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1.1Abstract 1.2Project overview 1.3Introduction and Motivation1.4 Problem Definition
1.5Literature Review Technical Paper 1.6Scope Chapter 2. Project Design: Development Model 2.1Lifecycle Model 2.2 Requirement Analysis : Feasibility and Risk Analysis 2.3Software Requirements Specification Document 2.4Software Design Document 2.5UML Diagrams / DFD , CFD, ERD Chapter 3. Project Management Plan
3.1Software Architecture 3.2Task & Responsibility Assignment Matrix 3.3Project Timeline Chart Chapter 4. Project Implementation (Implementation Details) 4.1Approach / Main Algorithm / Methodology 4.2Programming Language used for Implementation 4.3Tools used Chapter 5. Integration & Testing
5.1Testing Approach 5.2Testing Plan 5.3Unit Test Cases 5.4Integrated System Test CasesChapter 6.
Conclusion&Future work (Enhancements) References
Appendix I) Minimum System Requirement II) Users Manual III) Technical Reference Manual IV) Data Sheets of chips used ( for hardware projects only)
1. Introduction1.1) ABSTRACT Signature is the characteristic of the particular person and hence used globally for identifying a person, validity of the documents signed, banking etc. Up till now, in banks where signature of a person is the basic code for transaction, the validity of the signature is generally checked by a man. Our project simulates the ability of a man to
recognize a signature from the set of samples of signatures. A signature verification system may be either offline or online. The signature is captured using an optical scanner and stored in an image format (GIF).Then the image is converted into a bit pattern from which features are extracted. These features are said to be static. Artificial Neural Network is used in our project. Our system is trained to identify similarities and patterns among different signature samples. Any given signature is verified based on training that is provided. Our project incorporates database management, image preprocessing, feature extraction, learning and verification modules (Artificial Neural Networks).
1.2) PROJECT OVERVIEW Our project is designed to speed up the process of verification and minimize manual intervention. Our system automates the process of recognition and verification of signatures. The features of standard signatures of customers along with their account number and their name are stored in the database. The Artificial Neural Network is trained using the features extracted from the database. The operator will provide the customers signature in the form of an image. The features extracted from this signature image are used to test the system (Recognition and Verification). The output of neural network provides a serial number which corresponds to a customer record in the database. The error rate is calculated by comparing the features of original signature image with the features of signature image to be tested. This error rate should be less than the threshold value for the signature to be recognized and genuine. STEPS IN SIGNATURE RECOGNITION A) Image Pre-processing: The data is transformed to a standard format. 1. Conversion of colored to gray scale image. 2. Image Enhancement 3. Noise Reduction 4. Image Normalization 5. Image Thinning 6. Cropping B) Feature extraction: converts each image into a set of binary features. 1. Global feature 2. Moment Invariant Method
C) Artificial Neural networks: It is used for identification and verification. Back Propagation neural network is used. 1.3) INTRODUCTION AND MOTIVATION There exist a number of biometrics methods today e.g. Signatures, Fingerprints, Iris etc. There is considerable interest in authentication based on handwritten signature verification system as it is the cheapest way to authenticate the person. Signature verification does not require the installation of costly equipments and hence can be used at day to day places like Banks etc. The objective of the project is to make software for Offline Signature Recognition and Verification. It involves recognition of signature that has been read optically. The method starts with a scanned image of a handwritten signature. A signature is treated as an image carrying a certain pattern of pixels that pertains to a specific individual. There is a growing interest in the area of signature recognition and verification (SRVS) since it is one of the important ways to identify a person. Recognition is finding the identification of the signature owner . Verification is the decision about whether the signature is genuine or forged. Signature is a special case of handwriting in which special characters and flourishes are viable. Signature verification is a different pattern recognition problem as no two genuine signatures of a person are precisely the same. Signature Recognition and Verification (SRVS) are categorized into two major classes: On-line Signature Recognition and Verification System Off-line Signature Recognition and Verification System
The difference between the off-line and on-line lies in how data are obtained. In the on-line SRVS data are obtained using special peripheral device, while in the off-line SRVS images on the signature written on a paper are obtained using scanner or a camera.
1.4) PROBLEM DEFINITION Our project is designed to speed up the process of verification and minimize manual intervention. Our system automates the process of recognition and verification of signatures. The operator who is using Offline Signature Recognition and Verification software will provide the customers signature in the form of an image. Our system is able to recognize the owner of the image and provides the identification number and name of the customer to whom the signature belongs to. Our system recognizes all signatures that the artificial neural network is trained for.
1. 5) LITERATURE SURVEYED
1] Integration of Offline and Online Signature Verification System By: Deepthi Uppalapati, Department of Computer Science & Engineering, Indian Institute of Technology, Kanpur, India, July 2007 In this thesis, an integrated verification system has been proposed in which the feature vector comprises of static and dynamic features. It not only provides a way to match and compare an online signature versus an offline signature and vice versa, but also improves the system performance. 2] Signature recognition and Verification with ANN By: Cemil oz, Fikret Ercal, Zafer Demir, 2005 In this paper, we present an off-line signature recognition and verification system which is based on moment invariant method and ANN. Two separate neural networks are designed; one for signature recognition, and another for verification (i.e. for detecting forgery). Both networks use a four-step process. First step is to separate the signature from its background. Second step performs normalization and digitization of the original signature. Moment invariant vectors are obtained in the third step. And the last step implements signature recognition and verification. 3] Paper on Offline Signature Recognition and Verification Based on Artificial Neural Network By: Mohammed A. Abdala , Noor ayad Yousif, December 2008 In this paper, a problem for Offline Signature Recognition and Verification is presented. A system is designed based on two neural networks classifier and three powerful features (global, texture and grid features). Our designed system consist of three stages: the first is preprocessing stage, second is feature extraction stage and the last is neural network (classifiers) stage which consists of two classifiers, the first classifier consists of three Back Propagation Neural Network and the second classifier consists of two Radial Basis Function Neural Network. The final output
is taken from the second classifier which decides to whom the signature belongs and if it is genuine or forged. The system is found to be effective with a recognition rate of (%95.955) if two back propagation of the first classifier recognize the signature and (%99.31) if all three back propagation recognize the signature. 1.6) SCOPE Our system involves two separate but strongly related tasks: 1) Identification of the signature owner (Recognition) 2) The decision about whether the signature is genuine or forged (Verification) Many of the applications use Offline Signature Recognition as they are simple and do not require any additional tools (like stylus). The features of the standard signatures of the customers along with their name and identification number are stored in the database with the help of tools like Microsoft Access. The signature to be recognized and verified is in an image format. Various image processing and neural network techniques are to be used. The signature image to be tested is identified and verified by using a threshold value.
2) PROJECT DESIGN: DEVELOPMENT MODEL2.1) Lifecycle Model Waterfall model Waterfall Model is used to implement our system. The modules in our project are organized in a linear order. It begins with feasibility analysis and on the successful demonstration of the feasibility analysis, the requirements analysis and project planning begins. The design starts after the requirements analysis is done. And coding begins after the design is done. Once the coding is completed, it is integrated and testing is done. On succeeful completion of testing, the system is installed. After this the regular operation and maintenance of the system takes place. The following figure demonstrates the steps involved in waterfall life cycle model.
fig 2.1: The Waterfall Software Life Cycle Model With the waterfall model, the activities performed in our project are requirements analysis, project planning, system design, detailed design, coding and unit testing, system integration and testing. When the activities of a phase are completed, there should be an output product of that phase and the goal of a phase is to produce this product. The outputs of the earlier phases are often called intermediate products or design document. For the coding phase, the output is the code. After each phase is completed and its outputs are certified, these outputs become the inputs to the next phase and should not be changed or modified. The changes in one phase may affect
the later phases. These changes are to be made in a controlled manner after evaluating the effect of each change on the project.
2.2 ) REQUIREMENT ANALYSIS : FEASIBILITY ANALYSIS A good feasibility study shows the strengths and deficits before the project is planned or budgeted for. By doing the research beforehand, it is possible to save money and resources in the long run by avoiding projects that are not feasible.
Technical Feasibility The project requires technical tools that are easily available. Also, the system requirements are not very high. The project can run on any machine which fulfills the basic requirements. MATLAB is the programming language used which is highly accessible and extensively used. Hence the system is technically feasible. Schedule Feasibility The time available for the completion of the project was approximately of 8-9 months. Hence it was ea to achieve the deadline for project submission. Economic Feasibility The project is economically feasible. All the tools required for the completion of the project are open source and freeware softwares. The hardware requirements were also not very high. Hence much investment is not required for the technical tools. Resource Feasibility All the software and hardware resources necessary for the project were easily available and hence resource feasibility is achieved. Operational Feasibility The functionalities of the system will have to be tested from time to time for errors or any other drawbacks.It is important to provide an efficient software which provides all the required functionalities to the client.
RISK ANALYSIS Schedule Risk: No schedule risk in our project. Budget Risk: No budget risk in our project. Operational Risks:
Insufficient resources like availability of scanner. No proper training of Signature images.
Technical risks: Difficult project modules integration.
2.3) Software Requirement Specification Document 2.3.1) Introduction: 184.108.40.206) Purpose/Problem Definition: Our project is designed to speed up the process of verification and minimize manual intervention. The system automates the process of recognition and verification of signatures. 220.127.116.11) Scope: a) In our project we are using offline signature recognition. b) Standard signatures are stored in the database. c) Signature to be recognized and verified is an image. d) Image Pre-processing is done on the image e) Feature Extraction is done on the pre-processed image. f) Neural Networks is used for training and verification. 18.104.22.168) Overall Description: 22.214.171.124.1) Product Perspective: The product will have the following modules:
Artificial Neural Networks
a) Image Acquisition: Handwritten signatures of customers are scanned and converted into images. b) Image Pre-processing: The data is transformed in a standard format. 1. Conversion of colored to gray scale image.
2. Image Enhancement 3. Noise Reduction 4. Size Normalization 5. Thinning 6. Cropping c) Feature extraction: converts each image into a set of binary features. 1. Global features 2. Moment Invariant Method d) Artificial Neural networks: It is used for identification and verification. Back Propagation neural network is used. 126.96.36.199.2) USER PERSPECTIVE: The user has to deal with the user interface only. He/she must not be concerned with the backend processing. All the internal processing details will be hidden. 188.8.131.52.3) GENERAL CONSTRAINTS: Only one user will access the application at a time. 184.108.40.206.4) ASSUMPTION AND DEPENDENCIES: The system should be compatible with most of the operating systems i.e. previous and latest ones. 2.3.2) REQUIREMENTS220.127.116.11) EXTERNAL INTERFACE REQUIRED: 18.104.22.168.1) USER INTERFACE: The user must be able to access the interface which interacts with modules Loading image to be tested Recognition button which implements recognition and verification
All these interfaces have different design and include all elements to achieve the respective functionalities. 22.214.171.124.2) SOFTWARE INTERFACE: The Operating Systems can be any version of Windows.
126.96.36.199) PERFORMANCE REQUIREMENTS: 188.8.131.52.1) Maintainability: The system should manage the changes effectively i.e. easy to be maintained. 184.108.40.206.2) Compatibility: The system must be compatible with all the operating systems and the underlying database. 220.127.116.11.3) Scalability: The System should be scalable. 18.104.22.168.4) Security: Data abstraction needs to be implemented properly. 22.214.171.124.5) Usability: The user interface should be easy enough to use. 126.96.36.199) DESIGN CONSTRAINTS: The constraints at the designing time are that the needs may keep on changing so the designers must keep this in view and design the product in this way that it is easily updatable. 188.8.131.52) HARDWARE REQUIREMENTS: 1) RAM-1GB or above 2) Any Intel Processor of 1.0 GHz or above 184.108.40.206) SOFTWARE REQUIREMENTS: 1) MATLAB 7.0 or later versions. 2) Microsoft Excel and Access
2.4) SOFTWARE DESIGN DOCUMENT 2.4.1) Introduction: 220.127.116.11) Design Overview: Modular design of the system helps us to have clear goal and logically correct view of the design. We will try to isolate the functionality of each module and will also try to make the design of the system simple irrespective of the interdependency of between the modules. Good system is characterized by highly cohesive module. Our project consists of four modules which are almost dependent on each other. We will design each module separately to keep it clear and easy to understand. 2.4.2) System Architectural Design
Image PreprocessingConversion of colored to grayscale image Image Enhancement Noise Reduction Size Normalization Thinning Image Cropping
Feature ExtractionMoment Invariant . Method Global features like signature height, Image Area, Maximum Vertical and Horizontal Projection.
Neural NetworksBack-propagation Artificial Neural Network for Training and Verification
Fig 2.2: Architectural design
2.4.3) System Overview: Offline Signature Recognition and Verification System helps in identifying the owner of the signature and their verification. Our project deals with designing a system which is aimed at speeding up the process of recognition and verification and minimizing manual intervention. The system will automate the process of recognition and verification of signatures. 2.4.4) Design Constraints: The general design constraints for our project are as follows: i) Our system works only for windows operating system. ii) Handwritten signatures must be scanned using Canon 4350d scanner. iii) Access database consisting of one table i.e. original which stores the features of original signatures along with customer account number and their name must be imported. iv) 2 Microsoft Excel files i.e. sn.xls and testd.xls must be imported. v) The original table of Access database and sn.xls must be consistent. v) MATLAB 7.0 or later versions should be incorporated into the environment. 2.4.5) System Software Architecture: The Software modules used are as follows: 18.104.22.168) Microsoft Access: It is used as an input/output database. It consists of one table i.e. original. The original table stores sr_no, account number, customer name and features of original signatures of each customer. 22.214.171.124) Microsoft Excel: It is for training and testing purpose. The file sn.xls is a copy of original table of our database which is used to provide as input to artificial neural network. One extra column of target is added to sn.xls file. The testd.xls file is used to store the features of the signature to be tested. 126.96.36.199) MATLAB 7.0 or later versions: It forms the base of our project as all our codes run in MATLAB. Why MATLAB 7.0? a) MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming environment. b) MATLAB is a modern programming language environment: it has sophisticated data structures, contains built-in editing and debugging tools, and supports object-oriented programming. These factors make MATLAB an excellent tool for teaching and research.
c) MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. d) It has powerful built-in routines that enable a very wide variety of computations. It also has easy to use graphics commands that make the visualization of results immediately available. Specific applications are collected in packages referred to as toolbox. There are toolboxes for signal processing, symbolic computation, control theory, simulation, optimization, and several other fields of applied science and engineering. 2.4.6) Database Design: The database named db is created using Microsoft Access 2003. This database consists of the following: 188.8.131.52) Original signature table: It consists of sr_no, account number, name of customer, path of Original signature images and various features of original signatures of each customer. The original table consists of three original signature images of each customer which are signed at different instants of time. There are three customers in our database so total 9 signatures are present which is used for training the artificial neural network. Apart from Microsoft Access 2003, we also use two Microsoft Excel 2003 files. They are as follows: 184.108.40.206) sn.xls: This file is a copy of the original table. Only an extra column of target vector is added. They are used for training purpose. 220.127.116.11) testd.xls: This file stores all the features of the signature that is to be tested. It is used for testing of signatures. 2.4.7) Input and Output Formats: The scanned image is saved in gif format which is provided as input to the pre-processing module. The output of this module is saved as a jpeg image on which feature extraction is carried out. These features are provided in vector form to the last stage i.e. artificial neural networks. The error rate obtained by comparing original signature image with the tested signature image should be less than a threshold value for it to be recognized and genuine.
2.5) UML DIAGRAMS: 2.5.1) Activity Diagram: a) Image Pre-processing
b) Feature Extraction:
c) Sequence Diagram:
3) Project management plan:3.1) Software Architecture: 3.2) Tasks: Table 3.1: Sr. No. Task Description Deliverab Resources les and Needed Milestone 3.2.1 Interacting Get with client 3.2.2 Developm ent the requirement specificatio s Prepare analysis report MATLAB of Code Getting right respective modules Developer manuals Dependen cies Constrain ts Coding started Version of Availability software of v/s software waiting Risks es Fixing of and and Contingenci
cannot be appointment
ns Develop the Actual actual application developm ent
project Execute and Validatin check project the g the code
for it Availability of le people for testing
inputs for knowledgeab
Table 3.2: Tasks Requirement Gathering
Description 1) Collection of information 2) Analysis of various papers 3) Design Generation 4) Coordinating
Name Snehal S. Pradhan Manasi D. Mahajan Snehal S. Pradhan Manasi D. Mahajan Manasi D. Mahajan Snehal S. Pradhan Snehal S. Pradhan Snehal S. Pradhan Manasi D. Mahajan Manasi D. Mahajan Snehal S. Pradhan Manasi D. Mahajan Snehal S. Pradhan Manasi D. Mahajan Manasi D. Mahajan Snehal S. Pradhan Snehal S. Pradhan Manasi D. Mahajan Snehal S. Pradhan Manasi D. Mahajan
1) Software design document-data and architecture 2) Designing user interface 3) Designing the database
1) Image Acquisition 2) Image Pre-processing 3) Feature Extraction 4) Artificial Neural Network for Training and Verification
2) Integrating and then testing integrated modules. Documentation Generating different reports(Requirements Specification, Design, Planning)
3.3) Project Time Allocation:
Project timeline is made to track the progress in the project. By making careful analysis we have decided to schedule the project in the following way: Table 3.3: Tasks Gathering information Description Collection information papers Software document-data Coding Days allotted of 15 and Start date 1st Aug 2010 End date 15th Aug 2010
analysis of various Designing design and 171 10th Sept 2010 1st March 2011 20 16th Aug 2010 5th Sept 2010
architecture 1.Image Acquisition 2.Image processing 3.Feature Extraction 4. Artificial Neural Networks Training for and Pre-
Verification. Testing various modules Generating different reports(Requirements Specification, Design, Planning)
4th March 2011 30th 2011
2011 March 5th April 2011
Project Timeline Chart The flow of the activities can be shown by using Gantt chart
SR NO. 1 2 3 4 5 6 7
WORK TASK Collection papers Analysis of of
papers Software Design GUI Design Database Design Preprocessing Feature Extraction Pattern Matching Using Dynamic Programming Testing Documentation Fig : Project Timeline Chart (Gnatt Chart)
8 9 10
4) Project Implementation4.1) METHODOLOGY
The modules in our project and the algorithms used for each module are as follows
Image PreprocessingConversion of colored to grayscale image Image Enhancement Noise Reduction Size Normalization Thinning Image Cropping
Feature ExtractionMoment Invariant Method Global features like signature height, Image Area, Maximum Vertical and Horizontal Projection.
Neural NetworksBack-propagation Artificial Neural Network for Training and Verification.
Fig 4.1: System Architectural Design 1) Image Acquisition: The handwritten original signatures of the customer are scanned and the path of the scanned images is stored in the database along with their identification number and their name along with their features of signatures like the seven moments, image area, signature width, vertical center, horizontal center, number of cross points and edge points are stored in original database. The operator has to load a signature image that is to be tested using the given GUI. This image to be tested is provided as input to the Image Pre-processing module.
fig 4.2:Original Signature image 2) Image Pre-processing: It consists of the following stages: a) Conversion of colored to grayscale image: A color image consists of coordinate matrix and three color matrix. Color matrices are known as Red (R), Green (G) and Blue (B). The designed system is based on gray scale images; therefore, colored image must be converted to gray scale using the equation below : G=0.299*Red+0.5876*Green+0.14*Blue Algorithm: Color to grayscale 1) x = image obtained from the image path provided in the database. 2) Applying MATLAB inbuilt function to x: y = rgb2gray(x). 3) y is the grayscale image. b) Image Enhancement: Light and camera cause Characteristics can case problem in the image such as poorly lighted image or image with bad contrast. This filter attempts to enhance the brightness and contrast of image. We use Adaptive contrast enhancement algorithm for this stage. Algorithm: Image enhancement 1) Initialize threshold = 20 and constant = 1.0.
2) Calculate the standard deviation with the MATLAB inbuilt function std: deviation = std(double(y(i-1:i+1,j-1:j+1))). Where i is row no and j is column no. 3) If ( y(i,j ) - deviation ) > threshold then e = y(i,j) * constant. 4) e is the enhanced image.
Fig 4.3: Image after enhancement c) Noise Reduction: The purpose of applying this filter is to eliminate noise as much as possible. We are using Salt andPepper filter to remove salt and pepper noise. Algorithm: Noise Reduction 1) e is the enhanced image which is used in this stage. 2) Applying 3 * 3 mask to e we get al=[e(x-1,y-1) e(x-1,y) e(x-1,y+1) e(x,y-1) e(x,y) e(x,y+1) e(x+1,y1) e(x+1,y) e(x+1,y+1)]; // x is row and y is column. 3) Sort al 4) Calculate median ie al(4). 5) Replace e(x,y) by median. 6) e obtained is noise free.
fig 4.4: Image after noise reduction d) Size Normalization: Signature dimension may vary due to the scanning and capturing process. Furthermore, width and height of signature vary from person to person and sometimes even for the same person. The image size is adjusted so that a few rows are added to the signature image to facilitate the calculation of the next step. Algorithm: Size normalization 1) e is the enhanced and noise free image to be normalized. 2) Using MATLAB inbuilt function we get, r = imresize (e,[128 ,128]); 3) r is normalized image.
Fig 4.5: Image after normalization e) Thinning: This filter aims to reduce the width of the signature from several pixels to a single pixel. This process is performed on binary image. Algorithm: Thinning 1) Convert r to a binary image b. i.e b = im2bw (r). 2) Thinning the image b using the MATLAB function. t = bwmorph (b, 'thin', inf); 3) t is the thinned image.
fig 4.6: Image after thinning f) Image Cropping: The capture image may contain the signature and the area surrounding the signature which is empty of data. Thus to get the signature containing area cropping is used. Algorithm: Image Cropping 1) t is the image to be cropped. 2) Let xstart, xend, ystart, yend be the threshold values. 3) If (t(r,c) = =0) then if (ryend)) then yend=r; if (cxend) then xend=c. 4) Copy t into p: p((i-ystart+1),(j-xstart+1))= t(i,j). 5) p is the final output of pre-processed module. 6) Save this p as jpeg type of image.
Fig 4.7: Image after cropping 3) Feature Extraction: It consists of the following two techniques: a) Moment Invariant Method: Moment invariants are properties of connected regions in binary images that are invariant to translation, rotation and scaling. They can be easily calculated from region properties and they are very useful in performing shape classification and part recognition. Moment invariants are usually specified in terms of centralized moment. Here, the moment is measured with respect to the center of mass, (x, y). The central moment, , with respect to the centroid, and the normalized central moment, , are calculated as:
The moment invariants used in our research are computed using the equations given in Table below for all signatures at various angles. Central Moments Derived Invariant Moments 00=m00 I1=20 + 02
10=0 01=0 20= m20-xm00 02= m02- ym01
I2=(20 -02)^2+411^2 I3=(30 - 312)^2+ (321-03)^2 I4=(30 + 12)^2+ (21-03)^2 I5=(30 - 312) (30 + 12)^2( (30 + 12)^2 -3(21 + 03)^2) + (321 - 03) (21 + 03)(3 (30 + 12)^2 (21 + 03)^2)
11= m11- ym10 30= m30-3xm20 +2xm10
I6=(20 - 02) ((30 + 12)^2- (21 + 03)^2 )+ 411 ( 30 + 21 )(21+ 03) I7=(312 - 30) (30 + 12)( (330 12) - 3(21 + 03)2) + (321- 03) (21 + 03)(( 330 12)^2 -(21 + 03)^2)
Algorithm:Moment Invariant 1) Input pre-processed image p whose feature is to be extracted. 2) Calculate centroid of image. 3) Calculate central moment ( ). 4) Calculate normalized central moment ( ). 5) Calculate moment invariants. b) Global Feature Extraction: It provides information about specific cases concerning the structure of the signature. It consists of: i) Signature height: The height of the signature can be considered as a way of representation, height-to-width ratio Algorithm: Signature height 1) Get width (w) and height (h) of image p using MATLAB inbuilt function size(). 2) Calculate h/w to get signature height. ii) Image Area: Image area is the number of black pixels in the signature image. Algorithm: Image area
1) Get pre-processed image p. 2) Initialize counter to 0 3) If p(i,j)= = 0 then counter+1. //0 stands for black pixels i.e. signature 4) area = counter. iii) Vertical center of signature: Algorithm: Vertical center of signature 1) Get pre-processed image p. 2) Traverse each column and row 3) count=count+(col*pixelvalue(col,row)) 4) Traverse all row and column 5) count1=count1+pixelvalue(row,col) 6) vc = count/count1.
iv) Horizontal center of signature: Algorithm: Horizontal center of signature 1) Get pre-processed image p. 2) Traverse each row and col 3) count=count+(row*pixelvalue(row,col)) 4) Traverse all row and column 5) count1=count1+pixelvalue(row,col) 6) hc = count/count1. v) Number of cross point and edge point: Number of cross point is the number of pixels having neighbors greater than or equal to 3 else it is a edge point. Algorithm: Number of cross and edge point 1) Get pre-processed image p. 2) Traverse each row and col 3) Sum=sum of all its neighbor pixels
4) If Sum