Research And Application Of Image Segmentation Based On Partial Differential Equations

Image segmentation is the important process of image analysis and understanding.Partial differential equations(PDE)as an important branch of mathematics,has strong theoretical system,and its numerical solution algorithms are constantly being developed and updated.Currently,PDE has been applied to image denoising,image segmentation,image reconstruction,image restoration and other fields,and has achieved great success.The whole paper takes PDE model realization as the fundamental mainline,summarizes the status of PDE image segmentation and application,and sums up the theory of level set and L1 regularization at the process of PDE solution.Three PDE models are proposed for image segmentation,and are applied for the video image sequence moving target segmentation and wood defects classification,the experimental results show the effectiveness and reality value of the proposed PDE image segmentation model.First,the cultural C-V(Chan-Vese)level set image segmentation model is proposed,abbreviated as CC-V model,the model takes use of cultural algorithms characteristics of global optimization to solve the C-V level set initial parameter setting problem.The CC-V model sets the initialization segmentation parameters at wide range of cultural algorithms initial population space,and then guides the population evolution through the situational knowledge and the normative knowledge in the belief space to realize the segmentation parameters global optimization,finally can stop at proper time according to the image entropy fitness value.The CC-V model improves the segmentation effect of C-V model through the initial parameters setting.The experimental results show that the CC-V model is better than C-V model.The PDE image segmentation models were applied for video image sequence moving target segmentation.First,quickly build background modeling using block statistical histogram,then obtain the contours of moving targets and take multi-targets minimum exterior rectangle as model segmentation initial contours using background subtraction,finally realize the moving target segmentation taking use of stop criteria DRLSE(Distance Regularized Level Set Evolution)model,C-V model and CC-V model.The experimental results show the reality value of the proposed CC-V model for moving target segmentation.Second,the adaptive global minimization segmentation model is proposed,the model adds the edge detection function to the total variation of CEN(Chan-Esedoglu-Nikolova)model.The adaptive global minimization segmentation model combines edge and region active contour(AC)model,has the ability of intensity inhomogeneity image segmentation.At the process of image segmentation,it can adaptively change the decline speed of edge detection function depend on the active contour gray value of inside and outside,so can keep more images details structure at high segmentation efficiency.The experimental results for medical image,synthetic image and intensity inhomogeneity image illustrate the advantage of proposed segmentation model.The three parameters of probabilistic Rand index,variation of information and global consistency error were used to evaluate the model segmentation accuracy,adaptive global minimization model compared to the CEN model has higher segmentation accuracy.The experimental results of adaptive global minimization model for video image sequence moving target segmentation further illustrate the usefulness of the model.Third,the NL-CEN(nonlocal CEN)segmentation model is proposed for the texture image segmentation problem based on nonlocal process PDE.L1 regularization is the basic mathematical model on image denoising and compressive sensing signal reconstruction in the field of image processing,the Split-Bregman algorithm for nonlocal image segmentation and compressive sensing signal reconstruction has a very high computational efficiency.The NL-CEN model improves the total variation option of CEN model to the nonlocal total variation,measures the similarity depend on cumulative distribution function and wasserstein distance between the image blocks,realizes the segmentation algorithm use of Split-Bregman iteration based on the nonlocal PDE image segmentation.The comparison of typical texture image segmentation results show the NL-CEN model advantages for natural texture image segmentation.The NL-CEN model is applied to the video image sequence moving target segmentation,segmentation efficiency higher than CC-V model,lower than the adaptive global minimization model.Fourth,on the basis of PDE segmentation model realization,the PDE image segmentation models are applied for wood defect classification.First,using PDE image segmentation models obtain wood defect segmentation,second,using mathematical morphology process segmentation results,remove excessive small structure and empty hole,finally using the feature data among the inside region gray mean value,the outside region gray mean value,the defect inscribed rectangle region gray mean value and texture features,defect region circularity,distinguish the dry knot,live knot and worm holes three types of wood defect.The classification accuracy rate shows the CC-V model,adaptive global minimization model and NL-CEN image segmentation effectiveness and application value in practice.