Research On Image Processing And Sequence Prediction Algorithm Based On Fractal Theory

In recent years,fractal theory has become a research hotspot in image processing,and it has prominent performance in image coding,image classification and texture analysis.At the same time,fractal theory is also increasingly used in time series prediction and analysis.This study improved the fractal dictionary encoding algorithm which Xu Rudan et al.had proposed and extended Xu's fractal dictionary to apply the fractal dictionary encoding to the medical image encoding.At the same time,a new fractal dimension estimating method based on the box-counting method was proposed.Finally,it was proposed to apply the fractal dimension of the curve to the time series prediction.The main tasks included the following:1.For the defects in the application of fractal dictionary coding to CT image coding,the fractal dictionary coding algorithm has been improved,and Xu's fractal dictionary has been extended.The improvement of the coding algorithm solved the problem of “black block and white block reverse” appearing in the CT decoded image;the expansion of the fractal dictionary greatly improved the severe block effect in the CT decoded image by adding extreme edge blocks to the fractal dictionary.The PSNR of the CT image was raised to 30 or more.Finally,combining the characteristics of the CT image itself,it was proposed to use the average value of the gray value of the image block to encode a large-area background area in the CT image.Without affecting the visual effect,the coding time of CT images has been reduced by more than 60%.2.Aiming at the two major shortcomings of the differential box-counting method,a new method based on the box-counting method was proposed to calculate the fractal dimension.The new method proposed to place the pixels of the grayscale image at the vertices of the box used to cover the image.There were three specific improvements: selecting the proper height of the box,improving the calculation of the number of boxes,and proposing a mechanism for changing adjacent blocks.The experimental results showed that compared with the other four methods,the average fitting error of the fractal dimension calculated by the new method was the lowest,as low as 0.007086,which was at least 60% lower than other methods.For images with dramatic texture changes,the new method had the best stability when calculating its fractal dimension.For 112 sets of images with the same texture and different sizes,when calculating the standard deviation of the fractal dimension of each set of images,the standard deviation of the fractal dimension of the 79 images calculated by the new method was the smallest,accounting for about 70.5%.3.Applied the fractal dimension of the merchant history traffic curve to sequence prediction.We used the box dimension method to calculate the fractal dimension of the curve and add this feature to the feature vector.Extremely random tree models in machine learning were used for the prediction of passenger flow sequences.Experimental results showed that the addition of the fractal dimension feature model of the historical data curve can reduce the error of sequence prediction to some extent.