Research Of Level Set Image Segmentation Based On Rough Set Theory And The Extended Watershed Transformation

Image segmentation is an important technique for image processing,and of great significance in computer vision for a variety of applications,e.g.object recognition,scene analysis,or image retrieval.The problems of image segmentation have received an extensive attention in the past decades.Among many different methods and techniques,the level set image segmentation method which is the active contour model implemented via a level set method has been successfully applied.The advantage of this method is that the image segmentation problem is transformed to an energy minimization problem.Since the contour of the object regions can be described implicitly by the zero-level set of a high dimensional function,it can flexibly deal with the topological changes for the evolution of the contour.Although many successful level set image segmentation models have been proposed in different ways.There are some problems yet to be solved practically such as the problems of low accuracy and low iterative efficiency produced by the models for various types of images,the problems of low iterative efficiency,too expensive time complexity,and quite sensitiveness to initial segmentation caused by the models for images with serious inhomogeneity.A new feature selection method along with its algorithm is proposed on the basis of the ordered discernibility set and the significance of feature in rough set theory.Firstly,a novel algorithm for the simplified discernibility-matrix is proposed without being sorted and at a fewer cost of traversing,which can notably raise the speed of simplification to obtain the ordered and simplified discernibility set.Secondly,a new criterion of the significance of feature combined with the ordered and simplified discernibility set is put forward as a new method for features selection.The worst-case time complexity of this feature selection algorithm is less than the other ones based on discernibility-matrix.Lastly,many comparative experiments show that the new feature selection method is effective and can largely yield a minimal feature selection set.In order to avoid hardware restrictions,a complementary algorithm for image data feature selection is also proposed.The result of image data feature selection produced by this complementary algorithm or the aforementioned algorithm will be used to construct the new level set image segmentation model for images with intensity inhomogeneity.Aiming at the problems of segmentation models for various types of images,both definition and method of image data discretization are proposed based on the rough set theory and applied to an improved Kernel Mapping(KM)model and a new level set segmentation model(REK).The image discretization enhances intensity homogeneity so that the region parameters can better express the gray value among the evolving regions.Hence the image can be more accurately segmented.Experimental results on synthetic and natural images show that the improved KM model has better segmentation quality and iteration efficiency than KM model.A new energy functional of REK is proposed on the basis of image data discretization and proved right in theory,which can be used to deal with many types of images.By using the weighted kernel function to map discrete image data into a higher dimension,the proposed model can segment many types of images,even in a certain noise-signal ratio.The new energy functional and the region parameters which are deduced by this energy functional can better express the gray level of the homologous region.Therefore,the proposed model can properly and accurately segment the image.Compared with the traditional methods,the new level set function is constructed by using a new energy functional and the information of the discrete regions from the image,each element from the level set function may have a different step-size during iteration.The higher the weight value,the faster the element is updated and the less iteration the method has.Experiments on synthetic images,brain images and natural images demonstrate that REK model is superior in terms of accuracy and iteration efficiency as compared with LIF model,KM model and BCLBF model.To address the abovementioned problems,the level set image segmentation is not limited to using the innovations based on rough set theory.An extended watershed transformation method based on spring simulation is introduced and its corresponding algorithm is presented to preprocess the image data.The extended watershed transformation can provide the weighted information for evolving level set function and for updating region parameters.Moreover,it reduces the impact of noise and intensity inhomogeneity.Because the image data discretization can also improve intensity homogeneity,the differences between them are presented in this dissertation.A new level set image segmentation model is proposed based on the extended watershed transformation,which is called EWK model,and its theoretical proof is also given.Compared with the popular KM model and MBCLBF model,EWK model can achieve better segmentation results for various types of color images in terms of iteration efficiency,segmentation accuracy and initialization robustness.Aiming at the problems of segmentation models for images with serious inhomogeneity,a new local region-based level set image segmentation model is proposed on the basis of image data feature selection,which is named as LSISFS model.The redundant points of the local region will be removed after the features selection and then the computational cost of the level set image segmentation can be reduced.The value of the feature point is close to the average value of a local region and it will have the priority to be selected.This will also indirectly play roles of the low-pass filter and the intensity inhomogeneity correction to improve the segmentation accuracy.Therefore,traditional term of bias field correction can be removed in performing the level set image segmentation.In the first iteration,a pre-specified threshold for the initialization of the level set contour can result in implementing the rough threshold segmentation which can be regarded as the coarse pre-segmentation.Traditionally,the threshold segmentation methods are free from the initial contour conditions,and thus the LSISFS model is not sensitive to the shape,size,and position of the initial contour.Experiments on images with serious inhomogeneity further demonstrate the advantages of the LSISFS model over the LBF,BCLBF,MBCLBF,and LSACM models in terms of both iteration efficiency and initialization robustness.