Symmetry based fast marching method for icosahedral virus segmentation

A fast marching algorithm for the factored eikonal equation

The pyruvate dehydrogenase multienzyme complexes are among the largest multifunctional catalytic machines in cells, catalyzing the production of acetyl CoA from pyruvate. We have previously reported the molecular architecture of an 11-MDa subcomplex comprising the 60-mer icosahedral dihydrolipoyl acetyltransferase (E2) decorated with 60 copies of the heterotetrameric (alpha(2)beta(2)) 153-kDa pyruvate decarboxylase (E1) from Bacillus stearothermophilus (Milne, J. L. S., Shi, D., Rosenthal, P. B., Sunshine, J. S., Domingo, G. J., Wu, X., Brooks, B. R., Perham, R. N., Henderson, R., and Subramaniam, S. (2002) EMBO J. 21, 5587-5598). An annular gap of approximately 90 A separates the acetyltransferase catalytic domains of the E2 from an outer shell formed of E1 tetramers. Using cryoelectron microscopy, we present here a three-dimensional reconstruction of the E2 core decorated with 60 copies of the homodimeric 100-kDa dihydrolipoyl dehydrogenase (E3). The E2E3 complex has a similar annular gap of approximately 75 A between the inner icosahedral assembly of acetyltransferase domains and the outer shell of E3 homodimers. Automated fitting of the E3 coordinates into the map suggests excellent correspondence between the density of the outer shell map and the positions of the two best fitting orientations of E3. As in the case of E1 in the E1E2 complex, the central 2-fold axis of the E3 homodimer is roughly oriented along the periphery of the shell, making the active sites of the enzyme accessible from the annular gap between the E2 core and the outer shell. The similarities in architecture of the E1E2 and E2E3 complexes indicate fundamental similarities in the mechanism of active site coupling involved in the two key stages requiring motion of the swinging lipoyl domain across the annular gap, namely the synthesis of acetyl CoA and regeneration of the dithiolane ring of the lipoyl domain.

Intravascular ultrasound (IVUS) is a vascular imaging technique that is used to study atherosclerosis since it has the ability to show the lumen and the vessel wall. Cross-sectional images of blood vessels are produced and they provide quantitative assessment of the vascular wall, information about the nature of atherosclerotic lesions, as well as the plaque shape and size. Due to the ultrasound speckle, catheter artifacts, or calcification shadows, the automated analysis of large IVUS data sets represents an important challenge. A multiple interface 3D fast-marching method is presented for the detection of the lumen and external vessel wall boundaries. The segmentation is based on a combination of region and contour information, namely, the gray level probability density functions of the vessel structures and the intensity gradient. The detection of the lumen boundary is fully automatic. The segmentation method includes an interactive initialization procedure of the external vessel wall border. The segmentation method was applied to 20 in vivo IVUS data sets acquired from femoral arteries. This database contained three subgroups: Pullbacks acquired before balloon angioplasty (n=7), after the intervention (n=7), and at a 1 yr follow-up examination (n=6). Results were compared to validation contours that were manually traced by two experts on more than 1500 individual frames. For all subgroups, no significant difference was found between the area measurements of the segmentation and validation contours for the lumen and external vessel wall. Moreover, high intraclass correlation coefficients (> 0.96) between the area of the manually traced contours and detected boundaries with the fast-marching method were obtained for both vessel layers over the whole database. The segmentation performance was also evaluated with point-to-point contour distances between segmentation results and manually traced contours. A good overall accuracy was obtained with average distances < 0.13 mm and maximum distances < 0.46 mm, indicating a good performance in regions lacking information or containing artifacts. Only small differences of less than a pixel (0.02 mm) were observed between the average distance metrics of each subgroup, which prove the segmentation consistency. This new IVUS segmentation method provides accurate results that correspond well to the experts' manually traced contours, but requires much less manual interactions and is faster.

Computing seismic traveltime constitutes an essential task for seismic imaging and inversion processes. Accurate traveltime computation provides essential parameters for simulating seismic wave propagation, locating seismic sources, establishing velocity models, and seismic imaging. Therefore, a method for calculating seismic traveltime that is accurate, efficient, and stable holds significant research and practical value. The Multi-Stencils Fast Marching (MSFM) method improves upon the Fast Marching Method by employing multiple stencils to enhance accuracy, addressing the issue of significant errors in diagonal directions. However, its computational complexity increases exponentially with the number of stencils, leading to efficiency bottlenecks in large-scale models. This study proposes an enhanced MSFM method incorporating coarse-grid interpolation to compute seismic traveltime in complex velocity models. The technique extends the conventional MSFM framework by refining its narrowband expansion mechanism, utilizing coarse-grid technology to interpolate values from coarse-grid nodes to fine-grid nodes, thereby improving computational efficiency and reducing memory usage. The improved MSFM algorithm is validated using multiple models, demonstrating that it significantly enhances computational efficiency while maintaining good accuracy.

We present an algorithm for computing the closest point, transform to an explicitly described manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for the points in a grid. We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm solves the eikonal equation |∇u| = 1 with the method of characteristics. For many problems, the computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Many query problems can be aided by using orthogonal range queries (ORQ). There are several standard data structures for performing ORQ's in 3-D, including kd-trees, octrees, and cell arrays. We develop additional data structures based on cell arrays. We study the characteristics of each data structure and compare their performance. We present a new algorithm for solving the single-source, non-negative weight, shortest-paths problem. Dijkstra's algorithm solves this problem with computational complexity O ((E + V)log V) where E is the number of edges and V is the number of vertices. The new algorithm, called Marching with a Correctness Criterion (MCC), has computational complexity O (E + RV), where R is the ratio of the largest to smallest edge weight. Sethian's Fast Marching Method (FMM) may be used to solve static Hamilton-Jacobi equations. It has computational complexity O (N log N), where N is the number of grid points. The FMM has been regarded as an optimal algorithm because it is closely related to Dijkstra's algorithm. The new shortest-paths algorithm discussed above can be used to develop an ordered, upwind, finite difference algorithm for solving static Hamilton-Jacobi equations. This algorithm requires difference schemes that difference not only in coordinate directions, but in diagonal directions as well. It has computational complexity O(RN), where R is the ratio of the largest to smallest propagation speed and N is the number of grid points.

The cryo-EM structure of ETB-Gi complex, obtained using the Fusion-G system, provides insights into the distinct activation mechanism and G-protein promiscuity of ETB, aiding in the design of ETB agonists for therapeutic applications.

With the breakthroughs in protein structure prediction technology, constructing atomic structures from cryo-electron microscopy (cryo-EM) density maps through structural fitting has become increasingly critical. However, the accuracy of the constructed models heavily relies on the precision of the structure-to-map fitting. In this study, we introduce DEMO-EMfit, a progressive method that integrates deep learning-based backbone map extraction with a global-local structural pose search to fit atomic structures into density maps. DEMO-EMfit was extensively evaluated on a benchmark data set comprising both cryo-electron tomography (cryo-ET) and cryo-EM maps of protein and nucleic acid complexes. The results demonstrate that DEMO-EMfit outperforms state-of-the-art approaches, offering an efficient and accurate tool for fitting atomic structures into density maps.

Feature extraction from mammographic images using fast marching methods

One of the most popular level set algorithms is the so-called fast marching method. In this paper, a medical image segmentation method is proposed based on the combination of fast marching method and watershed transformation. First, the original image is smoothed using nonlinear diffusion filter, then the smoothed image is over-segmented by the watershed algorithm. Last, the image is segmented automatically using the modified fast marching method. Due to introducing over-segmentation, the arrival time the seeded point to the boundary of region should be calculated. For other pixels inside the region of the seeded point, the arrival time is not calculated because of the region homogeneity. So the algorithm's speed improves greatly. Moreover, the speed function is defmed again based on the statistical similarity degree of the nearby regions. Experiments show that the algorithm can fast and accurately obtain segmentation results ofmedical images.

Cryo-electron microscopy (Cryo-EM) has become central to the study of large-scale molecular interactions and has produced three-dimensional (3D) density maps at various resolutions. Secondary structure element (SSE) identification from volumetric protein density maps is critical for de novo backbone structure derivation in cryo-EM. Multiple methods have been developed to detect helix and β-sheet from density maps at medium resolutions (~5-10A). β-barrel as a special β-sheet structure has been found in many proteins. However, currently there are no methods aimed to automatically and accurately extract the β-barrel as a complete chunk of density from cryo-EM map of β-barrel protein. We present an effective approach, BarrelMiner, to automatically extract the β-barrel region from cryo-EM density maps based on the conspicuous cylindrical shape of β-barrel. BarrelMiner has been tested using ten simulated density maps at 10A resolution and seven experimental cryo-EM maps between 5.5A and 8.25A resolution. The result suggests that BarrelMiner can be used for the detection of β-barrel from medium resolution cryo-EM density maps of β-barrel proteins.

We introduce the Fast Marching farthest point sampling (FastFPS) approach for the progressive sampling of planar domains and curved manifolds in triangulated, point cloud or implicit form. By using Fast Marching methods 2 , 3, 6 for the incremental computation of distance maps across the sampling domain, we obtain a farthest point sampling technique superior to earlier point sampling principles in two important respects. Firstly, our method performs equally well in both the uniform and the adaptive case. Secondly, the algorithm is applicable to both images and higher dimensional surfaces in triangulated, point cloud or implicit form. This paper presents the methods underlying the algorithm and gives examples for the processing of images and triangulated surfaces. A companion report 4 provides details regarding the application of the FastFPS algorithm to point clouds and implicit surfaces.

An accurate and effective FMM-based approach for freehand 3D ultrasound reconstruction

Shape‐from‐shading (SfS) is a fundamental problem in computer vision. Its goal is reconstruction of surface depth (i.e., distance from camera plane) based on a single image of the surface. The problem was introduced in the early 1970s by Horn. A very common assumption in this field is that image projection is orthographic. We will present the orthographic shape‐from‐shading problem and an algorithm for its solution: the fast marching method of Kimmel and Sethian. We shall than reexamine the basis of SfS, which is the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but on its natural logarithm, and as such it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then described; it is a modification of the aforementioned orthographic fast marching method. Then, a comparison of the orthographic fast marching, perspective fast marching, and the perspective algorithm of Prados and Faugeras on synthetic images is are presented. The two perspective methods equate with each other and show better reconstruction results than the orthographic. We then compare the orthographic and perspective versions of the fast marching method on endoscopic images. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real‐life applications in fields such as endoscopy.

Liver segmentation is the fundamental step in computer-aided liver disease diagnosis and surgery planning. In this study, we developed a fully automatic liver extraction scheme based on an adaptive fast marching method (FMM). Firstly, a thresholding operation was applied to remove the ribs, spines and kidneys. Followed by a smooth filter for noise reduction. Secondly, a nonlinear gray scale converter was used to enhance the contrast of the liver parenchyma. The enhanced image is then eroded with 3-voxel radius so that small regions are deleted. The seed points located in the liver were selected automatically. Finally, using the processed image as a speed function, FMM was employed to generate the liver contour. Clinical validation has performed on 30 abdominal computed tomography (CT) datasets. The proposed algorithm achieved an overall true positive rate (TPR) of 0.98. It takes about 0.30 s for a 512×512-pixel slice. The method has been applied successfully for fast and accurate liver segmentation.

Fast marching method assisted permeability upscaling using a hybrid deep learning method coupled with particle swarm optimization