Research On Problem Of Digital Image Segmentation And CT Image Reconstruction With Variational Theory

Image segmentation is the process of extracting some regions, namely foreground or target, from the whole image, and obtains the boundary of the target at the same time. Several algorithms have been developed for image segmentation, and the variational approach based on variational framework has attached significant attentions due to its unique advantage. Another topic of this thesis, image reconstruction is the process of acquiring shape information of 3-dimentional objects by processing metrical information measured by equipment. X-ray computed tomography(CT) based image reconstruction is a very important application of image reconstruction. The procedure of CT scanning is composed by the following three steps. First, X-rays are emitted from the X-ray generator. Then, X-rays pass through the 3-dimensional object. At last, metrical information of this object are measured by equipment. CT based image reconstruction can then reconstruct 2-dimensinal slices from these metrical information. In this way, many diseased tissues can be easily identified from these 2-dimensional slices.This thesis focuses on image segmentation and CT image reconstruction using the varational approach. A new segmentation scheme is inspired by the representation formula of the level set function. Also, we introduced Mumford Shah Total Variation into the energy function of CT image segmentation and developed a new CT image segmentation method based on this idea. The main contributions of this thesis are:1. For inhomogeneous image, its gray intensity will present a complex behavior.Typically, pixels near boundary of images will have inhomogeneous gray intensities,and the rest pixels will have homogeneous gray intensities. Thus, this thesis devised an adaptive function with parameters, which can adaptively adjust the weight between the global features and local features of image. We also improved initial estimates of level set function by filtering the level set function with Gaussian function, this lead to a significant performance boost. The proposed method overcomes the segmentation difficulty of inhomogeneous image by considering the behavior of the inhomogeneous image and collecting statistical information of image regions.2. The thesis integrates CT image reconstruction and CT image segmentation into a variational framework through a new energy function. We can obtain two outcomes,the reconstructed image and its boundary. In the actual implementation, we cast the proposed method as a constrained optimization. The whole algorithm is composed by the following three steps. We first reconstructed CT image from the metric data. Then,we extract the corresponding boundary. And the CT image is denoised at the last.These three steps are not standalone. In fact, they affect each others. Besides, this three-step optimization strategy can deal with different image more flexibly. In case that CT image has a strong noise, we will spend more time for denoising the CT image. Finally, experiments shows that the new proposed method has a better reconstructed image and a clearer boundary than the traditional Total variation based reconstruction method.