The main objective of image enhancement is to process the image so that the result is more suitable than the original image for a specific application. Image enhancement is a field that is being used in various areas and disciplines. In this paper we study how fuzzy logic can be used in image processing and with image enhancement. A case study on Diagnosis of Pulmonary Embolism is also given to show the use of image enhancement with fuzzy logic in diagnosing medical diseases.
Key Words: Image Enhancement, Fuzzy Logic, Fuzzy Image Processing, Fuzzy Image Enhancement, Pulmonary Embolism.
The principle objective of Image Enhancement  is to process an image so that the result is more suitable than the original image for a specific application. The word specific is important because a method useful for enhancing X-ray images may not necessarily be the best approach for enhancing the pictures of Mars transmitted by the space probe. Image Enhancement approaches fall in two broad categories:
The term Spatial Domain refers to the image plane itself and the approaches in this category are based on direct manipulation of pixels in an image. Frequency Domain processing techniques are based on modifying the Fourier transform of an image.
Advances in computers, microcontroller and DSP boards have opened new horizons to digital image processing, and have opened many avenues to the design and implementation of new innovative techniques.
Fuzzy logic  has rapidly become one of the most successful of today's technologies for developing sophisticated control systems. The reason for which is very simple. Fuzzy logic addresses such applications perfectly as it resembles human decision making with an ability to generate precise solutions from certain or approximate information. It fills an important gap in engineering design methods left vacant by purely mathematical approaches (e.g. linear control design), and purely logic-based approaches (e.g. expert systems) in system design.
On the other hand , many difficulties in image processing arise because the data/task/result is uncertain. This uncertainty is not always due to the randomness but due to ambiguity and vagueness. Besides randomness which can be managed by probability theory, there are other three kinds of uncertainty in image processing, these are:
- Grayness Ambiguity
- Geometrical Fuzziness
- Uncertain Knowledge
These problems are fuzzy in nature. The question that whether the pixel should become darker or brighter than it already is, the question where the boundary between two segments, all of these and other similar questions are examples for situations where a fuzzy approach can be the more suitable ways to manage the uncertainties.
What Is Fuzzy Image Processing?
Fuzzy image processing is not a unique theory. It is a collection of different fuzzy approaches to image processing. The following definition can be regarded as an attempt to determine the boundaries:
Fuzzy image processing  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:
- Image fuzzification,
- Modification of membership values, and,
- If necessary, Image defuzzification.
The fuzzification and defuzzification steps are due to the fact that we do not possess fuzzy hardware. Therefore, the coding of image data (fuzzification) and decoding of the results (defuzzification) are steps that make possible to process images with fuzzy techniques. The main power of fuzzy image processing is in the middle step (modification of membership values, see Fig.2). 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.
Fuzzy Image Enhancement
Fuzzy Image Enhancement is based on gray level mapping into fuzzy plane, using a membership transform function. The aim is to generate an image of higher contrast than the original image by giving the larger weight to the gray levels that are closer to the mean gray level of the image than to those that are farther from the mean. An image I of size MN and L gray levels can be considered as an array of fuzzy singletons, each having a value of membership denoting its degree of brightness relative to some brightness level. For an image I we can write in the notation of fuzzy sets:
Diagnosis of Pulmonary Embolism
What is Pulmonary Embolism?
Pulmonary embolism (PE)  is a blockage of the pulmonary artery or one of its branches, usually occurring when a deep vein thrombus (blood clot from a vein) becomes dislodged from its site of formation and travels, or embolizes, to the arterial blood supply of one of the lungs. This process is termed thromboembolism.
Common symptoms include difficulty breathing, chest pain on inspiration, and palpitations. Clinical signs include low blood oxygen saturation (hypoxia), rapid breathing (tachypnea), and rapid heart rate (tachycardia). Severe cases of untreated PE can lead to collapse, circulatory instability, and sudden death.
Diagnosis is based on these clinical findings in combination with laboratory tests and imaging studies. While the gold standard for diagnosis is the finding of a clot on pulmonary angiography, CT pulmonary angiography is the most commonly used imaging modality today.
Treatment is typically with anticoagulant medication, including heparin and warfarin. Severe cases may require thrombolysis with drugs such as tissue plasminogen activator (TPA) or may require surgical intervention via pulmonary thrombectomy.
The various diagnostic criteria for pulmonary embolism are:
- Modified PIOPED - Prospective Investigation of Pulmonary Embolism Diagnosis .
- Biello's Criteria .
- Inputs from Expert Radiologists.
Inputs to the Fuzzy Machine
- Size of the largest perfusion defect with respect to the size of the lung.
- Number of small (< 25% of a segment) segmental perfusion defects with a normal CXR.
- Number of matched V/Q defects with normal CXR
- Number of non-segmental perfusion defects
- Number of perfusion defects surrounded by normally perfused lung
- Number of corresponding V/Q defects with CXR parenchymal opacity in upper or middle lung zone.
- Number of corresponding V/Q defects with large pleural effusion.
- Number of perfusion defects with substantially larger CXR abnormality.
- Number of moderate matched V/Q defects with normal CXR.
- Number of corresponding V/Q defects with CXR parenchymal opacity in lower lung zone.
- Number of corresponding V/Q defects with small pleural effusion.
- Number of large (>75% of a segment) perfusion defect with normal CXR.
- Number of moderate (25% - 75% of a segment) perfusion defects without CXR abnormality.
The algorithm starts with initialization of image parameters, minimum and maximum gray level. By fuzzification of gray levels (i.e. membership values to the dark, gray, bright) sets gray level. The inference procedure evaluating appropriately the following rules:
- If dark then Black
- If gray then Gray
- If bright then White
Finally, defuzzification of the output using minimum (gmin), maximum (gmax ) and medium (gmid ) of the gray levels such that the new enhanced gray level is computed by the equation:
- Implementation of Fuzzy Logic Inference Engine in the diagnosis of medical diseases is feasible and can be very easily extended to cover different diseases.
- The methods utilized to diagnose Pulmonary Embolism effectively capture the spirit of the modified PIOPED criteria.
- This system has the ability to make accurate and quick diagnosis.
- Intensity adjustment is done to raise the average pixel intensity in the image to a value between 65% and 70%
- Nonlinear mapping using an 'S' curve is used to improve the contrast of the image.
Fuzzy image processing is a powerful tool for formulation of expert knowledge edge and the combination of imprecise information from different sources. The technique discussed for PIOPED gives lower grayness ambiguity.
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