Fuzzy set theory originates to a great extent of interest among the researchers in past decades. It is a key tool to handle the imperfect of information in the diverse field. Typically, it plays a very important role in image processing and found the significant development in many active areas such as pattern recognition, neural network, medical imaging, etc. The use of fuzzy set theory is to tackle uncertainty in the form of membership functions when there is an image gray levels or information is lost. This chapter concerns the preliminaries of fuzzy, intuitionistic fuzzy, type-2 fuzzy and intuitionistic type-2 fuzzy set theory and its application in the fingerprint image; furthermore, the contrast enhancement and edge detection are carried out for that with the assistance of fuzzy set theory. It is useful to the students who want to self-study. This chapter composed just to address that issue.
TopIntroduction
In 1965, Zadeh defined the notion of fuzzy set theory. It deals with degree of membership function. Later in 1985, Atanassov introduced the perception of intuitionistic fuzzy set theory which deals with degree of membership and non-membership function. He discussed the degree of non-membership function is equal to 1 minus degree of membership function, which is not always true, but there may be some hesitation degree will occur in the membership function. Likewise, it begins a vital role in image processing, for example, image enhancement, morphological image, edge detection and so on.
Physical attributes and behavior are the parameters for identifying a person in biometric security. The biometric traits, for example, face, gait, ear, odor fingerprint, hand geometry, iris, retina, hand vein, facial thermogram, signature, voice print, and keystroke dynamics which are exceptionally suitable for human acknowledgment because of their singularity, integrality and consistency (Maltoni, Maio, Jain, & Prabhakar, 2009). Among all biometric traits, fingerprints have the elevated amount of dependability and widely used by criminological specialists as a part of criminal examinations (Figure 1). Fingerprints are fully fledged at around seven months of fetus development and finger ridge configuration don't change duration the life of an individual except due to the accident such as wounds and cuts on the finger. Even for twins, it has never changed (Babler, 1991). Fingerprint patterns are shaped in the epidermis on the fingertip. The ridge orientation map and frequency map, pores, incipient ridges, singular points, dots and minutiae are the features of the fingerprints. Minutiae points are strictly defined by the ridge ending and bifurcation points. Fingerprint image have contained three types of patterns like Arch, Loop and Whorl and have nine- types of classifications, namely, arch, tent arch right loop, left loop, double loop, right pocket loop, left pocket loop, whorl, and mixed figure (Jain, Flynn, & Ross, 2007).
Image enhancement is required before handling any image. It assumes a principal part in image handling where human specialists make vital choices in view of image data. It is utilized to restore an image that has decayed or to improve certain elements of an image. The purpose behind image improvement is to change an image to another structure that is more suitable for further handling. To recognize the crime person, fingerprint examiner should have a decent knowledge of the images. Fingerprint images are poorly illuminated and hardly visible and many regions and boundaries are ambiguous in nature. Along these lines, if the quality of the image is enhanced, handling might get to be less demanding. Consequently, fingerprint image enhancement is extremely important. In an enhanced image, it becomes easier for forensic departments to identify the crime individuals. Image enhancement partitioned into contrast enhancement and edge enhancement.
The motivation behind contrast enhancement is to build the general visual differentiation of the image, which the human eye can envision unmistakably, to be more qualified for further examination. It is useful when the intensity of important regions of images such as fingerprint image, latent fingerprint image and it turns out be exceptionally hard to make out the structure with the human eye. Contrast enhancement and edge enhancement are utilized to expand the region of low intensity and unclear edges respectively. The histogram equalization is the most used crisp method of image enhancement among the gray-level transformation and modification. Clearly, fingerprint images are less in quality and contain uncertainties, so crisp may not improve the image appropriately. The mathematical tools are needed to overcome with such kind of vague images, for example, fuzzy set theory and some advanced fuzzy set theories such as intuitionistic fuzzy set and type-2 fuzzy set. It considers some more uncertainties are used to obtain better quality images comparable than fuzzy set.