A fast-marching eikonal solver for tilted transversely isotropic media

Fast and accurate traveltime computation for quasi-P waves in anisotropic media is an essential ingredient of many seismic processing and interpretation applications such as Kirchhoff modeling and migration, microseismic source localization, and traveltime tomography. Fast-sweeping methods are widely used for solving the anisotropic eikonal equation due to their flexibility in solving general equations compared to the fast-marching method. However, it has been observed that fast sweeping can be much less efficient than fast marching for models with curved characteristics and practical grid sizes. By representing a tilted transversely isotropic (TTI) equation as a sequence of elliptically isotropic (EI) eikonal equations, we determine that the fast-marching algorithm can be used to compute fast and accurate traveltimes for TTI media. The tilt angle is absorbed into the description of the effective EI model; therefore, the adopted approach does not compromise on the solution accuracy. Through tests on benchmark synthetic models, we test our fast-marching algorithm and discover considerable improvement in accuracy by using factorization and a second-order finite-difference stencil. The adopted methodology opens the door to the possibility of using the fast-marching algorithm for a wider class of anisotropic eikonal equations.

AUTOMATED EXTRACTION OF LIVER OUTLINES FROM COMPUTED TOMOGRAPHY SCAN IMAGES USING A CUDA-BASED SEGMENTATION METHOD

<p><strong>Abstract.</strong> The traditional fast marching algorithm for segmentation of the liver is suitable for processing on the central processing unit (CPU) platform, however, it is not suitable for implementation on Graphics Processing Unit (GPU). The fuzzy connection algorithm is used to extract the blood vessels in the liver, but there is a calculation error. The refinement algorithm is very time consuming when extracting the target skeleton line from the 3D image. In this paper, the fast-marching algorithm and the thinning algorithm are improved, which can be applied to the GPU computing, The fuzzy algorithm is also improved, and the calculation error of the algorithm is solved, making it more suitable for medical image processing. The computing speed of GPU is far faster than CPU. Medical image processing is one of the earliest applications where the computing performance is improved by GPU. These three segmentation methods, fast marching method, fuzzy connecting method and refinement algorithm are very common in medical image segmentation. Because the increment of medical image data results in the extension of computing time for medical image processing, it is necessary to apply the high parallelism of the GPU to speed up these algorithms. The experiment results demonstrate the feasibility of our accelerating algorithm.</p>

Liver Tumor Segmentation from MR Images Using 3D Fast Marching Algorithm and Single Hidden Layer Feedforward Neural Network

Objective. Our objective is to develop a computerized scheme for liver tumor segmentation in MR images.Materials and Methods. Our proposed scheme consists of four main stages. Firstly, the region of interest (ROI) image which contains the liver tumor region in the T1-weighted MR image series was extracted by using seed points. The noise in this ROI image was reduced and the boundaries were enhanced. A 3D fast marching algorithm was applied to generate the initial labeled regions which are considered as teacher regions. A single hidden layer feedforward neural network (SLFN), which was trained by a noniterative algorithm, was employed to classify the unlabeled voxels. Finally, the postprocessing stage was applied to extract and refine the liver tumor boundaries. The liver tumors determined by our scheme were compared with those manually traced by a radiologist, used as the “ground truth.”Results. The study was evaluated on two datasets of 25 tumors from 16 patients. The proposed scheme obtained the mean volumetric overlap error of 27.43% and the mean percentage volume error of 15.73%. The mean of the average surface distance, the root mean square surface distance, and the maximal surface distance were 0.58 mm, 1.20 mm, and 6.29 mm, respectively.