Compared with classic integer-order calculus, fractional calculus is a more powerful mathematical method that non-linearly preserves and enhances image features in different frequency bands. In order to extend fractional-in-space diffusion scheme with matrix-valued diffusivity to perform superior image inpainting, the authors build the new fractional-order tensor regularisation (FTR) model by utilising the newly defined fractional-order structure tensor (FST) to control the regularisation process. The proposed model is derived as a process that minimises a functional proportional to the FST composed of the inner product of the fractional derivative vector and its transposition; hence, the new model not only inherits genuine anisotropism of tensor regularisation, but is also better equipped to handle subtle details and complex structures because of the characteristics of fractional calculus. To minimise the proposed functional, the corresponding Euler-Lagrange equation is deduced, and the anisotropism of the proposed model is analysed accordingly. Fractional-order derivative masks in positive x
 and y
 directions and negative x
 and y
 directions are implemented according to the shifted Grumwald-Letnikov definition, and a proper iterative numerical scheme is analysed. According to experimental results on various test images, the proposed FTR inpainting model demonstrates superior inpainting performance both in noiseless and noisy scenarios.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-ipr.2016.1004

Fractional-order tensor regularisation for image inpainting

The performance of classifier algorithms used for predictive analytics highly dependent on quality of training data. This requirement demands the need for noise free data or images. The existing partial differential equation based diffusion models can remove noise present in an image but lacking in preserving thin lines, fine details and sharp corners. The classifier algorithms can able to make correct judgement to which class the image belongs to only if all edges are preserved properly during denoising process. To satisfy this requirement the authors proposed a new improved partial differential equation based diffusion algorithm for edge preserving image denoising. The proposed new anisotropic diffusion algorithm is an extension of self-snake diffusion filter which estimates edge and gradient directions as eigenvectors of a structure tensor matrix. The unique feature of this proposed anisotropic diffusion algorithm is diffusion rate at various parts of an image matches with the speed of level set flow. In the proposed algorithm an efficient edge indicator function dependent on the trace of the structure tensor matrix is used. The proposed model performs best in preserving thin lines, sharp corners and fine details since diffusion happens only along edges and diffusion is totally stopped across edges in this model. The additional edge-stopping term which is a vector dot product of derivative of an edge stopping function and derivative of an image computed along gradient and edge orthogonal directions is used in this model as shock filter which enables increased sharpness at all discontinuities. The performance of proposed diffusion algorithm is compared with other classical diffusion filters like conventional perona-malik diffusion, conventional self-snake diffusion methods.

Improved self-snake based anisotropic diffusion model for edge preserving image denoising using structure tensor

The invention relates to a method for constructing morphological operators by using adaptive quasi-circular structural elements on the basis of a nonlinear structure tensor. For overcoming the shortcoming that by a linear structure tensor, inaccurate and even mistaken gradient information is easily estimated, the nonlinear structure tensor replaces the linear structure tensor at first, a feature value and a feature vector of the nonlinear structure tensor are calculated, then two measurement parameters including edge strength measurement and angular point strength measurement are defined, image features such as an edge region, a smooth region and corner are distinguished clearly, so that long semi-axes, short semi-axes and directions of adaptive oval structure elements are defined, in order to enable the obtained adaptive structure elements to be close to prefect oval shapes, the oval structural elements and original images are subjected to interpolation processing, and finally morphological operators such as adaptive corrosion, expansion, opening operation, closing operation and hit or miss transformation are redefined by the proposed adaptive quasi-circular structural elements. Confirmatory experiment results show that compared with other methods, the method has good effects in the aspects of structure adapting, angular point protection, filtering, target extracting and the like.

Method for constructing morphological operators by using adaptive quasi-circular structural elements on basis of nonlinear structure tensor

Brachytherapy is a form of radiation treatment for cancer that involves the placement of sealed radioactive sources inside or in close proximity to the tumour in order to deliver radiation dose to the cancerous cells. Although the growing use of imaging has improved the quality of treatment the patients receive, there are still challenges to overcome. In cervical brachytherapy the radiation dose is delivered using an applicator. The applicator position is used for treatment planning therefore misplacement of the applicator could result in inaccurate treatment, increased levels of toxicity in healthy tissues and even punctures in the uterus during the insertion process. During the insertion the applicator is not visible therefore the treatment may be compromised. It was shown in previous studies that the applicator displacement between each brachytherapy was greater than 1cm. The main question to achieve applicator tracking was to examine if the electromagnetic tracking system that is used to track the ultrasound probe during image registration could be used to solve this issue. Through this thesis a tracking system methodology was developed and its accuracy was measured in a trial and in clinic. For the phantom trial the magnitude of error was measured to be ≈ 3mm and for the clinical evaluation of the tracking system at Royal Surrey County hospital (RSCH) the magnitude of error was measured to be ≈ 5mm. In prostate brachytherapy a computer tomography (CT) scan is performed to the patient in order to aid the veriﬁcation process but unfortunately the seeds produce multiple artefacts that make the veriﬁcation process diﬃcult and sometimes impossible because the contour of the prostate is not clear therefore the dosimetry results are inaccurate. A ﬁlter methodology was developed to address that issue by performing exemplar image inpainting for the corrupted portion of post prostate CT images. The ﬁltered images were qualitatively compared with a state of the art ﬁlter for reducing metal artefact. Additionally the ﬁlter is currently being evaluated in a study where the aim is to measure the inter-observer reliability of contouring the prostate in unﬁltered and ﬁltered in post prostate brachytherapy CT scans. Two observers from the RSCH agreed on contouring 11 patient dataset for this study. There are only preliminary results for this study but they do not show any improvements in contouring the prostate. The trial is still on-going therefore more data will show the actual eﬀect of the ﬁlter.

New imaging techniques for brachytherapy

The extend structure tensor (EST) is a valuable descriptor for the texture feature of image. However, EST is highly dimensional data which would bring more computational complexity and local minimum in some image. Traditional dimension reduction approaches for EST may not full use of the inherent characteristics of image. In order to solve this problem, a new scalar texture descriptor based on invariant of the EST is presented in this paper. The scalar texture descriptor is composed of the eigenvalues of EST, and used the relationship between the eigenvalues and the element of the EST to avoid direct the computation . Then the scalar texture descriptor is embedded into the segmentation model we proposed which utilizes both global and local image information. The fast energy minimization algorithm instead of the level set method is applied to solve the model. Finally, the experiments on some synthetic and real images are show the efficiency and robustness of the our model.

Image Segmentation Using A New Scalar Texture Descriptor based on Extended Structure Tensor.

A variety of structure-adaptive filters are proposed to overcome the blurred effects of image structures caused by the classical Gaussian weighted mean filter. However, two major issues are needed to be dealt with carefully for structure-adaptive anisotropic filters. One is to properly construct the filter kernel and the other is to accurately estimate the orientation of the image structures. In this paper we propose to improve the structure-adaptive anisotropic filtering approach based on the nonlinear structure tensor NLST analysis technique. According to the anisotropism measurements of image structures, a new kernel construction method is designed to make the filter shape fine adapted to image features. Through the accurately estimated orientation of the image structures, the filter kernels are then properly aligned to perform the filtering process. Experimental results show that the proposed filter denoises the noisy images carefully and image features, such as corners and junctions are well preserved. Compared with some other known filters, the proposed filter obtains great improvements both in Mean Square Error MSE and visual quality.

/pdf/improved-structure-adaptive-anisotropic-filter-based-on-a-2ezbegjp6z.pdf

Zhigang Ren

Papers

Improved structure-adaptive anisotropic filter based on a nonlinear structure tensor