| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 100 === This thesis proposes an algorithm named Histogram Mixture Model Genetic Algorithm (HMMGA) combining histograms and mixture models for estimation of the gray level distributions of images. The most important and difficult problem for the finite mixture model is to decide the number of components. In this thesis, we solve this problem by using the genetic algorithm to evaluate the optimal coefficients of Gaussian functions. Beside of the coefficients, the genetic algorithm with the sum of square error (SSE) as the fitness function evaluate some other parameters of Gaussian function are determined. The SSE is the sum of square error between the curve of a frequency diagram and one of the linear combination of Gaussian functions. A frequency diagram is a histogram divided by the total number of the image pixel, where the histogram of an image gives the counting the number of every gray level.
In this thesis, the experiments test both synthetic images and real images to demonstrate the accuracy of proposed HMMGA method. We define the accuracy by the misclassification rate. By testing synthetic images, the HMMGA method has a better accuracy than Otsu method. The threshold of HMMGA is closer to the theoretically optimal threshold than the threshold of Otsu method. Results for testing real images demonstrate that HMMGA has better segmentation than Otsu method.
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