Saturday, April 24, 2010

Fuzzy Image Processing

Image processing is any form of information processing for which both the input and output are images, such as photographs or frames of video. Most image processing techniques involve treating the image as a two-dimensional signal and applying standard signal processing techniques to it. There are various techniques for processing an image such as linear scaling, optical ethods, digital processing, fuzzy techniques..
The few examples of fuzzy techniques are: Fuzzy contrast adjustment, Subjective Image Enhancement, Fuzzy Image Segmentation Fuzzy Edge Detection, Image enhancement:
The various image processing techniques employed such as linear scaling, optical methods have not been able to handle the disturbances occurring in processing an image Hence Fuzzy techniques used in processing an image, have evolved as the most efficient solution for this problem. These techniques with fuzzy sets give much-improved image compared to the others. Fuzzy techniques help us to cope up with the day-to-day problems
arising in the field of image processing


An image is defined as two dimensional function of f(x,y) ,where x ,y are spatial co-ordinates. Amplitude of f at any pair co-ordinates of x, y is called the intensity or gray level of image at that point.
The useful paradigm in determining an image type is to consider three types of computerized processors-low, mid and high level.
Low-level processors involve primitive operations such as image processing to reduce noise, contrast enhancement and sharpening. They are characterized by the fact that both its input and outputs are images.
Mid level processing of images involves tasks such as segmentation-(partitioning image into regions or objects).It characterized by the fact that its inputs are images but its output are attributes extracted from those images.
High level involves “ making sense ” of an ensemble of recognized object as an image analysis and performs cognitive functions normally associated with vision.
Image processing is any form of information processing for which both the input and output are images, such as photographs or frames of video. Most image processing techniques involve treating the image as a two-dimensional signal and applying standard signal processing techniques to it
The simplest processing method is linear scaling . In linear scaling one pixel from source image is multiplied by a scale factor, then an offset value is added. The original pixel value is then replaced with the resulting value. This process is applied on each pixel in the image.
A few decades ago, image processing was done largely in the analog domain, chiefly by optical devices. These optical methods are still essential to applications such as holography because they are inherently parallel; however, due to the significant increase in computer speed, these techniques are increasingly being replaced by digital image processing methods.
Digital image processing techniques are generally more versatile, reliable, and accurate; they have the additional benefit of being easier to implement than their analog counterparts. Specialized hardware is still used for digital image processing: computer architectures based on pipelining have been the most commercially successful. There are also many massively parallel architectures that have been developed for the purpose. Today, hardware solutions are commonly used in video processing systems. However, commercial image processing tasks are more commonly done by software running on conventional personal computers.
In recent years, many researchers have applied the fuzzy logic to develop new image processing algorithms. The Fuzzy image processing is one of the important application areas of fuzzy logic.

Some of the most commonly noticed problem while working with images are:
• Geometric transformations such as enlargement, reduction, and rotation
• Color corrections such as brightness and contrast adjustments, quantization, or conversion to a different color space
• Registration (or alignment) of two or more images
• Combination of two or more images, e.g. into an average, blend, difference, or image composite
• Interpolation, demosaicing, and recovery of a full image from a RAW image format like a Bayer filter pattern
• Segmentation of the image into regions
• Image editing and digital retouching
• Extending dynamic range by combining differently exposed images (generalized signal averaging of Wyckoff sets)
Besides static two-dimensional images, the field also covers the processing of time-varying signals such as video and the output of tomographic equipment. Techniques such as morphological image processing are specific to binary or grayscale images.
Most of the signals processing concepts that apply to one-dimensional signals also extend to the two-dimensional image signal. Some of these one-dimensional signal processing concepts become significantly more complicated in two-dimensional processing. Image processing brings some new concepts, such as connectivity and rotational invariance that are meaningful only for two-dimensional signals.
The Fourier transform, using coherent optics or digital fast Fourier transform is often used for image processing operations involving large-area correlation.
one dimentional techniques:
• Resolution
• Dynamic range
• Bandwidth
• Filtering
• Differential operators
• Edge detection
• Domain modulation
• Noise reduction
Two-dimensional techniques:
• Connectivity
• Rotational Invariance
• Scale-Space Representation
• Photography and Printing
• Satellite Image Processing
• Medical Image Processing
• Face Detection, Feature Detection, Face Identification
• Microscope Image Processing
• Car Barrier Detection
Fuzzy image processing (FIP) is the collection of all approaches that understand, represent and process the images, their segments and features as fuzzy sets. The representation and processing depend on the selected fuzzy technique and on the problem to be solved.
Fuzzy image processing has three main stages:
1. Image Fuzzification
2. Modification of membership values
3. Image Defuzzification
The steps fuzzification and defuzzification are due to the fact that there is no fuzzy hardware. Therefore, the coding of image data (fuzzification) and decoding of the results (defuzzification) make possible to process images with fuzzy techniques. The main power of fuzzy image processing is in the middle step (modification of membership values). After the image data are transformed from gray-level plane to the membership plane (fuzzification), appropriate fuzzy techniques modify the membership values. This can be a fuzzy clustering; a fuzzy rule-based approach, a fuzzy integration approach and so on.
The most important reasons for FIP are as follows:
1. Fuzzy techniques are powerful tools for knowledge representation and processing
2. Fuzzy techniques can manage the vagueness and ambiguity efficiently
In many image-processing applications, expert knowledge is used to overcome the difficulties (e.g. object recognition, scene analysis). Fuzzy set theory and fuzzy logic offer us powerful tools to represent and process human knowledge in form of fuzzy if-then rules. On the other side, many difficulties in image processing arise because the data/tasks/results are uncertain. This uncertainty, however, is not always due to the randomness but to the ambiguity and vagueness. Beside randomness which can be managed by probability theory can distinguish between three other kinds of imperfection in the image processing
• Grayness ambiguity
• Geometrical fuzziness
• Vague (complex/ill-defined) knowledge
These problems are fuzzy in the nature. The question whether a pixel should become darker or brighter than it already is, the question where is the boundary between two image segments, and the question what is a tree in a scene analysis problem, all of these and other similar questions are examples for situations that a fuzzy approach can be the more suitable way to manage the imperfection.
Fuzzy image processing is a collection of different areas of fuzzy set theory, fuzzy logic and fuzzy measure theory.
The most important theoretical components of fuzzy image processing:
• Fuzzy Geometry (Metric, topology,)
• Measures of Fuzziness and Image Information (entropy, correlation, divergence, expected values,)
• Fuzzy Inference Systems (image fuzzification, inference, image defuzzification)
• Fuzzy Clustering (Fuzzy c-means, possibility c-means,)
• Fuzzy Mathematical Morphology (Fuzzy erosion, fuzzy dilation,)
Fuzzy set:
Fuzzy set theory is the extension of conventional (crisp) set theory. It handles the concept of partial truth (truth values between 1 (completely true) and 0 (completely false)). It was introduced by Prof. Lotfi A. Zadeh of UC/Berkeley in 1965 as a mean to model the vagueness and ambiguity in complex systems.
Fuzzy geometry:
The digital geometry plays a key role in many image processing applications. Generally, the gray-level images will be threshold to calculate geometrical measures such as area, perimeter, diameter, compactness etc. of an object. Since the images or their segments have ill-defined or non-crisp boundaries, it is sometimes appropriate to consider them as fuzzy sets.
• Fuzzy Contrast Adjustment
• Subjective Image Enhancement
• Fuzzy Image Segmentation
• Fuzzy Edge Detection
• Image enhancement:

Image segmentation:
The different theoretical components of fuzzy image processing provide us with diverse possibilities for development of new segmentation techniques. The following table gives a brief overview of different fuzzy approaches to image segmentation:
F approach Brief Description
Fuzzy Clustering Algorithms Fuzzy clustering is the oldest fuzzy approach to image segmentation. Algorithms such as fuzzy c-means (FCM, Bezdek) and possibilistic c-means (PCM, Krishnapuram & Keller) can be used to build clusters (segments). The class membership of pixels can be interpreted as similarity or compatibility with an ideal object or a certain property.
Fuzzy Rule-Based Approach If we interpret the image features as linguistic variables, then we can use fuzzy if-then rules to segment the image into different regions. A simple fuzzy segmentation rule may seem as follows:
IF the pixel is dark
AND its neighbourhood is also dark AND homogeneous
THEN it belongs to the background.
Fuzzy Integrals Fuzzy integrals can be used in different forms:
Segmentation by weightening the features (fuzzy measures represent the importance of particular features)
Fusion of the results of different segmentation algorithms (optimal use of individual advantages)
Segmentation by fusion of different sensors (e.g. multispectral images, fuzzy measures represent the relevance/importance of each sensor)
Measures of Fuzziness and image information Measures of fuzziness (e.g. fuzzy entropy) and image information (e.g. fuzzy divergence) can be also used in segmentation and threshold tasks..
Fuzzy Geometry Fuzzy geometrical measures such as fuzzy compactness (A. Rosenfeld) and index of area coverage (S.K. Pal and A. Ghosh) can be used to measure the geometrical fuzziness of different regions of an image. The optimization of these measure (e.g. minimization of fuzzy compactness regarding to the cross-over point of membership function) can be applied to make fuzzy and/or crisp pixel classification

Fuzzy edge detection:
There are different possibilities for development of fuzzy edge detectors:
1.Definition of appropriate membership functions
2.Rule-based fuzzy edge detection
Image Enhancement:

In image processing, some objective quality criteria are usually used to ascertain the goodness of the results (e.g. the image is good if it possesses a low amount of fuzziness indicating high contrast). The human observer, however, does not perceive these results as good because his judgment is subjective. This distinction between objectivity and subjectivity is the first major problem in the human-machine-interaction. Another difficulty is the fact that different people judge the image quality differently. This inter-individual difference is also primarily due to the aforesaid human subjectivity.
1. The various image processing techniques employed such as linear scaling, optical methods have not been able to handle the disturbances occurring in processing an image.
2. Fuzzy techniques used in processing an image have evolved as the most efficient solution for this problem.
3. These techniques with fuzzy sets give much-improved image compared to the others

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