APPLICATION OF FUZZY LOGIC AND PSO IN SOME IMAGE PROCESSING AND ANALYSIS METHODS

Abstract

Image processing and analysis play key role in many spheres of today’s hi-tech life of mankind. Image processing methods such as image enhancement, image compression, image registration and image analysis tasks like edge detection, segmentation, recognition are of immense use in many day to day applications. Image properties by nature are expressed more appropriately in a subjective manner. In addition to this, image processing and analysis need to deal with many ambiguous situations. Fuzzy set theory, developed by Zadeh, is a useful mathematical tool for handling such ambiguity and subjective issue. Accordingly, fuzzy logic has been used in the past to solve many image processing and image analysis problems. Many image processing and image analysis methods require optimization of certain image parameters so as to achieve the desired goal. Traditional optimization techniques require formulating or approximating an objective function that is to be maximized or minimized so as to optimize the desired attribute. However, this may not be possible in cases where the image property to be optimized can only be defined subjectively. Also, difficulties associated with mathematical optimization in complex problems can only be tackled by following non-traditional and after heuristic optimization techniques. Evolutionary algorithms have recently been developed for the purpose. These algorithms are stochastic search methods that are inspired by the natural biological evolution and/or the social behavior of species such as reproduction, mutation and recombination, selection, swarming and foraging. Genetic algorithm (GA), particle swarm optimization (PSO), bacterial foraging algorithm (BFA) and ant colony optimization (ACO) are few examples of such popular evolutionary techniques used for optimization. Among these, the particle swarm optimization is one very widely used optimization technique due to its simplicity in operation, use of few parameters and relatively fast and stable convergence. In this thesis work, we have identified three image processing and image analysis applications that have been appropriately implemented by applying fuzzy logic along with particle swarm optimization. These three problems are image enhancement using gamma correction, edge detection and object boundary detection using active contour model. Images are underexposed when taken under low light conditions. Enhancement of such images is always a matter of key concern to attain the maximum possible details of an image. Gamma correction is one popularly used method for image enhancement. However, the ix Abstract method is effective only when the value of ‘gamma’ is appropriately chosen. Accordingly, ‘gamma’ value selection may be accomplished via optimization of the image exposure level. This in turn requires quantification of the image exposure level. Since the level of exposure is subjective and no standard measure for image exposure level is available, the same may be estimated using fuzzy measures. We propose to estimate the exposure level in an image by a set of fuzzy rules where the input parameters of the fuzzy rules are important image properties like image pixel mean intensity and variance, and the output parameter is in terms of exposure level of the given image. Based on this information of exposure level, ‘gamma’ value is chosen in such a manner so that exposure level of the enhanced image is optimum (neither overexposed nor under exposed). This is achieved by particle swarm optimization. Edge detection is one of the fundamental issues in image analysis. An edge is a set of connected pixels lying on the boundary between two regions that differ in pixel intensity. Accordingly, several gradient-based edge detectors have been developed that are based on measuring local changes in gray-value. A pixel is declared to be an edge pixel when the local change in the gray value at that pixel point is significant. However, since no absolute ground truth for the gradient threshold is available, clear demarcation between the pixels with high local intensity gradient (edge pixels) and those with low intensity gradient (non-edge pixels) does not exist. Fuzzy-based approach may be used to handle such ambiguous nature of the edge structures while the optimum gradient threshold may be selected via minimization of the overall probability of error in identifying edge pixels. In our research, we propose to use a set of fuzzy rules to estimate the edge strength. This is followed by selecting a threshold – only pixels having edge strength above the threshold are considered to be edge pixels. This threshold is selected such that the overall probability of error in identifying edge pixels, i.e. the sum of the probability of misdetection and the probability of false alarm, is minimum. Objective function minimization is achieved via PSO algorithm. This way optimal thresholding for image binarization is achieved by using fuzzy theory and optimization. Active contour models, popularly known as snakes, are quite popular for several applications such as object boundary detection, image segmentation, object tracking and classification. A snake is an energy minimizing curve that, starting from an initial contour, deforms iteratively thereby gradually moving towards the desired object boundary. Finally, it shrinks and wraps around the object. Therefore, the problem at hand is to find the contour that minimizes the snake energy. While energy minimization may be accomplished using traditional optimization methods, approaches based on nature-inspired evolutionary algorithms have been developed in recent years. One such evolutionary algorithm that has been used extensively in active contours is the particle swarm optimization. However, conventional PSO converges slowly and gets trapped in local minimum easily. The problem of local minimum results in inaccurate detection of concavities in the object boundary. In our proposed active contour model, we propose two different approaches. The first approach is based on multi-swarm PSO in which a swarm is set in the two-dimensional x Abstract image space for every control point in the snake and then all the swarms search for their best positions simultaneously and collaboratively through information sharing among them. Multi-swarm PSO helps in convergence due to the parallel nature of the algorithm. The second approach considers the whole contour as a point in an N-dimensional complex space, where N is the number of control points defining the contour. That is, the contour is represented by an N-dimensional complex vector; each element of the vector corresponds to the coordinate of a control point in the image space given in a complex number form. The object boundary is obtained by searching for the best position (minimum snake energy) of this N-dimensional point using particle swarm optimization procedure. The performance of the search process is further enhanced by using dynamic adaptation of the inertia factor. Inertia factor is used to balance the global and local search ability. We propose to use a set of fuzzy rules to adjust the inertia weight on the basis of the current normalized snake energy and the current value of inertia. Inertia updating based on the current state of the algorithm gives a good compromise between global and local search, as necessary. The proposed method is not only able to capture concavity more accurately but is also free from manual tuning of the inertia weight.