mango grading based on size using image processing

8/12/2019 Mango Grading Based on Size Using Image Processing

http://slidepdf.com/reader/full/mango-grading-based-on-size-using-image-processing 1/40

1. Central Electronics Engineering Research Institute (CEERI)

Central Electronics Engineering Research Institute (CEERI) is a

part of the Council of Scientific and Industrial Research (CSIR) and is committed to

research and developments in electronics to meet the requirements of its customers.

CEERI has been continually identifying the thrust areas of key National/Industrial

relevance and has been developing competitive technologies with a goal to achieve

excellence and self-reliance in these areas.

CEERI Centre Chennai, a pioneering Institute in the field of

Quality Control Instrumentation for process industries, is a regional Centre of Central

Electronics Engineering Research Institute (CEERI), Pilani Rajasthan. The center has

a rich experience and expertise in this field and has developed many online

monitoring systems for various process industries like pulp and paper, plastics, food

processing, leather, etc.,

CEERI concentrates on indigenous development of special

sensors and systems suited to the online measurement and control and these involve

varying technologies such as near infrared gauging, beta gauging, optical,electromechanical methods and the currently emerging image processing techniques.

Presently the center has been extensively contributing its expertise for fruit sorting.

1



2. INTRODUCTION

IMAGE PROCESSING is one of the most stimulating research

areas under both the scientific and technology perspective in the present millennium.

Many research organizations have started involving themselves in some aspect of

image processing and recently emphasis has been laid on making it real–time. Our

project is a part of effort by CEERI,Chennai to develop fruit-sorting and grading

system.

In India, manual inspection techniques are widely used for sorting

foodstuffs. The bruises are detected in India by looking for discolored tissues or dents

in the check. In order to check for internal defects, fruits from each batch are

randomly chosen and cut open. These methods are not reliable and could lead to large

losses.

Machine vision techniques, which when used in conjunction with

manual inspection would guarantee international food quality and there by help in

improving Indian economy through export.

Most of the time the importer provides the specifications, normally

for machine sorted and packed products. Due to this Indian exporters find it very

difficult to make the employees involved in manual sorting understand the exact

requirements. Further, in manual sorting, it is impossible to maintain uniform sorting

as each person involved in the sorting will not take identical decisions if the sorting is

based on color, shape and size etc.

With all these things in mind, the government of our country is

putting more emphasis on value added agriculture product exports.

2.1 SCOPE OF THE PROJECT

The principle steps in the project include reading the image ,

converting the image into a binary image and extracting the feature such as major and

minor axes of the mango.

These steps are done using Image Processing Toolbox in Matlab,

where in the functions for reading, processing, writing, analyzing, etc., are already

present. Our project mainly aims to find the minor axis of the mango, which is the

measure for the size of the mango.

2



3. IMAGE PROCESSING

3.1 INTRODUCTION

Digital Image Processing refers to processing the digital images by means of digital

images. Digital Image Processing can be divided into three types of processes:

Low Level Processes

Medium Level Processes

High Level Processes

Low Level Processes These involve primitive processes such as image processing to

reduce the noise, contrast enhancement, and image sharpening. Low-level processes

are characterized by the fact that both inputs and outputs are images.

Medium Level Processes These involve task such as segmentation (portioning of

image into regions or objects) and classification of these objects. Mid-level processes

are characterized by the fact that inputs generally are images, but outputs are the

attributes of these images.

High Level Processes These involve ‘making sense’ of an ensemble of recognizedobjects, as in image analyses and at the far end performing the functions relates to

human vision.

3.2 IMAGE REPRESENTATION

An image may be defined as a two-dimensional function, f(x, y),

where x and y are spatial (plane) coordinates, and 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 amplitude 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.

3



PIXEL

A digital image is composed of a finite number of elements, each of which has a

particular location and value. These elements are referred to as picture elements,

image elements, pels, and pixels.

3.2.1 FUNDAMENTAL STEPS IN DIGITAL IMAGE PROCESSING

All the methodologies that can be applied to images for different purposes and

possibly with different objectives are as follows:

Image acquisition Compression

Image enhancement Morphological processing

Image restoration Segmentation

Color image processing Representation & description

Wavelets and multiresolution

processing

Object recognition

Image Acquisition: This stage involves preprocessing, such as scaling. This can be as

simple as being given an digital image.

Image Enhancement: The idea is to bring out detail that is obscured, or simply to

highlight certain features of interest in an image. It is based on human subjective

preferences regarding what constitutes a “good” enhancement result.

Image Restoration: This deals with improving the appearance of an image.

However, unlike enhancement, which is subjective, image restoration is objective, in

the sense that restoration techniques tend to be based on mathematical or probabilistic

models of image degradation.

Color Image Processing: Color is used as the basis for extracting features of interest

in an image. It has been gaining in importance because of the significant increase in

the use of digital images over the Internet.

4



Wavelets: These are the foundation for representing images in various degrees of

resolution.

Compression: It deals with techniques for reducing the storage required to save an

image, or the bandwidth required to transmit it. Although storage technology has

improved significantly over the past decade, the same cannot be said for transmission

capacity.

Morphological processing: It deals with tools for extracting image components that

are useful in the representation and description of shape .

Segmentation: This procedures partition an image into its constituent parts or objects.

In general, autonomous segmentation is one of the most difficult tasks in digital image

processing. A rugged segmentation procedure brings the process a long way toward

successful solution of imaging problems that require objects to be identified

individually. On the other hand, weak or erratic segmentation algorithms almost

always guarantee eventual failure. In general, the more accurate the segmentation, the

more likely recognition is to succeed .

Representation and description : This almost always follow the output of a

segmentation stage, which usually is raw pixel data, constituting either the boundary

of a region (i.e., the set of pixels separating one image region from another) or all the

points in the region itself. Description, also called feature selection, deals with

extracting attributes that result in some quantitative information of interest or are

basic for differentiating one class of objects from another.

Recognition: This is the process that assigns a label (e.g., “vehicle”) to an object

based on its descriptors.

3.2.2 REPRESENTATION OF DIGITAL IMAGE

If an image f(x, y) is sampled so that the resulting digital image has

M rows and N columns. The values of the coordinates (x, y) now become discrete

quantities. Integer values are used to represent these discrete coordinates. Thus, the

values of the coordinates at the origin are (x, y)=(0, 0). The next coordinate values

5



along the first row of the image are represented as (x, y)=(0, 1). These are the actual

values of physical coordinates when the image was sampled.

Hence these digital images can be represented as matrices of size

M*N. Each element of this matrix array is called an image element , picture element ,

pixel, or pel.

3.2.3 RELATIONS BETWEEN PIXELS

3.2.3.1 NEIGHBORS OF PIXELS

A pixel p at coordinates (x, y) has four horizontal and vertical

neighbors whose coordinates are given by

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

This set of pixels, called the 4-neighbors of p, is denoted by N4(p).

Each pixel is a unit distance from (x, y), and some of the neighbors of p lie outside the

digital image if (x, y) is on the border of the image.

The four diagonal neighbors of p have coordinates

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

and are denoted by ND(p). These points, together with the 4-neighbors, are called the

8-neighbors of p, denoted by N 8(p). As before, some of the points in N D(p) and N 8(p)

fall outside the image if (x, y) is on the border of the image.

3.2.3.2 ADJACENCY

There are 3 types of adjacency:

4-adjacency: Two pixels p and q with values from V are 4-adjacent if q is

in the set N4(p).

8-adjacency.:Two pixels p and q with values from V are 8-adjacent if q is

in the set N8(p).

m-adjacency (mixed adjacency): Two pixels p and q with values from V are

m-adjacent if

(i) q is in N4(p), or(ii) q is in ND(p) and the set N4(p)∩ N4(q) has no pixels whose values

6



are from V.

Mixed adjacency is a modification of 8-adjacency. It is introduced to eliminate the

ambiguities that often arise when 8-adjacency is used.

3.2.3.3 CONNECTIVITY

Connectivity between pixels is a fundamental concept that

simplifies the definition of numerous digital image concepts, such as regions and

boundaries.To establish if two pixels are connected, it must be determined if they are

neighbors and if their gray levels satisfy a specified criterion of similarity.

In a binary image with values 0 and 1, two pixels may be 4-

neighbors, but they are said to be connected only if they have the same value.

A (digital) path (or curve) from pixel p with coordinates (x, y) to

pixel q with coordinates (s, t) is a sequence of distinct pixels with coordinates

(x0,y0),(x1,y1),……..(xn,yn)

where pixels (xi,yi) and (xi-1,yi-1) are adjacent for 1≤i≤n

.

3.2.3.4 CONNECTED COMPONENT

Let S represent a subset of pixels in an image. Two pixels p and

q are said to be connected in S if there exists a path between them consisting entirely

of pixels in S. For any pixel p in S, the set of pixels that are connected to it in S is

called a connected component of S. If it only has one connected component, then set S

is called a connected set .

3.2.3.5 BOUNDARY

Let R be a subset of pixels in an image. We call R a region of the

image if R is a connected set. The boundary (also called border or contour) of a

region R is the set of pixels in the region that have one or more neighbors that are not

in R.

7



3.3 MORPHOLOGICAL IMAGE PROCESSING

3.3.1 INTRODUCTION

In the processing and analysis of images it is important to be able to

extract features, describe shapes and recognize patterns. Such tasks refer to

geometrical concepts such as size, shape, and orientation. Mathematical morphology

uses concepts from set theory, geometry and topology to analyze geometrical

structures in an image.

The word ‘morphology’ stems from the Greek words morphe and

logos, meaning ‘the study of forms’. Mathematical morphology examines the

geometrical structure of an image by probing it with small patterns, called ‘structuring

elements’, of varying size and shape.

The above procedure results in nonlinear image operators, which are

well suited to exploring geometrical and topological structures. A succession of such

operators is applied to an image in order to make certain features apparent,

distinguishing meaningful information from irrelevant distortions, by reducing it to a

sort of caricature (skeletonization).

3.3.2 EROSION, DILATION, OPENING, CLOSING

Erosion: It is an operation that ‘shrinks and ‘thins’ objects in a binary image.

Dilation: It is an operation that ‘grows’ and ‘thickens’ objects in a binary image.

Opening: It is defined as erosion followed by dilation.

Closing: It is defined as dilation followed by erosion.

Figure 3.1 (a) shows an example binary image. Figures 3.1 (b) and 3.1 (c) show how

the image is changed by the two most common morphological operations, erosion and

dilation.

8



Figure 3.1 Morphological Operation (erosion, dilation, opening, closing)

In erosion, every object pixel that is touching a background

pixel is changed into a background pixel. In dilation, every background pixel that is

touching an object pixel is changed into an object pixel. Erosion makes the objects

smaller, and can break a single object into multiple objects. Dilation makes the

objects larger, and can merge multiple objects into one.

Figures 3.1 (d) and 3.1 (e) how the image is changed by the two

other morphological operations, opening removes small islands and thin filaments of

object pixels. Likewise, closing removes islands and thin filaments of background

pixels. These techniques are useful for handling noisy images where some pixels have

the wrong binary value.

9



4. MATLAB

4.1 INTRODUCTION

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 include

Math 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 anarray that does not require dimensioning. This allows you to solve many technical

computing problems, especially those with matrix and vector formulations. The name

MATLAB stands for matrix laboratory.

MATLAB features a family of add-on application-specific

solutions called toolboxes. MATLAB toolboxes allow us to learn and apply

specialized technology. Toolboxes are comprehensive collections of MATLABfunctions (M-files) that extend the MATLAB environment to solve particular classes

of problems. Areas in which toolboxes are available include image processing, signal

processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and

many others.

10



4.2 MATRICES

4.2.1 ENTERING THE MATRICES

Different ways to enter matrices:

Enter an explicit list of elements.

Load matrices from external data files.

Generate matrices using built-in functions.

Create matrices with your own functions in M-files.

Basic conventions used to enter matrices:

Separate the elements of a row with blanks or commas.

Use a semicolon (;) to indicate the end of each row.

Surround the entire list of elements with square brackets, [ ].

Once we have entered the matrix, it is automatically remembered in the MATLAB

workspace. We can refer to it as the variable itself to which we assigned the matrix.

4.2.2 SUBSCRIPTS

The element in row i and column j of A is denoted by A(i,j). For

example, A(4,2) is the number in the fourth row and second column.

It is also possible to refer to the elements of a matrix with a single

subscript, A(k). In a two-dimensional matrix the array is regarded as one long column

vector formed from the columns of the original matrix.

4.2.3 THE COLON OPERATOR

The colon, :, is one of the most important MATLAB operators. It

occurs in several different forms.

The expression 1:10 is a row vector containing the integers from 1 to 10,

1 2 3 4 5 6 7 8 9 10

To obtain nonunit spacing, specify an increment. For example, 100:-7:50 is

100 93 86 79 72 65 58 51

11



Subscript expressions involving colons refer to portions of a

matrix. A(1:k,j) is the first k elements of the jth column of A. The colon by itself

refers to all the elements in a row or column of a matrix and the keyword end refers to

the last row or column. So sum (A(:,end)) computes the sum of the elements in the

last column of A.

4.2.4 VARIABLES

MATLAB does not require any type declarations or dimension

statements. When MATLAB encounters a new variable name, it automatically creates

the variable and allocates the appropriate amount of storage. If the variable already

exists, MATLAB changes its contents and, if necessary, allocates new storage.

Variable names consist of a letter, followed by any number of

letters, digits, or underscores. MATLAB uses only the first 31 characters of a variable

name. MATLAB is case sensitive; it distinguishes between uppercase and lowercase

letters. A and a are not the same variable. To view the matrix assigned to any variable,

simply enter the variable name.

4.2.5 GENERATING MATRICES

MATLAB provides four functions that generate basic matrices.

Zeros All zeros

Ones All ones

Rand Uniformly distributed random elements

randn Normally distributed random elements

4.2.6 SUPRESSING OUTPUT

If you simply type a statement and press Return or Enter,

MATLAB automatically displays the results on screen. However, if you end the line

with a semicolon, MATLAB performs the computation but does not display any

output.

12



4.3 PROGRAMMING

Programming includes:

Flow Control

Data Structures

Scripts and Functions

4.3.1 FLOW CONTROL

MATLAB has several flow control constructs:

• if

• switch and case

• for

• while

• continue

• break

• try - catch

• return

IFThe if statement evaluates a logical expression and executes a

group of statements when the expression is true. The optional elseif and else

keywords provide for the execution of alternate groups of statements. An end

keyword, which matches the if, terminates the last group of statements. The groups of

statements are delineated by the four keywords -- no braces or brackets are involved.

SWITCH AND CASE

The switch statement executes groups of statements based on the

value of a variable or expression. The keywords case and otherwise delineate the

groups. Only the first matching case is executed. There must always be an end to

match the switch.

Unlike the C language switch statement, MATLAB switch does not

fall through. If the first case statement is true, the other case statements do not

execute. So, break statements are not required.

13



FOR

The for loop repeats a group of statements a fixed, predetermined

number of times. A matching end delineates the statements

WHILE

The while loop repeats a group of statements an indefinite number

of times under control of a logical condition. A matching end delineates the

statements.

CONTINUE

The continue statement passes control to the next iteration of the

for loop or while loop in which it appears, skipping any remaining statements in the

body of the loop. In nested loops, continue passes control to the next iteration of the

for loop or while loop enclosing it.

BREAK

The break statement lets you exit early from a for loop or while

loop. In nested loops, break exits from the innermost loop only.

TRY-CATCH

The general form of a try-catch statement sequence is

try

statement

...

statement

catch

statement

...

statement

end

In this sequence the statements between try and catch are executed until an error

occurs. The statements between catch and end are then executed.

14



RETURN

Return terminates the current sequence of commands and returns

control to the invoking function or to the keyboard. Return is also used to terminate

keyboard mode. A called function normally transfers control to the function that

invoked it when it reaches the end of the function. We can insert a return statement

within the called function to force an early termination and to transfer control to the

invoking function.

4.3.2 DATA STRUCTURES

The other data structures in MATLAB include

Multidimensional Arrays

Cell Arrays

MULTIDIMENSIONAL ARRAYS

Multidimensional arrays in MATLAB are arrays with more than

two subscripts. One way of creating a multidimensional array is by calling zeros,

ones, rand, or randn with more than two arguments.

A three-dimensional array might represent three-dimensional

physical data, say the temperature in a room, sampled on a rectangular grid. Or it

might represent a sequence of matrices, A(k), or samples of a time-dependent matrix,

A(t). In these latter cases, the (i, j)th element of the kth matrix, or the tkth matrix, is

denoted by A(i,j,k).

CELL ARRAYS

Cell arrays in MATLAB are multidimensional arrays whose

elements are copies of other arrays. A cell array of empty matrices can be created with

the cell function. But, more often, cell arrays are created by enclosing a miscellaneous

collection of things in curly braces, {}. The curly braces are also used with subscripts

to access the contents of various cells.

15



4.3.3 SCRIPTS AND FUNCTIONS

MATLAB is a powerful programming language as well as an

interactive computational environment. Files that contain code in the MATLAB

language are called M-files. You create M-files using a text editor, then use them as

you would any other MATLAB function or command.

There are two kinds of M-files:

Scripts, which do not accept input arguments or return output arguments. They

operate on data in the workspace.

Functions, which can accept input arguments and return output arguments.

Internal variables are local to the function.

SCRIPTS

When we invoke a script, MATLAB simply executes the

commands found in the file. Scripts can operate on existing data in the workspace, or

they can create new data on which to operate. Although scripts do not return output

arguments, any variables that they create remain in the workspace, to be used in

subsequent computations. In addition, scripts can produce graphical output using

functions like plot.

FUNCTIONS

Functions are M-files that can accept input arguments and return

output arguments. The names of the M-file and of the function should be the same.

Functions operate on variables within their own workspace, separate from the

workspace you access at the MATLAB command prompt.

TYPES OF FUNCTIONS

MATLAB offers several different types of functions to use in your programming.

Anonymous Functions

An anonymous function is a simple form of MATLAB function

that does not require an M-file. It consists of a single MATLAB expression and anynumber of input and output arguments. You can define an anonymous function right

16



at the MATLAB command line, or within an M-file function or script. This gives you

a quick means of creating simple functions without having to create M-files each

time. The syntax for creating an anonymous function from an expression is f =

@(arglist)expression

Primary and Subfunctions

All functions that are not anonymous must be defined within an

M-file. Each M-file has a required primary function that appears first in the file, and

any number of subfunctions that follow the primary. Primary functions have a wider

scope than subfunctions. That is, primary functions can be invoked from outside of

their M-file (from the MATLAB command line or from functions in other M-files)

while subfunctions cannot. Subfunctions are visible only to the primary function and

other subfunctions within their own M-file.

Private Functions

A private function is a type of primary M-file function. Its unique

characteristic is that it is visible only to a limited group of other functions. This type

of function can be useful if you want to limit access to a function, or when you choose

not to expose the implementation of a function.

Private functions reside in subdirectories with the special name

private. They are visible only to functions in the parent directory.

Nested Functions

You can define functions within the body of any MATLAB M-file

function. These are said to be nested within the outer function. A nested function

contains any or all of the components of any other M-file function

Like other functions, a nested function has its own workspace

where variables used by the function are stored. But it also has access to the

workspaces of all functions in which it is nested.

17



5. IMAGE PROCESSING TOOLBOX

5.1 INTRODUCTION

The Image Processing Toolbox (IPT) is a collection of functions

that extend the capability of the MATLAB numeric computing environment. The

toolbox supports a wide range of image processing operations, including

Spatial image transformations

Morphological operations

Neighborhood and block operations

Linear filtering and filter design

Transforms

Image analysis and enhancement

Image registration

Deblurring

Region of interest operations

5.2 IMAGES IN MATLAB AND IPT

The basic data structure in MATLAB, array is naturally suited to

the representation of images, real-valued ordered sets of color or intensity data.

MATLAB stores most images as two-dimensional arrays (i.e.,

matrices), in which each element of the matrix corresponds to a single pixel in the

displayed image. For example, an image composed of 200 rows and 300 columns of

different colored dots would be stored in MATLAB as a 200-by-300 matrix.

Some images, such as RGB, require a three-dimensional array,

where the first plane in the third dimension represents the red pixel intensities, the

second plane represents the green pixel intensities, and the third plane represents the

blue pixel intensities.

18



5.3 IMAGE TYPES IN TOOLBOX

The Image Processing Toolbox supports four basic types of images:

Indexed images

Intensity images

Binary images

RGB images

INDEXED IMAGES

An indexed image consists of a data matrix, X, and a colormap

matrix, map. The data matrix can be of class uint8, uint16, or double. The colormap

matrix is an m-by-3 array of class double containing floating-point values in the range

[0,1]. Each row of map specifies the red, green, and blue components of a single

color. An indexed image uses direct mapping of pixel values to colormap values. The

color of each image pixel is determined by using the corresponding value of X as an

index into map. The value 1 points to the first row in map, the value 2 points to the

second row, and so on.

INTENSITY IMAGES

An intensity image is a data matrix, I, whose values represent

intensities within some range. MATLAB stores an intensity image as a single matrix,

with each element of the matrix corresponding to one image pixel. The matrix can be

of class double, uint8, or uint16.While intensity images are rarely saved with a

colormap, MATLAB uses a colormap to display them.

The elements in the intensity matrix represent various intensities,

or gray levels, where the intensity 0 usually represents black and the intensity 1, 255,

or 65535 usually represents full intensity, or white.

BINARY IMAGES

In a binary image, each pixel assumes one of only two discrete

values. Essentially, these two values correspond to on and off. A binary image is

stored as a logical array of 0's (off pixels) and 1's (on pixels).

RGB IMAGES

An RGB image, sometimes referred to as a true-color image, isstored in MATLAB as an m-by-n-by-3 data array that defines red, green, and blue

19



color components for each individual pixel. The color of each pixel is determined by

the combination of the red, green, and blue intensities stored in each color plane at the

pixel's location.

CONVERTING IMAGE TYPES

The following table lists all the image conversion functions in the

Image Processing Toolbox.

Function Description

dither Create a binary image from a grayscale intensity image by dithering;

create an indexed image from an RGB image by dithering

gray2ind Create an indexed image from a grayscale intensity image

grayslice Create an indexed image from a grayscale intensity image by thresholding

im2bw Create a binary image from an intensity image, indexed image, or RGB

image, based on a luminance threshold

ind2gray Create a grayscale intensity image from an indexed image

ind2rgb Create an RGB image from an indexed image

mat2gray Create a grayscale intensity image from data in a matrix, by scaling the

data

rgb2gray Create a grayscale intensity image from an RGB image

rgb2ind Create an indexed image from an RGB image

5.4 READING AN IMAGE

The imread function reads an image from any supported graphics

image file format, in any of the supported bit depths. Most image file formats use 8

bits to store pixel values.

Syntax

A = imread(filename,fmt)

[X,map] = imread(filename,fmt)

MATLAB supports many common graphics file formats, such as

Microsoft Windows Bitmap (BMP), Graphics Interchange Format (GIF), Joint

Photographic Experts Group (JPEG), Portable Network Graphics (PNG), and Tagged

Image File Format (TIFF) formats.

20



5.5 WRITING AN IMAGE

The function imwrite writes an image to a graphics file in one of

the supported formats. The most basic syntax for imwrite takes the image variable

name and a filename. If you include an extension in the filename, MATLAB infers

the desired file format from it.

Syntax

imwrite(A,filename,fmt)

imwrite(X,map,filename,fmt)

5.6 COORDINATE SYSTEMS

The two main coordinate systems used in the Image Processing Toolbox are

Pixel Coordinates

Spatial Coordinates

PIXEL COORDINATES

The most convenient method for expressing locations in an image is

to use pixel coordinates. In this coordinate system, the image is treated as a grid of

discrete elements, ordered from top to bottom and left to right.

For pixel coordinates, the first component r (the row) increases

downward, while the second component c (the column) increases to the right. Pixel

coordinates are integer values and range between 1 and the length of the row or

column. There is a one-to-one correspondence between pixel coordinates and the

coordinates MATLAB uses for matrix subscripting.

SPATIAL COORDINATES

In the spatial coordinate system, locations in an image are positions

on a plane, and they are described in terms of x and y (not r and c as in the pixel

coordinate system). The spatial coordinate system corresponds closely to the pixel

coordinate system in many ways. For example, the spatial coordinates of the center

point of any pixel are identical to the pixel coordinates for that pixel.

In pixel coordinates, the upper left corner of an image is (1,1),

while in spatial coordinates, this location by default is (0.5,0.5). This difference is due

to the pixel coordinate system's being discrete, while the spatial coordinate system iscontinuous.

21



5.7 DISPLAYING IMAGES

The Image Processing Toolbox includes two display functions

imview

imshow

5.7.1 IMVIEW

The imview function displays the image in a separate, Java-based

window called the Image Viewer. The Image Viewer provides tools for flexible

navigation, especially for large images, and for pixel value inspection.

5.7.2 IMSHOW

The imshow function creates a Handle Graphics image object and

displays the image in a MATLAB figure window. imshow automatically sets the

values of certain figure, axes, and image object properties to control how image data

is interpreted.

DISPLAYING DIFFERENT IMAGES

Image Type Syntax

Indexed Images imshow(X,map), imview(X,map)

Intensity Images imshow(I), imview(I)

Binary Images imshow(BW), imview(BW)

RGB Images imshow(RGB), imview(RGB)

5.8 SPATIAL TRANSFORMATIONS

5.8.1 INTERPOLATION

Interpolation is the process used to estimate an image value at a location in between

image pixels. For example, if you resize an image so it contains more pixels than it

did originally, the toolbox uses interpolation to determine the values for the additional

pixels.

22



INTERPOLATION METHODS

The Image Processing Toolbox provides three interpolation methods:

Nearest-neighbor interpolation

Bilinear interpolation

Bicubic interpolation

The interpolation methods all work in a fundamentally similar

way. In each case, to determine the value for an interpolated pixel, they find the point

in the input image that the output pixel corresponds to. They then assign a value to the

output pixel by computing a weighted average of some set of pixels in the vicinity of

the point. The weightings are based on the distance each pixel is from the point.

Nearest-neighbor interpolation: The output pixel is assigned the value of the pixel that

the point falls within. No other pixels are considered.

Bilinear interpolation: The output pixel value is a weighted average of pixels in the

nearest 2-by-2 neighborhood.

Bicubic interpolation: The output pixel value is a weighted average of pixels in the

nearest 4-by-4 neighborhood.

The number of pixels considered affects the complexity of the

computation. Therefore the bilinear method takes longer than nearest-neighbor

interpolation, and the bicubic method takes longer than bilinear. However, the greater

the number of pixels considered, the more accurate the effect is.

5.8.2 IMAGE ROTATION

To rotate an image, use the imrotate function. imrotate accepts

four arguments:

The image to be rotated

The rotation angle(in degrees)

The interpolation method

The size of the output image

Syntax

B = imrotate(A,angle)B = imrotate(A,angle,method)

23



Specifying the Interpolation Method

This table lists the supported interpolation methods in order of complexity

Argument Value Interpolation Method

'nearest' Nearest-neighbor interpolation (the default)

'bilinear' Bilinear interpolation

'bicubic' Bicubic interpolation

B = imrotate(A,angle,method,bbox)

The bbox argument specifies the bounding box of the returned image. bbox is a string

that can have one of these values.

Argument

Value

Description

'crop' Output image B includes only the central portion of the rotated image

and is the same size as A.

'loose' Output image B includes the whole rotated image and is generally

larger than the input image A. imrotate sets pixels in areas outside the

original image to zero.

(default)

5.9 LINEAR FILTERING

Filtering is a technique for modifying or enhancing an image.

Filtering is a neighborhood operation, in which the value of any given pixel in the

output image is determined by applying some algorithm to the values of the pixels in

the neighborhood of the corresponding input pixel. A pixel's neighborhood is some set

of pixels, defined by their locations relative to that pixel.

Linear filtering is filtering in which the value of an output pixel is

a linear combination of the values of the pixels in the input pixel's neighborhood.

5.9.1 CONVOLUTION

Linear filtering of an image is accomplished through an operation called convolution.

In convolution, the value of an output pixel is computed as a weighted sum of

neighboring pixels. The matrix of weights is called the convolution kernel, also

known as the filter.

24



5.9.2 CORRELATION

The operation called correlation is closely related to convolution. In correlation, the

value of an output pixel is also computed as a weighted sum of neighboring pixels.

The difference is that the matrix of weights, in this case called the correlation kernel,

is not rotated during the computation.

5.9.3 IMFILTER

Filtering of images, either by correlation or convolution can be performed using the

toolbox function imfilter .

Syntax:

B = imfilter(A,H)

Above syntax filters the multidimensional array A with the multidimensional filter H.

In addition optional arguments can also be given to imfilter function.

Correlation and Convolution Options:

Option Description

'corr' imfilter performs multidimensional filtering using correlation, which is the

same way that filter2 performs filtering. When no correlation or convolution

option is specified, imfilter uses correlation

'conv' imfilter performs multidimensional filtering using convolution.

The fspecial function produces several kinds of predefined filters, in the form

of correlation kernels. After creating a filter with fspecial, you can apply it

directly to your image data using imfilter .

5.10 NOISE REMOVAL

Digital images are prone to a variety of types of noise. There are

several ways that noise can be introduced into an image, depending on how the image

is created.

The toolbox provides a number of different ways to remove or

reduce noise in an image. Different methods are better for different kinds of noise.

25



The methods available include:

Using Linear Filtering

Using Median Filtering

Using Adaptive Filtering

LINEAR FILTERING

We can use linear filtering to remove certain types of noise. Certain

filters, such as averaging or Gaussian filters, are appropriate for this purpose. For

example, an averaging filter is useful for removing grain noise from a photograph.

Because each pixel gets set to the average of the pixels in its neighborhood, local

variations caused by grain are reduced.

MEDIAN FILTERING

Median filtering is similar to using an averaging filter, in that each

output pixel is set to an average of the pixel values in the neighborhood of the

corresponding input pixel. However, with median filtering, the value of an output

pixel is determined by the median of the neighborhood pixels, rather than the mean.

The median is much less sensitive than the mean to extreme

values (called outliers). Median filtering is therefore better able to remove these

outliers without reducing the sharpness of the image. The medfilt2 function

implements median filtering.

Syntax:

B = medfilt2(A,[m n])

The above syntax performs median filtering of the matrix A in

two dimensions. Each output pixel contains the median value in the m-by-n

neighborhood around the corresponding pixel in the input image.

ADAPTIVE FILTERING

The Wiener2 function applies a Wiener filter (a type of linear

filter) to an image adaptively, tailoring itself to the local image variance. Where the

variance is large, wiener2 performs little smoothing. Where the variance is small,

wiener2 performs more smoothing.

26



This approach often produces better results than linear filtering.

The adaptive filter is more selective than a comparable linear filter, preserving edges

and other high-frequency parts of an image.

5.11 MORPHOLOGICAL OPERATIONS

Morphology is a technique of image processing based on

shapes. The value of each pixel in the output image is based on a comparison of the

corresponding pixel in the input image with its neighbors.

5.11.1 DILATION AND EROSIONDilation and erosion are two fundamental morphological

operations. Dilation adds pixels to the boundaries of objects in an image, while

erosion removes pixels on object boundaries. The number of pixels added or removed

from the objects in an image depends on the size and shape of the structuring element

used to process the image.

RULES FOR DILATION AND EROSION

Operation Rule

Dilation The value of the output pixel is the maximum value of all the pixels in the

input pixel's neighborhood. In a binary image, if any of the pixels is set to

the value 1, the output pixel is set to 1.

Erosion The value of the output pixel is the minimum value of all the pixels in the

input pixel's neighborhood. In a binary image, if any of the pixels is set to

0, the output pixel is set to 0.

DILATING AN IMAGE

To dilate an image, use the imdilate function. The imdilate function

accepts two primary arguments: The input image to be processed (grayscale, binary,

or packed binary image) A structuring element object, returned by the strel function,

or a binary matrix defining the neighborhood of a structuring element.

Syntax:

IM2 = imdilate(IM,SE)

27



ERODING AN IMAGE

To erode an image, use the imerode function. The imerode

function accepts two primary arguments: The input image to be processed (grayscale,

binary, or packed binary image) A structuring element object, returned by the strel

function, or a binary matrix defining the neighborhood of a structuring element.

Syntax

IM2 = imerode(IM,SE)

STREL

The strel function creates a morphological structuring element

Syntax

SE = strel(shape,parameters)

Flat Structuring Elements

Arbitrary Rectangle

Pair Line

Diamond Square

Periodicline octagon

Disk

Nonflat Structuring Elements

Arbitrary

ball

5.11.2 MORPHOLOGICAL OPENING

Morphological opening of an image is an erosion followed by

a dilation, using the same structuring element for both operations.

Syntax

IM2 = imopen(IM,SE)

IM2 = imopen(IM,SE) performs morphological opening on

the grayscale or binary image IM with the structuring element SE. The argument SE

must be a single structuring element object, as opposed to an array of objects.

28



5.11.3 MORPHOLOGICAL CLOSING

Morphological closing of an image is an dilation followed by

a erosion, using the same structuring element for both operations.

Syntax

IM2 = imclose(IM,SE)

IM2 = imclose(IM,SE) performs morphological closing on

the grayscale or binary image IM, returning the closed image, IM2.

5.11.4 IMFILL

The imfill function performs a flood-fill operation on binary

and grayscale images. For binary images, imfill changes connected background pixels

(0's) to foreground pixels (1's), stopping when it reaches object boundaries. For

grayscale images, imfill brings the intensity values of dark areas that are surrounded

by lighter areas up to the same intensity level as surrounding pixels.

Syntax

BW2 = imfill(BW,locations)

BW2 = imfill(BW,'holes')

BW2 = imfill(BW,'holes') fills holes in the binary image BW. A

hole is a set of background pixels that cannot be reached by filling in the background

from the edge of the image.

Imfill differs from the other object-based operations in that it

operates on background pixels. When you specify connectivity with imfill, you are

specifying the connectivity of the background, not the foreground.

29



6. PROJECT DESCRIPTION

PROJECT TITLE: MANGO GRADING BASED ON SIZE USING IMAGE

PROCESSING TECHNIQUES

6.1 INTRODUCTION

Our project is a part of the ongoing project “MANGO SORTER”.

The objective of the project ‘Mango Sorter’ is to develop machine

vision & image analysis methodologies for fast sorting & grading of mangoes as per

the required grading standards.

The following diagram shows the various parameters considered

for grading mangoes:

PARAMETERS FOR

GRADINGMANGOES

COLOR SIZE WEIGHTSHAPE EXTERNAL

DEFECTS

INTERNALDEFECTS

AREA MAJORAXIS

MINORAXIS

30



6.2 EXPLANATION

Mangoes are graded mainly based on the following parameters:

Color

Size

Shape

Weight

External defects

Internal defects

For the mangoes of export quality:

• Color, size, shape & weight are the major parameters.

• Grading is required before processing the fruit.

• Fruits must be free from black spots on the surface and internal defects are

also important.

• Ripening and maturity are the other factors to be considered.

HARDWARE SETUP

Firewire output cameras are being used because they do not

require additional frame grabber and are also cheaper relative to camera link based

cameras. TMS32DM642 DSP based EVM is being used for implementation of the

algorithms under DSP environment. Firewire camera SONY Model XCD-X710CR

has been interfaced with our application program to capture the images in real time.

COLOR COMPUTATION

It can be done by the following method, background removal,

conversion of RGB components to HSI components, median value of the Hue

histogram to be computed and this value to be used for grading.

SHAPE ANALYSIS

It can be represented in several ways with a combination of the size

measurements. It can be found by comparing major and minor axes.

31



SIZE COMPUTATION

The following diagram shows the commonly used features for size measurement:

SIZE

AREA PERIMETER MAJOR AXIS MINOR AXIS

In the food industry the minor axis (width) is some times referred

to the size of the fruit. Most convenient is to measure the area. It includes the

measurement of number of white pixels in the area of interest of binary image of the

mango.

The project we are assigned is to develop an algorithm to find the

minor axis, which is one of the criterion to determine the size of the mangoes.

6.3 ALGORITHM FOR SIZE COMPUTATION

Following steps are used to compute the minor axis

The first step is to read the image from the directory in which images are

stored after acquisition.

Converting the acquired image (with blue background) to binary image by

converting all the background (blue) pixels to logical value 0 and remaining

pixels to logical 1.

Performing morphological operations (closing, filling holes in binary image)

to smoothen the image and fill all the holes inside the binary image.

Using median filter to filter the image for noise removal.

The next step is to find the length of longest intercept (major axis) which is

horizontal.

32



Final step is o find the minor axis which is perpendicular to the major axis

determined above.

6.4FLOWCHART:

START

READ THERGB IMAGE

CONVERTTO BINARY

FIND MAJORAXIS

FIND MINORAXIS

MAJOR &MINOR AXES

STOP

6.5 EXPLANATION OF OUR PROJECT:

Converting the image from RGB to Binary:

To read the image, the predefined function imread is used. We used

the images with the blue background (as assigned) for our project. Naturally the

mango has relatively low blue content than the red and green component. This is

taken as the criteria for converting the image to binary. The pixels having low blue

33



value than the red or green are assigned logical value 1. The other pixels are assigned

logical 0.

Processing of binary image

To fill any holes present in the binary image the function imfill is

used. To remove noise, filtering is done using median filter and the function used is

medfilt2. We also used imclose to smoothen the boundary of binary image and also to

fill any remaining holes.

Finding the major axis

The orientation of the major axis is found to use it as a reference

for minor axis. The longest intercept in the image is taken as the major axis. The

image is rotated every one degree through 180 degrees and the length of the longest

horizontal intercept is found. All the lengths are compared and the maximum length is

considered as the major axis. The orientation of the major axis is found and the image

is rotated to make the major axis horizontal.

Finding the minor axis

The axis perpendicular to the major axis is taken as the minor axis.

All the vertical intercepts are calculated for the image with the horizontal major axis.

They are compared and the longest one taken as the minor axis. The length of minor

axis (no. of pixels) is displayed.

34



7. CONCLUSION AND RECOMMENDATIONS

The minor axis of the mango which is one of the criterions to grade

mangoes based on the size was successfully measured using Image processing

toolbox in MATLAB. Both major and minor axes were measured. Minor axis was

measured with reference to the major axis. The result was displayed immediately on

the Matlab Command Window.

Images with blue background are only considered in developing

the algorithm because of the simplicity in removing the blue background and also

because of the availability of algorithm to remove any type of background which was

developed previously.

Efficiency of our program depends on how much angle do we

rotate each time to find the length of horizontal intercepts. The loop which we had

written executes 180 times if we rotate the image one degree each time and hence the

efficiency of the program decreases ,but the value of the minor axis can be determined

correctly. We also checked by rotating the image for 5 degrees each time and the error

came out to be 1 pixel on an average for both major and minor axis.

Modifications can be made for the program to reduce the

execution time by rotating to angle more than 1 degree and also by knowing the

approximate value the image may deviate from the supposed angle .If the image does

not go beyond 45 degrees on both sides of the almost horizontal major axis image

then the program can be modified and can be written to rotate the image through 45

degrees on both sides in steps of 1 or 5 degrees. This can be done by only examining

the deviation the image undergoes by human inspection of images.

8. REFERNCES

“Digital Image Processing using MatLab” by Rafael C. Gonzalez

“Digital Image Processing” by Rafeal C. Gonzalez

“Matlab 7” Documentation

35



9. APPENDIX

Program for finding the minor axis

function minoraxis=pro(image)clearimview close all

%......................converting image to binary…………….%

a=im2double(image);r=a(:,:,1);g=a(:,:,2);

b=a(:,:,3);dim=size(a);row=dim(1);col=dim(2);i=1;

j=1;q=zeros(row,col);while i<=row

while j<=colif (r(i,j) > b(i,j)) | (g(i,j) > b(i,j))q(i,j)=1;

end

j=j+1;end j=1;i=i+1;

end

s=imfill(q,'holes');l = medfilt2(s,[6 6]);imview(l)

%............finding lengths of major axes……………%

j=1;major=zeros(1,36);

for i=0:5:179im=imrotate(l,i,'bilinear','crop');

%........................leftmost pixel………………..%

u=1;v=1;

36



h=0;while u<=col

while v<=rowif im(v,u)==1

lmp=u;

h=1; break

endv=v+1;

endif h==1

breakendv=1;u=u+1;

end

%......................rightmost pixel……………….%

u=col;v=1;h=0;

while u>=1while v<=row

if im(v,u)==1rmp=u;h=1;

breakend

v=v+1;end

if h==1 break

endv=1;u=u-1;

end

%.........................length of major axis………………%

major(j)=(rmp-lmp); j=j+1;

end

%..........................finding longest majoraxis……………%

37



majormax=major(1);for j=1:36

if major(j)>=majormaxmajormax=major(j);

end

endmajoraxis=majormax

%.............finding the required orientation…………..%

for j=1:36if major(j)==majormax

jmax=j; break

endend

ro=jmax*5;fim=imrotate(l,ro,'bilinear','crop');imview(fim)

%..............finding minor axis…………..%

i=1; j=1;count=0;while j<=col

while i<=rowif fim(i,j)==1

count=count+1;end

i=i+1;end

minor(j)=count;count=0;i=1;

j=j+1;

end

%..............finding the longest minor axis…………….%

j=1;max=0;while j<=col

if minor(j)>=maxmax=minor(j);

end j=j+1;

endminoraxis=max;

38



39

mango grading based on size using image processing

Documents