Research On Fast Algorithm Of Multi-threshold OTSU

In the field of image processing,image segmentation is a basic work,,however,image segmentation is a significant and challenging research topic,It has a wide range of applications in pattern recognition,Computer Vision,ML,and medical image processing.Image segmentation is a basic work in image processing,which is the basis of image understanding and image recognition,The main purpose of image segmentation is to extract the objects of interest from the complex background,so as to lay the foundation for the next target recognition and scene analysis.Compared with other methods,threshold segmentation method is simple,efficient and easy to understand,so it is the most widely used technology.Among them,the Otsu method as a representative algorithm in the threshold method has very good segmentation performance and accuracy.The principle of Otsu method is based on two important functions,namely maximum variance and minimum class variance analysis and get the optimal segmentation threshold based stability is very good,the success rate is also in line with most of the requirements.Another point is that the Otsu method is not affected by the contrast and brightness of the image under certain conditions,so it can be used in most real-time image processing systems.The Otsu method is based on the principle of least squares.The basic idea is that the best threshold should be chosen to make the maximum separation degree between the results of the segmentation.In order to make the Otsu method adapt to more complex images,many scholars have carried out the multi threshold.But with the increase of threshold number,multi threshold Otsu is used for the traditional exhaustive method to find the optimal threshold,and the variance calculation parameters in the process of calculation formula without corresponding optimization,.Therefore,the multi threshold Otsu method has the disadvantages of high computation complexity,high time complexity and low efficiency.Aiming at this problem,this paper studies the fast algorithm of multi threshold Otsu,first of all,the mathematical properties of the optimal threshold selected by the multi threshold Otsu are studied,and the efficiency of the Otsu algorithm is optimized based on the basic theory,It is proved in theory that the optimal threshold value obtained by using the multi threshold Otsu method and the mathematical relation between the intra class mean of the class obtained by the threshold segmentation,The relationship is according to the properties of the optimal threshold and the classical multi threshold Otsu algorithm and exhaustive search the shortcomings of low efficiency,the establishment of a new search model.The model is based on the properties of multi threshold Otsu algorithm the optimal threshold for the effective pruning of the search tree,can automatically analyze the search during calculating threshold is Otsu the optimal threshold can be independent of the end of the search process,greatly reducing the threshold range,the redundant threshold interval most are eliminated.From the theoretical principle for the fast algorithm are analyzed,as a result of this algorithm is deduced based on Otsu theory,so it is a strict fast algorithm of multi threshold Otsu,the optimal threshold is obtained in accordance with the strict Otsu criteria.Although these methods have been optimized to a certain extent,the Otsu algorithm is not a linear algorithm,and the efficiency of the algorithm is decreased with the increase of the threshold number,In view of the above problems,this paper presents a new fast algorithm,the time complexity of this algorithm is completely linear,not because of the increase in the number of threshold exponential growth,for the determination of the threshold,the algorithm uses the idea of partition,the search resolution of Otsu multi threshold single threshold search,avoiding the exhaustive search in the process of multi threshold.For the shortcomings of the calculation of the mean value,variance and probability in the calculation of the threshold,the dynamic programming method is used to establish the recursive formula,which greatly reduces the amount of variance between classes,finally,for the search of Otsu threshold,we use the improved multi swarm firefly algorithm to find the optimal value of the objective function,This algorithm theoretically reflects the time complexity optimization,which makes the time complexity of multi threshold Otsu algorithm reduced to O(n).