http://research.engr.oregonstate.edu/immiscibles/sites/research.engr.oregonstate.edu.immiscibles/files/Papers/Wildenschild_Sheppard_AWR_2012.pdf

X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems

This paper presents a robust and fully automatic filter-based approach for retinal vessel segmentation. We propose new filters based on 3D rotating frames in so-called orientation scores, which are functions on the Lie-group domain of positions and orientations $\mathbb {R}^{2} \rtimes S^{1}$ . By means of a wavelet-type transform, a 2D image is lifted to a 3D orientation score, where elongated structures are disentangled into their corresponding orientation planes. In the lifted domain $\mathbb {R}^{2} \rtimes S^{1}$ , vessels are enhanced by means of multi-scale second-order Gaussian derivatives perpendicular to the line structures. More precisely, we use a left-invariant rotating derivative (LID) frame, and a locally adaptive derivative (LAD) frame. The LAD is adaptive to the local line structures and is found by eigensystem analysis of the left-invariant Hessian matrix (computed with the LID). After multi-scale filtering via the LID or LAD in the orientation score domain, the results are projected back to the 2D image plane giving us the enhanced vessels. Then a binary segmentation is obtained through thresholding. The proposed methods are validated on six retinal image datasets with different image types, on which competitive segmentation performances are achieved. In particular, the proposed algorithm of applying the LAD filter on orientation scores (LAD-OS) outperforms most of the state-of-the-art methods. The LAD-OS is capable of dealing with typically difficult cases like crossings, central arterial reflex, closely parallel and tiny vessels. The high computational speed of the proposed methods allows processing of large datasets in a screening setting.

Robust Retinal Vessel Segmentation via Locally Adaptive Derivative Frames in Orientation Scores

Generation of 3D representative volume elements for heterogeneous materials: a review

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research.In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1C84F0E91BF20EC36D8E846EF8CCB830/S0962492918000016a.pdf/div-class-title-modern-regularization-methods-for-inverse-problems-div.pdf

Modern Regularization Methods for Inverse Problems

This paper presents new structural statistical matrices which are gray level size zone matrix (SZM) texture descriptor variants. The SZM is based on the cooccurrences of size/intensity of each flat zone (connected pixels with the same gray level). The first improvement increases the information processed by merging multiple gray-level quantizations and reduces the required parameter numbers. New improved descriptors were especially designed for supervised cell texture classification. They are illustrated thanks to two different databases built from quantitative cell biology. The second alternative characterizes the DNA organization during the mitosis, according to zone intensities radial distribution. The third variant is a matrix structure generalization for the fibrous texture analysis, by changing the intensity/size pair into the length/orientation pair of each region.

Advanced Statistical Matrices for Texture Characterization: Application to Cell Classification

Computed tomography is a non-destructive testing technique based on X-ray absorption that permits the 3D-visualisation of materials at micron-range resolutions. In this article, computed tomography is used to investigate fibre orientation and fibre position in various fibre-reinforced materials such as ceramic matrix composites, glass fibre-reinforced plastics or reinforced concrete. The goal of this article is to determine the quantitative orientation of fibres in fibre-reinforced materials. For this purpose, a mathematical technique based on the structure tensor is used to determine the local orientation of fibres. The structure tensor is easy to implement and results in a fast algorithm relying solely on local properties of the given reconstruction. In addition, the local X-ray transform is used to denoise fibres and to segment them from the matrix.

Determination of the fibre orientation in composites using the structure tensor and local X-ray transform

We introduce a fast image processing system that allows to analyse digital data-bases of retinal images in a short time, and to process the image in situ while the patient is examined. While it achieves a comparable quality as state-of-the-art methods, it differs from most of them by the fact that it is extremely fast. Retinal blood vessels are enhanced via convolution with the second derivative of the local Radon kernel. It is rotated by different angles, and it adapts itself via a maximisation procedure to the vessel directions. We combine smoothing along vessel directions with contrast enhancement across them. We detect vessels as connected structures with very few interruptions. A subsequent skeletonisation allows a higher-level description of the vessel tree. To end up with a very fast system, we combine efficient algorithms for numerical integration, differentiation and interpolation, and we propose an automatic parameter selection strategy. Our convolution kernels are precomputed and stored into cached constant memory. All essential subroutines are intrinsically parallel, and the resulting system is implemented on GPUs using CUDA. Our qualitative evaluations with the DRIVE database and our own database show that the system achieves competitive performance. It is possible to process images of size 4, 288 × 2, 848 pixels in 1.2 s on an NVIDIA Geforce GTX680. Compared to our sequential implementation, this amounts to a speed-up by two orders of magnitude.

/pdf/fast-retinal-vessel-analysis-cdabnof7qy.pdf

Fast retinal vessel analysis

For the automatic detection of retinal blood vessels a preprocessing of the noisy original images is necessary. Retinal blood vessels are assumed to be line-like structures and can therefore be enhanced via convolution with suitable, elongated kernels. Consequently we use the local Radon kernel as a prototype of an elongated kernel for this task. The Radon kernel is rotated at different angles and adapts via a maximisation procedure to the directions of the vessels. The proposed algorithm is easy to implement and combined with edgeand coherence-enhancing anisotropic diffusion as a preprocessing step it offers higher robustness than the Laplacian of Gaussian or Haralick operator. Furthermore, our algorithm detects vessels as connected structures with very few interruptions. The performance is evaluated in experiments on the publicly available databases DRIVE and STARE as well as on selected examples of our clinical database. Since our algorithm does not depend on a priori directional and branching models, in its generality it is capable to detect other vessel structures in the human eye such as the conjunctiva vessels.

/pdf/retinal-vessel-detection-via-second-derivative-of-local-4838rgtdxh.pdf

Retinal vessel detection via second derivative of local radon transform

The detection of cracks and micro-cracks in materials or structures is an important and non-trivial task. A typical method is optical microscopy, providing a 2D image with the crack showing as a line in the material. The use of 3D-visualisationmethods, such as computed tomography (CT), permits the visualisation of materials as complete 3D volumes. In this case, occuring cracks are locally plane-like structures that can be described as 2D surfaces with a 3D topography. To receive the necessary data, the images of the investigated objects are obtained via X-ray computed tomography, providing a 3D-visualisation of materials at micron-range resolutions. In this article, computed tomography is used to investigate cracks in composite materials such as short-fibre reinforced carbon fibre reinforced plastics (CFRP). The goal of this article is to detect all relevant cracks inside an object in a stable way, reducing the effect of noise. The results show the cracks to be smooth and locally connected, resulting in connected components containing a large number of voxels. For this purpose, a mathematical technique based on the local Radon transform is applied. In order to achieve an improvement in speed, the structure tensor is applied to guess the orientation of the local structure. The aim is to determine cracks and to follow crack growth and evolution to increasing loads.

(Micro)-Crack detection using local Radon transform

Computed tomography (CT) has become a common analysis method in the materials sciences.
It allows the internal visualisation of the complete volume of an object, providing 3D information about the internal structures.
One field where CT is applied is the examination of fibre-reinforced composite structures.
Fibre-reinforced composites are typically composed of two types of material, mainly of high strength fibres embedded in a surrounding matrix.
In this material class, the fibres typically determine the strength of the composite materials, which is largely dependent on the orientation of the fibres.
Knowledge of the fibre orientation is therefore essential for the evaluation of maximal loading or for the prediction of failure.
The easiest way to determine the fibre orientation is to compute it from the reconstructions received from the tomograph.
A different method to determine fibre orientation is to compute it directly from Radon data
using the combination of reconstruction and image analysis introduced by Louis [A. K. Louis, Combining Image Reconstruction and Image Analysis with an Application to 2D - Tomography,
SIAM J. Imaging Sciences 1 (2008), 188--208].
This can be achieved by adapting the reconstruction process in computed tomography by the use of anisotropic, elongated convolution filters,
leading to a set of reconstruction kernels that are dependent on the angle of the projections, thereby reflecting the anisotropy of the filters.
In this paper, the two-dimensional case of computing fibre orientation directly from simulated Radon data is presented.

Michael Krause

Papers

Determination of the fibre orientation in composites using the structure tensor and local X-ray transform

Fast retinal vessel analysis

Retinal vessel detection via second derivative of local radon transform

(Micro)-Crack detection using local Radon transform

Computing the fibre orientation from Radon data using local Radon transform