Geometric Variational Principle Based Image Processing Method

This paper studies some theoretical and practical problems in image processing usingthe principle of geometrical variation.In the theoretical part,we propose a uniform frame to tackle the models of energyminimization using the techniques of compressed sensing and operator splitting.Thesemodels include 1)denoising models based on L₁ regularization;2)denoising and de-blurring models based on L₁ regularization;3)denoising models based on total varia-tion regularization;4)denoising models based on weighted total variation regularization;5)denoising and de-blurring models based on total variation regularization;6)generalmodels based on total variation regularization;7)denoising models based on dictionarymethod and total variation regularization;8)denoising and de-blurring models based ondictionary method and total variation regularization;9)denoising and de-blurring modelswith updated dictionary;10)denoising and texture removal models with updated dictio-nary;and 11)denoising and texture removal models with small scale dictionary.We showtheir energy functionals and the corresponding iteration formulas for minimizers.In the application part,we propose a registration and data fusion method for imageswith different resolutions and modalities using mutual information.Given one high res-olution grey image and one low resolution color image,our aim is to construct a highresolution color image.Our first stage is the registration,and the second stage is the datafusion.In the stage of registration,we compute the local mutual information between thegrey image and the non-rigid deformations of the color image,as well as the local mutualinformation between the color image and the non-rigid deformations of the grey image.The images are regarded as registered if the local mutual information reaches maximal.The second stage,data fusion,is using the two registered images from the first stage.Af-ter registration,the low resolution color image has become a high resolution color image,although the colorization is performed by a coarse technique:interpolation.Thus the highresolution image is regarded to be an image with noise,and the second stage is actually a denoising process.The high the noise,the lower the mutual information between thehigh resolution color image and grey image.Therefore,the denoised image is the imagewhich has the maximal mutual information with the grey image,and it can be obtainedby the minimization of the negative mutual information.We also improve the geodesic active contour (GAC) and Chan-Vese models.Weintroduce a discrimination function of object(s) of interests (OOI) into the stopping func-tion of both models.Therefore,the evolution curves of the improved GAC and Chan-Vesemodel will no longer stop at any locations with large gradients.Instead,they will stop atthe boundaries of OOI.Experimental results of remotely sensed images show the effec-tiveness of the algorithms.