EFFICIENT VARIATIONAL MODELS IN IMAGE SEGMENTATION AND APPLICATIONS

Abstract

Image segmentation is the task of dividing an image into different regions such that each region is homogeneous in color, intensity or texture i.e., the same in some sense. The aim is to select specific features out of an image from distinguishing them from the background. For image segmentation, and in general for image processing, the variational modeling is a well established technique. In this thesis we propose four efficient variational active contour image segmen- tation models to segment variety of hard images. The active contours technique is a famous method in image processing and computer vision due to its simplicity, efficiency and frequent use in application. This method relies on rich mathemat- ical theory and it uses the well-known level set formulation which offers stable numerical schemes. The first new variational model in this thesis is based on signed pressure force functions to segment efficiently images with multi regions/objects. The active con- tour model by Zhang et al [98] is based on the signed pressure force (Spf) function which may segment two phase constant intensity images but it may not segment multi region images or images having multiple objects of various intensities. We will introduce generalize averages and Spf functions to develop a model for multi region segmentation. We will see that these averages and Spf functions hold good mathematical properties and provide efficient results on hard images. The second new variational model in this thesis is a two phase model based on two fitting terms which utilizes regions and edges enhanced quantities respec- tively from multiplicative and difference images to segment images efficiently with intensity inhomogeneity. The case of images with essentially piecewise constant intensities is satisfactorily dealt within the well-known work of ChanVese (2001) and its many variants. However for images with intensity inhomogeneity or multi- vphases within the foreground of objects, such models become inadequate because the detected edges and even phases do not represent objects and are hence not meaningful. Tests and comparisons will show that our new model outperforms two previous models. Both synthetic and real life images are used to illustrate there reliability and advantages of our new model. The third new model in this thesis is the extension of our second model to a multi-phase model for segmenting images having noise and intensity inhomogeneity at the same time. In proposed model, the segmentation process is carried out via locally computed function which is updated with local means on image domain. To ensure that locally computed function truly reflects local and global features of a given image other than noise, we employ two data terms from well known denoising models. These data terms produce efficient results in noise and handle intensity inhomogeneity. Comparative experiments show the advantages of the proposed method. Furthermore, the proposed algorithm maintains the performance on clean and noisy vector-valued images. Finally, we propose a novel variational image selective segmentation model in which we utilize an enhanced image information. By utilizing the average image of channels, which handles texture and noise, our model is capable to selectively segment and extract objects with noise and textural details. Recently developed models for selective segmentation [11, 12, 44, 48] are not designed for the case when objects of interest are textural. Experiments show that the proposed method achieves better results than the latest selective segmentation models. Moreover, the proposed approach maintains the performance in real and synthetic color images. Overall, in this research work we are concerned with efficient variational models which can robustly segment images with intensity inhomogeneity, noise, texture and multiphases within the foreground of objects.