Image Processing Through Fuzzy Logic

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graphic-based cryptography for digital signature. ... signatures as an alternative to digital signatures. .... are important because accepting a small amount.
Image Processing Through Fuzzy Logic Abstract The signature verification is a popular problem and the fuzzy approach is one of the existing techniques. The paper presents the concept of authentication by a graphical signature to validate the origin of digital documents. The process consists of encoding, decoding, transmission of data and the comparison of signatures using fuzzy logic. This work presents a methodology for addressing digital handwritten signatures and the authentication of it for validating legal operations. Data authentication is a problem. There remains always a fear that a transaction has been changed. Further, transmitting system may suffer from lossy. These problems can be solved by graphical representation of any figure to be preserved and transmitted. The main theme of the paper is the use of graphical representation for data authentication. Also the paper presents a graphic-based cryptography for digital signature. The paper discusses the use of image processing techniques, for example, to verify actual signatures as an alternative to digital signatures. Thus it proposes a method for enhancing the process of data authentication by applying fuzzy logic to the transmission of 'graphical signatures' to enhance the authentication process. Key Words Pixel, Coordinates, Array, Image Processing, Pattern Recognition, Handwritten Signature, Finger Print, Voice Recognition, Eye Detection, i-v Fuzzy Sets, Pseudo Zernike Moments, Fuzzy Logic Classifier Introduction For the last 30 years, organizations worldwide have been trying to move from a paper-intensive environment to a paper-less environment. Word processors have replaced the writing pad and pen, spreadsheet applications have replaced manual spreadsheets and emails have supplanted handwritten letters. One of the key problems not yet solved in the transition from a paperintensive to a paper-less environment is dataauthentication, validating that a certain document or transaction was not changed. In the paperintensive world, people authenticate written data with their handwritten signatures. When moving

to a paperless environment, organizations have failed to find an easy-to-use and an easy-todeploy electronic signature solution. The need to validate data has therefore, often interrupted the organization’s progression to paper-less transactions [6]. Hence, the present researcher feels it necessary to find out the solution of this key problem. Digital signatures are an important application of cryptography. A digital signature is a way of marking an electronic message in a manner that is unique and probably traceable to the originator. It is supposed to establish the sender’s authenticity much as the ordinary written signature does. The receiver will get the identical image as contributed by the sender. The variations between two images both produced by the sender, must be recognized instead of rejection. Here lies the secrecy of cryptography. The sanctity of cryptography of digital signatures can also be protected through graphical representation. Thus graph, by its unique property, gives another solution to digital signatures through cryptography which is the objective of this study. Research Problem Static signature verification has a significant use in establishing the authenticity of bank checks, insurance and legal documents based on the signatures they carry[2].When a customer submits a cheque, putting signature manually, to withdraw money the bank manager compares the present signature with the preserved one. If the two signatures are identical he allows to withdraw money and if differs he rejects the cheque. The co-ordinates of two signatures, from 2-dimensional geometric point of view, can never be identical yet the brain can compare and identify the uniqueness of the two signatures and also identify the discrepancy. Now the question arises how computer will perform this job of compare and rejection as the brain does. Basic Principle A straight line is the combination of continuous dots. Conversely, discrete dots when come close together make a straight line. Similarly, a curve is also composed of dots. Thus dots make a figure. Now from geometrical point of view every dot situated on any plane has its unique 2D co-ordinates. From the value of 2D

co-ordinates (x, y) we can identify the location of any dot unique in question. The coordinates of the pixels forming the character is captured and stored in a special array [1] and we can retrieve the data and construct the figure again. Thus all the dots of any figure are mutually exclusive and collectively exhaustive. This is the basic principle of image processing, pattern recognition, finger print, voice recognition, eye detection [7], etc. Thus, if we transmit the value of the coordinates then through decoding the figure can be generated again. So, through transmission channel we can transmit the data from one computer to another computer. Here, coding and decoding can be done through cryptography for the sake of secrecy rendering the method secured and reliable as well. Data Compression Transmitting material in uncompressed form is beyond question and quite absurd, rather massive compression is done. All compression systems require two algorithms: one for compressing the data at the source and another for decompressing it at the destination. In the literature, these algorithms are referred to as the encoding and decoding algorithms, respectively. These algorithms have certain asymmetries that are important. First, for many applications a matter is encoded once but will be decoded many times. This asymmetry means that the encoding algorithm is slow and requires expensive hardware but the decoding algorithm is fast and does not require expensive hardware. A second asymmetry occurs when the decoded output is not exactly equal to the original input, the system is called lossy. If the input and output are identical, the system is lossless. Lossy systems are important because accepting a small amount of information loss can give a huge payoff in terms of the compression ratio possible. However, graphical representation is quite free from such lossy affair; rather it is a lossless operation. Application of Fuzzy Logic Every figure is unique. So two handwritten signatures [4], produced by an identical person, can never be identical. This difference can be attributed to the different packets of dots that construct the image. It is obvious that some dots of two packets are identical but some have different co-ordinates causing ultimate difference in between two signatures. However, different

types of graphical signatures can be transmitted uniquely. But this variation caused by different dots is to be considered instead of confusion or rejection. This imprecise situation can be managed by fuzzy logic. For, fuzziness does bear a precise meaning. In our daily life situations, we always experience a large number of attributes which are not precise. But human brain always processes such imprecise terms. If a doctor asks a patient “how are you”; patient replies “almost OK”. Here the media of communication for information passing is not mathematics but something else which are not well modeled in any way. The hedge “almost” is a vague term. But interestingly doctor processes this information in his brain and takes action accordingly. Actually fuzzy sets can handle imprecision by using truth values between the usual “true” and “false”. A symbol is called “genera” when it applies to a multiplicity of objects and retains only a common essential feature, it is ambiguous when it may denote several unrelated objects. But the fuzziness of a symbol lies in the lack of precise boundaries of the set of objects to which it applies. In 1975 Zadeh made an extension of the concept of a fuzzy set by a interval valued fuzzy set. Zadeh constructed a method of approximate reasoning using his i-v fuzzy sets [8]. Subsequently Gorzalczany studied the i-v fuzzy sets for approximate inference [3]. Fuzzy relations have been studied and applied by many authors in several directions like pattern recognitions, character recognitions. To recognize the signature patterns Nassery and Faez constructed a new approach using pseudo Zernike moments [5] and fuzzy logic criteria, according to statistical aspects of input space, which led to satisfactory experimental results. This method also brought following remarkable benefits. (i). It is rotation, scaling and shifting invariant and releases all environmental side-effects and also some physical spurious problems such as natural hand short vibrations. (ii). After the learning process that takes place only once, each input pattern can be classified almost rapidly. (iii). It is always applicable, provided that initial information is enough for classification. However input space complexity may cause huge and long learning process calculations. (iv). It adapts human thinking in many aspects. For example its accuracy in each class is directly dependent on number of the class prototypes. However the default accuracy can be varied by changing the initial fuzzy sets number and amount of overlap.

Standard Frame Every figure must be judged in the light of standard dimension. A figure may be larger or in diminutive form than the standard specification. Then that figure either to be reduced or enlarged to cage into standard frame as it usually happens in case of photographic film of a camera. Equidistant Line (∂x) A plane can be divided into infinite number of equidistant straight lines both horizontally or vertically. Let ∂x is the distance between two straight lines. This value of ∂x is very important and must be equal both in source and destination. Otherwise the image will suffer from distortion. So, before transmission the value of ∂x should clearly be defined and communicated as well. Method of Coding The co-ordinates of each dot should be identified first. The searching of dots present in each line may be performed from top to bottom i.e., vertically. In a line there may exist more than one dot. In such a case the dots to be searched from left to right. In case of retrieving the same method will follow i.e., from left to right. However, searching of dots present in a line may also be done from right to left and retrieving of data should be accordingly from right to left. A line may not have any dot. In such a case, the pointer will go ahead in search of next dot. If the number of blank lines is more, then a loop may be used for the blank lines till the pointer reaches to the next dot present in a new line. Data Storage After coding next comes data storage. Data storage of co-ordinate values can be done both in decimal and binary form. Instant Transmission Instead of data storage data can be transmitted to construct the image instantly. Decimal and Binary Representation In decimal the length of co-ordinate values will be variable but in binary representation the

bits will be fixed in number. Now for storage of identical value decimal may take lesser bit than the fixed length binary code that needs larger number of bits causing higher length and time as well. Example: Let a dot has the co-ordinate value (x, y) = (1, 3). If we denote the x-coordinate by 1 and y-co-ordinate by 0 then in decimal this may be represented as 1 and 000. Thus it will take 4 bits in total. But in case of binary representation say in 3-bit operation the corresponding co-ordinate value of decimal 1 and 3 will be 001 and 011 causing 6 bits in length. In case of 4-bit operation the binary form of 1 and 3 will be 0001 and 0011 totaling 8 bits. But the length of decimal will remain same i.e., 4 bits like before. Thus in case of binary operation due to higher length storage is liable for greater cost and time than decimal. However, in case of higher values decimal takes larger number of bits than fixed length binary code. Example: Decimal 7 is represented by binary 111 i.e., 3-bit operation and decimal 15 is represented by binary 1111 i.e., 4-bit operation. It means to represent decimal 7, decimal needs 7 bits but binary needs 3 bits. Similarly, to represent decimal 15, decimal needs 15 bits but binary needs 4 bits. Method of Transmission All the co-ordinates thus stored may be sent as stream of bits either in decimal or binary form. From stream of bits every dot can be identified by its co-ordinates. Thus a pair of coordinates which identifies a dot must be separated from the successive co-ordinates by a termination sign of a dot. This separation is very important and will occur just after passing of a pair of co-ordinates. Otherwise, error will occur. For example, the last co-ordinate(y) of any dot may inadvertently take the 1st co-ordinate(x) of the successive dot creating a new pair of coordinates that does not at all exist in that stream of bits. This type of error occurs mainly in case high speed of transmission. As such, more than 5 bits should not be transmitted for the sake of reliability of data transmission. This problem can be solved through fragmentation of each x and y co-ordinate. However, this type of error will be liable to render the entire stream of bits faulty causing distorted image. As such, in case of communication there should be different termination signs viz., DE (Dot End), BOR (Beginning Of Record), EOR (End Of Record), BL(Blank Line), ACK (Acknowledgement), etc. If the gap, between two successive lines

containing dots, is long then a loop may be used for repetitive operation. When vertical line number is considered sign of y-co-ordinate (+y and –y) becomes insignificant. But value of xco-ordinate will always be +ve i.e., +x. Method of Decoding As stated already, every dot has its two coordinates. So, every pair of co-ordinates of the stream of bits will produce the unique dot again. This co-ordinate value of dot can be stored or through dots thus decoded image can be constructed instantly. Bit pattern in decimal In decimal let x and y co-ordinate be represented by 1 and 0 bit respectively. So, every dot will start by bit 1 and finish by bit 0. Now, from stream of bits every dot can readily be identified uniquely by this algorithm. However, bit pattern in decimal is variable in nature. Bit pattern in binary Generally the bit pattern i.e., length of coordinate both in decimal and binary are variable in nature. In binary system every co-ordinate may be represented by the combination of both 1 and 0 bit. So, from stream of bits it is difficult to identify the co-ordinate of any dot. But in decimal system this problem has been solved by representing two co-ordinates either by 1 or 0. As such in binary system the algorithm of fixed length may be adopted to overcome this error. Then there will be no confusion whether the bits be composed of by the combination of 1 and 0. In such a situation every co-ordinate can be identified by its fixed length. For example, in 2D system in case of 3-bit algorithm every dot will require 6 bits to represent its both co-ordinates and in 4-bit algorithm every dot will require 8 bits to represent its two co-ordinates. Similarly, in 3D, bits required in 3-bit system and 4-bit systems are 9 and 12 bits respectively. Like wise in 4D case bits required in 3-bit system are 12 and 16 bits respectively. In this way the algorithm of multi-dimension may be introduced whenever required. Method of Image Construction The data thus received should be plotted from top to bottom and from left to right to construct the image. Here the image will always be in the

1st and 4th quadrant of XY axis. It means the image will always be in the right hand side of Y axis. Here, the value of x- co-ordinate will always be +ve and that of y will be both +y and – y. Also, the image can be constructed in all four quadrants. Thus the plotting of dots depends on the value of co- ordinates. Now it seems clear that dot is the building bloc unit of image construction. And two co-ordinates make a dot. Thus formation of dot is not a problem. Because it needs no termination sign at all. All the dots of a line will be plotted from left to right. When all the dots of a line are plotted then there comes the signal to start a new line. A line may not contain any dot. In such a case the cursor will proceed to the next line. In case of a long gap there may be a loop till the cursor reaches a line having dot. The blank line message will act accordingly. Value of Data In case of right hand side image the value of x will always be positive and that of y will be both +y and –y. The image may be spread in all 4 quadrants. In such a case the values of coordinates will be +x, -x, +y and –y. Retrieve of Value The data may be stored instead of image processing. In case of construction of figure the value of data may be retrieved and process accordingly. Here, retrieve can be done either call by value or call by reference. Virtual Image Construction In case of 2D image two co-ordinates are required. Similarly value of dot containing 3 coordinates, 4 co-ordinates can be transmitted for the formation of 3D, 4D images. Similarly n coordinates thus transmitted will construct ndimensional virtual image that, from mathematical point of view, has theoretical interest only. Conclusion & Future Direction Graphical representation, with the help of fuzzy logic, simplifies the method of pattern recognition, image processing, finger print, voice recognition, eye detection [7], etc., thus to offer unique Id. and has immense applications. It is recommend to use reconfigurable devices to run and evaluate graphical hand-written signature verification algorithms in order to provide

practical results; such as: error rate (good signature rejection / wrong signature acceptance), algorithm throughput (number of verification per second) etc.

[4].M.H. Shirali-Shahreza & K. Faez, “Recognition Of Handwritten Farsi…” ICSPAT, 1994 Conference, pp 998-1003, Oct 18-21 1993, Texas, USA

Reference

[5].P. Nassery & K. Faez, “Signature Pattern Recognition Using Pseudo Zernike Moments and a Fuzzy Logic Classifier” 1996 IEEE, pp196-200

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