the intensity of the
image at that point. Gray scale image: A grayscale image is a
function I (xylem) of the two spatial coordinates of the image
plane.I(x, y) is the intensity of the image at the point (x, y) on
the image plane.I (xylem) takes non-negative values assume the
image is bounded by a rectangle [0, a] [0, b]I: [0, a] [0, b] [0,
info) Color image: It can be represented by three functions, R
(xylem) for red, G (xylem) for green and B (xylem) for blue. 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 to be
digitized. Digitizing the coordinates values is called sampling.
Digitizing the amplitude values is called quantization. Coordinate
convention: The result of sampling and quantization is a matrix of
real numbers. We use two principal ways to represent digital
images. Assume that an image f(x, y) is sampled so that the
resulting image has M rows and N columns. We say that the image is
of size M X N. The values of the coordinates (xylem) are discrete
quantities. For notational clarity and convenience, we use integer
values for these discrete coordinates. In many image processing
books, the image origin is defined to be at (xylem)=(0,0).The next
coordinate values along the first row of the image are
(xylem)=(0,1).It is important to keep in mind that the notation
(0,1) is used to signify the second sample along the first row. It
does not mean that these are the actual values of physical
coordinates when the image was sampled. Following figure shows the
coordinate convention. Note that x ranges from 0 to M-1 and y from
0 to N-1 in integer increments. The coordinate convention used in
the toolbox to denote arrays is different from the preceding
paragraph in two minor ways. First, instead of using (xylem) the
toolbox uses the notation (race) to indicate rows and columns.
Note, however, that the order of coordinates is the same as the
order discussed in the previous paragraph, in the sense that the
first element of a coordinate topples, (alb), refers to a row and
the second to a column. The other difference is that the origin of
the coordinate system is at (r, c) = (1, 1); thus, r ranges from 1
to M and c from 1 to N in integer increments. IPT documentation
refers to the coordinates. Less frequently the toolbox also employs
another coordinate convention called spatial coordinates which uses
x to refer to columns and y to refers to rows. This is the opposite
of our use of variables x and y. Image as Matrices:The preceding
discussion leads to the following representation for a digitized
image function: f (0,0) f(0,1) .. f(0,N-1) f (1,0) f(1,1) f(1,N-1)
f (xylem)= . . . . . . f (M-1,0) f(M-1,1) f(M-1,N-1)The right side
of this equation is a digital image by definition. Each element of
this array is called an image element, picture element, pixel or
pel. The terms image and pixel are used throughout the rest of our
discussions to denote a digital image and its elements.
A digital image can be represented naturally as a MATLAB matrix:
f (1,1) f(1,2) . f(1,N) f (2,1) f(2,2) .. f (2,N) . . . f = . . . f
(M,1) f(M,2) .f(M,N)Where f (1,1) = f(0,0) (note the use of a
monoscope font to denote MATLAB quantities). Clearly the two
representations are identical, except for the shift in origin. The
notation f(p ,q) denotes the element located in row p and the
column q. For example f(6,2) is the element in the sixth row and
second column of the matrix f. Typically we use the letters M and N
respectively to denote the number of rows and columns in a matrix.
A 1xN matrix is called a row vector whereas an Mx1 matrix is called
a column vector. A 1x1 matrix is a scalar. Matrices in MATLAB are
stored in variables with names such as A, a, RGB, real array and so
on. Variables must begin with a letter and contain only letters,
numerals and underscores. As noted in the previous paragraph, all
MATLAB quantities are written using mono-scope characters. We use
conventional Roman, italic notation such as f(x ,y), for
mathematical expressions
Reading Images: Images are read into the MATLAB environment
using function imread whose syntax is Imread (filename) Format name
Description recognized extension TIFF Tagged Image File Format
.tif, .tiff JPEG Joint Photograph Experts Group .jpg, .jpeg GIF
Graphics Interchange Format .gif BMP Windows Bitmap .bmp
PNG Portable Network Graphics .png XWD X Window Dump .xwd Here
filename is a spring containing the complete of the image
file(including any applicable extension).For example the command
line >> f = imread (8. jpg);Reads the JPEG (above table)
image chestxray into image array f. Note the use of single quotes
() to delimit the string filename. The semicolon at the end of a
command line is used by MATLAB for suppressing output If a
semicolon is not included. MATLAB displays the results of the
operation(s) specified in that line. The prompt symbol (>>)
designates the beginning of a command line, as it appears in the
MATLAB command window. Data Classes: Although we work with integers
coordinates the values of pixels themselves are not restricted to
be integers in MATLAB. Table above list various data classes
supported by MATLAB and IPT are representing pixels values. The
first eight entries in the table are refers to as numeric data
classes. The ninth entry is the char class and, as shown, the last
entry is referred to as logical data class. All numeric
computations in MATLAB are done in double quantities, so this is
also a frequent data class encounter in image processing
applications. Class unit 8 also is encountered frequently,
especially when reading data from storages devices, as 8 bit images
are most common representations found in practice. These two data
classes, classes logical, and, to a lesser degree, class unit 16
constitute the primary data classes on which we focus. Many ipt
functions however support all the data classes listed in table.
Data class double requires 8 bytes to represent a number uint8 and
int 8 require one byte each, uint16 and int16 requires 2bytes and
unit 32. Name Description Double Double _ precision, floating_
point numbers the Approximate. Uint8 unsigned 8_bit integers in the
range [0,255] (1byte per Element). Uint16 unsigned 16_bit integers
in the range [0, 65535] (2byte per element). Uint 32 unsigned
32_bit integers in the range [0, 4294967295](4 bytes per element).
Int8 signed 8_bit integers in the range [-128,127] 1 byte per
element) Int 16 signed 16_byte integers in the range [32768, 32767]
(2 bytes per element). Int 32 Signed 32_byte integers in the range
[-2147483648, 21474833647] (4 byte per element). Single single
_precision floating _point numbers with values In the approximate
range (4 bytes per elements) Char characters (2 bytes per
elements). Logical values are 0 to 1 (1byte per element).Int 32 and
single required 4 bytes each. The char data class holds characters
in Unicode representation. A character string is merely a 1*n array
of characters logical array contains only the values 0 to 1,with
each element being stored in memory using function logical or by
using relational operators. Image Types:The toolbox supports four
types of images:1 .Intensity images;2. Binary images;3. Indexed
images;4. R G B images. Most monochrome image processing operations
are carried out using binary or intensity images, so our initial
focus is on these two image types. Indexed and RGB colour
images.Intensity Images:An intensity image is a data matrix whose
values have been scaled to represent intentions. When the elements
of an intensity image are of class unit8, or class unit 16, they
have integer values in the range [0,255] and [0, 65535],
respectively. If the image is of class double, the values are
floating point numbers. Values of scaled, double intensity images
are in the range [0, 1] by convention.
Binary Images:Binary images have a very specific meaning in
MATLAB.A binary image is a logical array 0s and1s.Thus, an array of
0s and 1s whose values are of data class, say unit8, is not
considered as a binary image in MATLAB .A numeric array is
converted to binary using function logical. Thus, if A is a numeric
array consisting of 0s and 1s, we create an array B using the
statement. B=logical (A)If A contains elements other than 0s and
1s.Use of the logical function converts all nonzero quantities to
logical 1s and all entries with value 0 to logical 0s.Using
relational and logical operators also creates logical arrays.To
test if an array is logical we use the I logical function:
islogical(c).If c is a logical array, this function returns a
1.Otherwise returns a 0. Logical array can be converted to numeric
arrays using the data class conversion functions.
Indexed Images:An indexed image has two components:A data matrix
integer, xA color map matrix, map Matrix map is an m*3 arrays of
class double containing floating point values in the range [0,
1].The length m of the map are equal to the number of colors it
defines. Each row of map specifies the red, green and blue
components of a single color. An indexed images uses direct mapping
of pixel intensity values color map values. The color of each pixel
is determined by using the corresponding value the integer matrix x
as a pointer in to map. If x is of class double ,then all of its
components with values less than or equal to 1 point to the first
row in map, all components with value 2 point to the second row and
so on. If x is of class units or unit 16, then all components value
0 point to the first row in map, all components with value 1 point
to the second and so on.
RGB Image: An RGB color image is an M*N*3 array of color pixels
where each color pixel is triplet corresponding to the red, green
and blue components of an RGB image, at a specific spatial
location. An RGB image may be viewed as stack of three gray scale
images that when fed in to the red, green and blue inputs of a
color monitorProduce a color image on the screen. Convention the
three images forming an RGB color image are referred to as the red,
green and blue components images. The data class of the components
images determines their range of values. If an RGB image is of
class double the range of values is [0, 1].Similarly the range of
values is [0,255] or [0, 65535].For RGB images of class units or
unit 16 respectively. The number of bits use to represents the
pixel values of the component images determines the bit depth of an
RGB image. For example, if each component image is an 8bit image,
the corresponding RGB image is said to be 24 bits deep. Generally,
the number of bits in all component images is the same. In this
case the number of possible color in an RGB image is (2^b) ^3,
where b is a number of bits in each component image. For the 8bit
case the number is 16,777,216 colors.
CHAPTER 8CONCLUSION
Conclusion This article has introduced a roughest based
binarization for fingerprint images. The rough set based method
avoids assumption that images are mostly bimodal whereas the same
assumption is the basis for widely used binarization technique such
as Otsus binarization method. The results obtained appear to be
equivalent, if not better than the existing Otsus technique.
Ideally the method can be compared with the other fuzzy based
approaches [15] [16], frequency based approaches [17], but it has
not been included here as Otsus method for binarization is
considered as widely used method. One limitation of the proposed
method is that it may not lead to a good binarization in case the
fingerprint image quality is very poor in the sense of over inking
or under inking. A good noise cleaning algorithm should then be
preceded by the process of binarization. Note that the same is true
even if one uses Otsus method. The method proposed for binarization
could be extended to classify the image pixels in more than two
classes as oppose to binarization which is classifying the image
pixels in to two classes. Table 1: Threshold values obtained from
rough-set based method and Otsus method for natural and fingerprint
images.
REFERENCES[1] M. Davide, M Dario, A. K. Jain, P. Salil, Handbook
of Fingerprint Recognition, 2nd Ed. Springer,2005. [2] Gonzalez C.
R., Woods E. R., Digital Image Processing, 3rd Ed., Pearson, 2008.
[3] Otsu Nobuyuki, A Threshold selection method from gray-level
histogram, in proceedings IEEE Transactions on systems, man, and
cybernetics, vol-9, no. 1, pp. 62-66, Jan 1979. [4] Pawlak Z.,
Grzymala B. Jerzy, slowinsky R., Ziarko W, Rough sets, in
proceedings communications of the ACM, vol. 38, no.11, pp. 89-95,
Nov, 1995. [5] Pal S. K, B. Uma, Mitra P., Granular computing,
rough entropy and object extraction, in proceedings Pattern
Recognition Letters, vol. 26, pp. 2509-2517, 2005. [6] Moayer B.,
Fu K., A tree system approach for fingerprint pattern recognition,
in proceedings IEEE Transaction on Pattern Analysis Machine
Intelligence, vol. 8, no. 3, pp. 376-388, 1986. [7] Xiao Q. Raafat
H., Fingerprint image post- processing: A combined statistical and
structural approach, in proceedings Pattern Recognition, vol. 24,
no. 10, pp. 985-992, 1991b. [8] Verma M.R., Majumdar A.K. and
Chatterjee B., Edge detection in fingerprints, in proceedings,
Pattern Recognition, vol. 20, pp. 513-523, 1987. [9] Ratha N.K.,
Chen S.Y., Jain A.K., Adaptive flow orientation-based feature
extraction in fingerprint images, in proceedings, Pattern
Recognition, vol. 28, no. 11, pp. 1657-1672, 1995. [10] Yager N.,
Amin A., Fingerprint verification based on minutiae features: a
review, in proceedings, pattern analysis Applications, vol. 7, pp.
94-113, Nov, 2004. [11] Zhao F., Tang X., Preprocessing for
Skeleton- based Minutiae Extraction, in Conference on Imaging
Science, Systems, and Technology02, pp. 742-745, 2007. [12] Zhang
T.Y, Suen C.Y, A Fast Parallel Algorithm for Thinning Digital
Patterns, in proceedings Communications of the ACM, Vol. 27, No 3,
pp. 236-239, March 1984. [13] Rutovitz D, Pattern recognition, in
proceedings of journal in Royal Statistical Society, vol. 129, ser.
A, pp. 504-530, May 1966. [14] Hwang H., Shin J., Chien S., Lee J.,
Run Representation based Minutiae Extraction in Fingerprint Image,
in proceedings International Association for Pattern Recognition
workshop on Machine Vision Applications, pp. 64-67, Dec 2002.
[15] T.C. Raja Kumar, S. Arumuga Perumal, N. Krishnan, and S.
Kother Mohideen , Fuzzy based Histogram Modeling for Fingerprint
Image Binarization, in proceedings of International Journal of
Research and Reviews in Computer Science, Vol 2, No5, pp.
1151-1154; Science Academy Publisher, United Kingdom October 2011
[16] Y. H. Yun, A study on fuzzy binarization method, Korea
Intelligent Information Systems Society, vol. 1, No. 1, pp.
510-513, 2002 [17] Taekyung Kim, Taekyung Kim, Soft Decision
Histogram-Based Image Binarization for Enhanced ID Recognition, in
proceedings Information Communication and Signal processing,
pp.1-4, Dec 2007
INTRODUCTION TO MATLAB What Is MATLAB? MATLAB is a
high-performance language for technical computing. It integrates
computation, visualization, and programming in an easy-to-use
environment where problems and solutions are expressed in familiar
mathematical notation. Typical uses includeMath and computation
Algorithm development Data acquisition Modeling, simulation, and
prototyping Data analysis, exploration, and visualization
Scientific and engineering graphics Application development,
including graphical user interface building. MATLAB is an
interactive system whose basic data element is an array that does
not require dimensioning. This allows you to solve many technical
computing problems, especially those with matrix and vector
formulations, in a fraction of the time it would take to write a
program in a scalar non interactive language such as C or FORTRAN.
The name MATLAB stands for matrix laboratory. MATLAB was originally
written to provide easy access to matrix software developed by the
LINPACK and EISPACK projects. Today, MATLAB engines incorporate the
LAPACK and BLAS libraries, embedding the state of the art in
software for matrix computation. MATLAB has evolved over a period
of years with input from many users. In university environments, it
is the standard instructional tool for introductory and advanced
courses in mathematics, engineering, and science. In industry,
MATLAB is the tool of choice for high-productivity research,
development, and analysis. MATLAB features a family of add-on
application-specific solutions called toolboxes. Very important to
most users of MATLAB, toolboxes allow you to learn and apply
specialized technology. Toolboxes are comprehensive collections of
MATLAB functions (M-files) that extend the MATLAB environment to
solve particular classes of problems. Areas in which toolboxes are
available include signal processing, control systems, neural
networks, fuzzy logic, wavelets, simulation, and many others.The
MATLAB System:The MATLAB system consists of five main
parts:Development Environment: This is the set of tools and
facilities that help you use MATLAB functions and files. Many of
these tools are graphical user interfaces. It includes the MATLAB
desktop and Command Window, a command history, an editor and
debugger, and browsers for viewing help, the workspace, files, and
the search path.The MATLAB Mathematical Function: This is a vast
collection of computational algorithms ranging from elementary
functions like sum, sine, cosine, and complex arithmetic, to more
sophisticated functions like matrix inverse, matrix eigen values,
Bessel functions, and fast Fourier transforms. The MATLAB Language:
This is a high-level matrix/array language with control flow
statements, functions, data structures, input/output, and
object-oriented programming features. It allows both "programming
in the small" to rapidly create quick and dirty throw-away
programs, and "programming in the large" to create complete large
and complex application programs. Graphics: MATLAB has extensive
facilities for displaying vectors and matrices as graphs, as well
as annotating and printing these graphs. It includes high-level
functions for two-dimensional and three-dimensional data
visualization, image processing, animation, and presentation
graphics. It also includes low-level functions that allow you to
fully customize the appearance of graphics as well as to build
complete graphical user interfaces on your MATLAB applications.The
MATLAB Application Program Interface (API): This is a library that
allows you to write C and Fortran programs that interact with
MATLAB. It includes facilities for calling routines from MATLAB
(dynamic linking), calling MATLAB as a computational engine, and
for reading and writing MAT-files.MATLAB WORKING ENVIRONMENT:
MATLAB DESKTOP:- Matlab Desktop is the main Matlab application
window. The desktop contains five sub windows, the command window,
the workspace browser, the current directory window, the command
history window, and one or more figure windows, which are shown
only when the user displays a graphic. The command window is where
the user types MATLAB commands and expressions at the prompt
(>>) and where the output of those commands is displayed.
MATLAB defines the workspace as the set of variables that the user
creates in a work session. The workspace browser shows these
variables and some information about them. Double clicking on a
variable in the workspace browser launches the Array Editor, which
can be used to obtain information and income instances edit certain
properties of the variable. The current Directory tab above the
workspace tab shows the contents of the current directory, whose
path is shown in the current directory window. For example, in the
windows operating system the path might be as follows:
C:\MATLAB\Work, indicating that directory work is a subdirectory of
the main directory MATLAB; WHICH IS INSTALLED IN DRIVE C. clicking
on the arrow in the current directory window shows a list of
recently used paths. Clicking on the button to the right of the
window allows the user to change the current directory. MATLAB uses
a search path to find M-files and other MATLAB related files, which
are organize in directories in the computer file system. Any file
run in MATLAB must reside in the current directory or in a
directory that is on search path. By default, the files supplied
with MATLAB and math works toolboxes are included in the search
path. The easiest way to see which directories are on the search
path. The easiest way to see which directories are soon the search
path, or to add or modify a search path, is to select set path from
the File menu the desktop, and then use the set path dialog box. It
is good practice to add any commonly used directories to the search
path to avoid repeatedly having the change the current directory.
The Command History Window contains a record of the commands a user
has entered in the command window, including both current and
previous MATLAB sessions. Previously entered MATLAB commands can be
selected and re-executed from the command history window by right
clicking on a command or sequence of commands. This action launches
a menu from which to select various options in addition to
executing the commands. This is useful to select various options in
addition to executing the commands. This is a useful feature when
experimenting with various commands in a work session.Using the
MATLAB Editor to create M-Files: The MATLAB editor is both a text
editor specialized for creating M-files and a graphical MATLAB
debugger. The editor can appear in a window by itself, or it can be
a sub window in the desktop. M-files are denoted by the extension
.m, as in pixelup.m. The MATLAB editor window has numerous
pull-down menus for tasks such as saving, viewing, and debugging
files. Because it performs some simple checks and also uses color
to differentiate between various elements of code, this text editor
is recommended as the tool of choice for writing and editing
M-functions. To open the editor , type edit at the prompt opens the
M-file filename.m in an editor window, ready for editing. As noted
earlier, the file must be in the current directory, or in a
directory in the search path.Getting Help: The principal way to get
help online is to use the MATLAB help browser, opened as a separate
window either by clicking on the question mark symbol (?) on the
desktop toolbar, or by typing help browser at the prompt in the
command window. The help Browser is a web browser integrated into
the MATLAB desktop that displays a Hypertext Markup Language(HTML)
documents. The Help Browser consists of two panes, the help
navigator pane, used to find information, and the display pane,
used to view the information. Self-explanatory tabs other than
navigator pane are used to perform a search.
DIGITAL IMAGE PROCESSING
BACKGROUND:Digital image processing is an area characterized by
the need for extensive experimental work to establish the viability
of proposed solutions to a given problem. An important
characteristic underlying the design of image processing systems is
the significant level of testing & experimentation that
normally is required before arriving at an acceptable solution.
This characteristic implies that the ability to formulate
approaches &quickly prototype candidate solutions generally
plays a major role in reducing the cost & time required to
arrive at a viable system implementation. What is DIP An image may
be defined as a two-dimensional function f(x, y), where x & y
are spatial coordinates, & 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 & the amplitude values of f are
all finite discrete quantities, we call the image a digital image.
The field of DIP refers to processing digital image by means of
digital computer. Digital image is composed of a finite number of
elements, each of which has a particular location & value. The
elements are called pixels.Vision is the most advanced of our
sensor, so it is not surprising that image play the single most
important role in human perception. However, unlike humans, who are
limited to the visual band of the EM spectrum imaging machines
cover almost the entire EM spectrum, ranging from gamma to radio
waves. They can operate also on images generated by sources that
humans are not accustomed to associating with image. There is no
general agreement among authors regarding where image processing
stops & other related areas such as image analysis&
computer vision start. Sometimes a distinction is made by defining
image processing as a discipline in which both the input &
output at a process are images. This is limiting & somewhat
artificial boundary. The area of image analysis (image
understanding) is in between image processing & computer
vision. There are no clear-cut boundaries in the continuum from
image processing at one end to complete vision at the other.
However, one useful paradigm is to consider three types of
computerized processes in this continuum: low-, mid-, &
high-level processes. Low-level process involves primitive
operations such as image processing to reduce noise, contrast
enhancement & image sharpening. A low- level process is
characterized by the fact that both its inputs & outputs are
images. Mid-level process on images involves tasks such as
segmentation, description of that object to reduce them to a form
suitable for computer processing & classification of individual
objects. A mid-level process is characterized by the fact that its
inputs generally are images but its outputs are attributes
extracted from those images. Finally higher- level processing
involves Making sense of an ensemble of recognized objects, as in
image analysis & at the far end of the continuum performing the
cognitive functions normally associated with human vision.Digital
image processing, as already defined is used successfully in a
broad range of areas of exceptional social & economic
value.What is an image? An image is represented as a two
dimensional function f(x, y) where x and y are spatial co-ordinates
and the amplitude of f at any pair of coordinates (x, y) is called
the intensity of the image at that point. Gray scale image: A
grayscale image is a function I (xylem) of the two spatial
coordinates of the image plane.I(x, y) is the intensity of the
image at the point (x, y) on the image plane.I (xylem) takes
non-negative values assume the image is bounded by a rectangle [0,
a] [0, b]I: [0, a] [0, b] [0, info) Color image: It can be
represented by three functions, R (xylem) for red, G (xylem) for
green and B (xylem) for blue. 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 to be digitized. Digitizing
the coordinates values is called sampling. Digitizing the amplitude
values is called quantization. Coordinate convention: The result of
sampling and quantization is a matrix of real numbers. We use two
principal ways to represent digital images. Assume that an image
f(x, y) is sampled so that the resulting image has M rows and N
columns. We say that the image is of size M X N. The values of the
coordinates (xylem) are discrete quantities. For notational clarity
and convenience, we use integer values for these discrete
coordinates. In many image processing books, the image origin is
defined to be at (xylem)=(0,0).The next coordinate values along the
first row of the image are (xylem)=(0,1).It is important to keep in
mind that the notation (0,1) is used to signify the second sample
along the first row. It does not mean that these are the actual
values of physical coordinates when the image was sampled.
Following figure shows the coordinate convention. Note that x
ranges from 0 to M-1 and y from 0 to N-1 in integer increments. The
coordinate convention used in the toolbox to denote arrays is
different from the preceding paragraph in two minor ways. First,
instead of using (xylem) the toolbox uses the notation (race) to
indicate rows and columns. Note, however, that the order of
coordinates is the same as the order discussed in the previous
paragraph, in the sense that the first element of a coordinate
topples, (alb), refers to a row and the second to a column. The
other difference is that the origin of the coordinate system is at
(r, c) = (1, 1); thus, r ranges from 1 to M and c from 1 to N in
integer increments. IPT documentation refers to the coordinates.
Less frequently the toolbox also employs another coordinate
convention called spatial coordinates which uses x to refer to
columns and y to refers to rows. This is the opposite of our use of
variables x and y. Image as Matrices:The preceding discussion leads
to the following representation for a digitized image function: f
(0,0) f(0,1) .. f(0,N-1) f (1,0) f(1,1) f(1,N-1) f (xylem)= . . . .
. . f (M-1,0) f(M-1,1) f(M-1,N-1)The right side of this equation is
a digital image by definition. Each element of this array is called
an image element, picture element, pixel or pel. The terms image
and pixel are used throughout the rest of our discussions to denote
a digital image and its elements. A digital image can be
represented naturally as a MATLAB matrix: f (1,1) f(1,2) . f(1,N) f
(2,1) f(2,2) .. f (2,N) . . . f = . . . f (M,1) f(M,2) .f(M,N)Where
f (1,1) = f(0,0) (note the use of a monoscope font to denote MATLAB
quantities). Clearly the two representations are identical, except
for the shift in origin. The notation f(p ,q) denotes the element
located in row p and the column q. For example f(6,2) is the
element in the sixth row and second column of the matrix f.
Typically we use the letters M and N respectively to denote the
number of rows and columns in a matrix. A 1xN matrix is called a
row vector whereas an Mx1 matrix is called a column vector. A 1x1
matrix is a scalar. Matrices in MATLAB are stored in variables with
names such as A, a, RGB, real array and so on. Variables must begin
with a letter and contain only letters, numerals and underscores.
As noted in the previous paragraph, all MATLAB quantities are
written using mono-scope characters. We use conventional Roman,
italic notation such as f(x ,y), for mathematical expressions
Reading Images: Images are read into the MATLAB environment
using function imread whose syntax is Imread (filename) Format name
Description recognized extension TIFF Tagged Image File Format
.tif, .tiff JPEG Joint Photograph Experts Group .jpg, .jpeg GIF
Graphics Interchange Format .gif BMP Windows Bitmap .bmp PNG
Portable Network Graphics .png XWD X Window Dump .xwd Here filename
is a spring containing the complete of the image file(including any
applicable extension).For example the command line >> f =
imread (8. jpg);Reads the JPEG (above table) image chestxray into
image array f. Note the use of single quotes () to delimit the
string filename. The semicolon at the end of a command line is used
by MATLAB for suppressing output If a semicolon is not included.
MATLAB displays the results of the operation(s) specified in that
line. The prompt symbol (>>) designates the beginning of a
command line, as it appears in the MATLAB command window. Data
Classes: Although we work with integers coordinates the values of
pixels themselves are not restricted to be integers in MATLAB.
Table above list various data classes supported by MATLAB and IPT
are representing pixels values. The first eight entries in the
table are refers to as numeric data classes. The ninth entry is the
char class and, as shown, the last entry is referred to as logical
data class. All numeric computations in MATLAB are done in double
quantities, so this is also a frequent data class encounter in
image processing applications. Class unit 8 also is encountered
frequently, especially when reading data from storages devices, as
8 bit images are most common representations found in practice.
These two data classes, classes logical, and, to a lesser degree,
class unit 16 constitute the primary data classes on which we
focus. Many ipt functions however support all the data classes
listed in table. Data class double requires 8 bytes to represent a
number uint8 and int 8 require one byte each, uint16 and int16
requires 2bytes and unit 32.Name Description Double Double _
precision, floating_ point numbers the Approximate. Uint8 unsigned
8_bit integers in the range [0,255] (1byte per Element). Uint16
unsigned 16_bit integers in the range [0, 65535] (2byte per
element).Uint 32 unsigned 32_bit integers in the range [0,
4294967295](4 bytes per element). Int8 signed 8_bit integers in the
range [-128,127] 1 byte per element) Int 16 signed 16_byte integers
in the range [32768, 32767] (2 bytes per element). Int 32 Signed
32_byte integers in the range [-2147483648, 21474833647] (4 byte
per element).Single single _precision floating _point numbers with
values In the approximate range (4 bytes per elements)Char
characters (2 bytes per elements).Logical values are 0 to 1 (1byte
per element).Int 32 and single required 4 bytes each. The char data
class holds characters in Unicode representation. A character
string is merely a 1*n array of characters logical array contains
only the values 0 to 1,with each element being stored in memory
using function logical or by using relational operators. Image
Types:The toolbox supports four types of images:1 .Intensity
images;2. Binary images;3. Indexed images;4. R G B images. Most
monochrome image processing operations are carried out using binary
or intensity images, so our initial focus is on these two image
types. Indexed and RGB colour images.Intensity Images:An intensity
image is a data matrix whose values have been scaled to represent
intentions. When the elements of an intensity image are of class
unit8, or class unit 16, they have integer values in the range
[0,255] and [0, 65535], respectively. If the image is of class
double, the values are floating point numbers. Values of scaled,
double intensity images are in the range [0, 1] by convention.
Binary Images:Binary images have a very specific meaning in
MATLAB.A binary image is a logical array 0s and1s.Thus, an array of
0s and 1s whose values are of data class, say unit8, is not
considered as a binary image in MATLAB .A numeric array is
converted to binary using function logical. Thus, if A is a numeric
array consisting of 0s and 1s, we create an array B using the
statement. B=logical (A)If A contains elements other than 0s and
1s.Use of the logical function converts all nonzero quantities to
logical 1s and all entries with value 0 to logical 0s.Using
relational and logical operators also creates logical arrays.To
test if an array is logical we use the I logical function:
islogical(c).If c is a logical array, this function returns a
1.Otherwise returns a 0. Logical array can be converted to numeric
arrays using the data class conversion functions.
Indexed Images:An indexed image has two components:A data matrix
integer, xA color map matrix, map Matrix map is an m*3 arrays of
class double containing floating point values in the range [0,
1].The length m of the map are equal to the number of colors it
defines. Each row of map specifies the red, green and blue
components of a single color. An indexed images uses direct mapping
of pixel intensity values color map values. The color of each pixel
is determined by using the corresponding value the integer matrix x
as a pointer in to map. If x is of class double ,then all of its
components with values less than or equal to 1 point to the first
row in map, all components with value 2 point to the second row and
so on. If x is of class units or unit 16, then all components value
0 point to the first row in map, all components with value 1 point
to the second and so on. RGB Image: An RGB color image is an M*N*3
array of color pixels where each color pixel is triplet
corresponding to the red, green and blue components of an RGB
image, at a specific spatial location. An RGB image may be viewed
as stack of three gray scale images that when fed in to the red,
green and blue inputs of a color monitorProduce a color image on
the screen. Convention the three images forming an RGB color image
are referred to as the red, green and blue components images. The
data class of the components images determines their range of
values. If an RGB image is of class double the range of values is
[0, 1].Similarly the range of values is [0,255] or [0, 65535].For
RGB images of class units or unit 16 respectively. The number of
bits use to represents the pixel values of the component images
determines the bit depth of an RGB image. For example, if each
component image is an 8bit image, the corresponding RGB image is
said to be 24 bits deep. Generally, the number of bits in all
component images is the same. In this case the number of possible
color in an RGB image is (2^b) ^3, where b is a number of bits in
each component image. For the 8bit case the number is 16,777,216
colors.
