### Concept: Level set

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##### Assessment of the renal corticomedullary (23)na gradient using isotropic data sets

- OPEN
- Academic radiology
- Published over 6 years ago
- Discuss

(23)Na magnetic resonance imaging is a promising technique for the noninvasive imaging of renal function. Past investigations of the renal corticomedullary [(23)Na] gradient have relied on imaging only in the coronal plane and on cumbersome calculations of [(23)Na], which require the use of external phantoms. The aim of this study is therefore two-fold: to use an isotropic three-dimensional data set to compare coronal measurements of renal [(23)Na] relative to measurements obtained in planes along the corticomedullary gradients and to investigate cerebrospinal fluid (CSF) (23)Na signal as an internal reference standard, obviating the need for time-intensive [(23)Na] calculations.

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##### Situating the default-mode network along a principal gradient of macroscale cortical organization

- OPEN
- Proceedings of the National Academy of Sciences of the United States of America
- Published about 3 years ago
- Discuss

Understanding how the structure of cognition arises from the topographical organization of the cortex is a primary goal in neuroscience. Previous work has described local functional gradients extending from perceptual and motor regions to cortical areas representing more abstract functions, but an overarching framework for the association between structure and function is still lacking. Here, we show that the principal gradient revealed by the decomposition of connectivity data in humans and the macaque monkey is anchored by, at one end, regions serving primary sensory/motor functions and at the other end, transmodal regions that, in humans, are known as the default-mode network (DMN). These DMN regions exhibit the greatest geodesic distance along the cortical surface-and are precisely equidistant-from primary sensory/motor morphological landmarks. The principal gradient also provides an organizing spatial framework for multiple large-scale networks and characterizes a spectrum from unimodal to heteromodal activity in a functional metaanalysis. Together, these observations provide a characterization of the topographical organization of cortex and indicate that the role of the DMN in cognition might arise from its position at one extreme of a hierarchy, allowing it to process transmodal information that is unrelated to immediate sensory input.

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##### Reinitialization-Free Level Set Evolution via Reaction Diffusion

- IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
- Published over 7 years ago
- Discuss

This paper presents a novel reaction-diffusion (RD) method for implicit active contours that is completely free of the costly reinitialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in an RD-LSE equation, from which a piecewise constant solution can be derived. In order to obtain a stable numerical solution from the RD-based LSE, we propose a two-step splitting method to iteratively solve the RD-LSE equation, where we first iterate the LSE equation, then solve the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly reinitialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and partial differential equation-based level set method. The RD-LSE method shows very good performance on boundary antileakage. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.

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##### An improved variational level set method for MR image segmentation and bias field correction

- OPEN
- Magnetic resonance imaging
- Published almost 7 years ago
- Discuss

In this paper, we propose an improved variational level set approach to correct the bias and to segment the magnetic resonance (MR) images with inhomogeneous intensity. First, we use a Gaussian distribution with bias field as a local region descriptor in two-phase level set formulation for segmentation and bias field correction of the images with inhomogeneous intensities. By using the information of the local variance in this descriptor, our method is able to obtain accurate segmentation results. Furthermore, we extend this method to three-phase level set formulation for brain MR image segmentation and bias field correction. By using this three-phase level set function to replace the four-phase level set function, we can reduce the number of convolution operations in each iteration and improve the efficiency. Compared with other approaches, this algorithm demonstrates a superior performance.

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##### A Lagrangian level set-like method for modelling and simulation in bioengineering.

- Computer methods in biomechanics and biomedical engineering
- Published about 7 years ago
- Discuss

The level set method has been used for 20 years in a wide range of physical applications to track moving interfaces instead of an explicit description of the geometry. This paper studies in detail the shape of the level set function, delimiting a sub-domain in solid mechanics, with an innovative update method based on the computation of a displacement field obtained with the values of the level set function. A criterion based on the values of the level set function is proposed in order to assign the material properties. With the help of this criterion, an optimal approach is proposed, which predicts an accurate evolution of the sub-domain boundary. To validate this method, it was first applied in two dimensions to a through-thickness hole plate case, and then to the cases of brain tumour expansion and grasping to demonstrate the applicability of the method.

#### 28

##### Efficient algorithm for level set method preserving distance function.

- IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
- Published over 7 years ago
- Discuss

The level set method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. First, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the level set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient l(1) optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods prove to be 5-6 times faster than standard distance preserving level set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our method stays generic and can be applied to any level set methods that require the distance information.

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##### Phenological response of a key ecosystem function to biological invasion

- Ecology letters
- Published almost 4 years ago
- Discuss

Although climate warming has been widely demonstrated to induce shifts in the timing of many biological events, the phenological consequences of other prominent global change drivers remain largely unknown. Here, we investigated the effects of biological invasions on the seasonality of leaf litter decomposition, a crucial freshwater ecosystem function. Decomposition rates were quantified in 18 temperate shallow lakes distributed along a gradient of crayfish invasion and a temperature-based model was constructed to predict yearly patterns of decomposition. We found that, through direct detritus consumption, omnivorous invasive crayfish accelerated decomposition rates up to fivefold in spring, enhancing temperature dependence of the process and shortening the period of major detritus availability in the ecosystem by up to 39 days (95% CI: 15-61). The fact that our estimates are an order of magnitude higher than any previously reported climate-driven phenological shifts indicates that some powerful drivers of phenological change have been largely overlooked.

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##### Analytical energy gradients for explicitly correlated wave functions. II. Explicitly correlated coupled cluster singles and doubles with perturbative triples corrections: CCSD(T)-F12

- The Journal of chemical physics
- Published over 1 year ago
- Discuss

We present an implementation of analytical energy gradients for the explicitly correlated coupled cluster singles and doubles method with perturbative triples corrections [CCSD(T)-F12]. The accuracy of the CCSD(T)-F12 analytical gradient technique is demonstrated by computing equilibrium geometries for a set of closed-shell molecules containing first- and second-row elements. Near basis-set limit equilibrium geometries are obtained with triple-zeta correlation consistent basis sets. Various approximations in the F12 treatment are compared, and the effects of these are found to be small.

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This paper presents a novel two-stage image segmentation method using an edge scaled energy functional based on local and global information for intensity inhomogeneous image segmentation. In the first stage, we integrate global intensity term with a geodesic edge term, which produces a preliminary rough segmentation result. Thereafter, by taking final contour of the first stage as initial contour, we begin second stage segmentation process by integrating local intensity term with geodesic edge term to get final segmentation result. Due to the suitable initialization from the first stage, the second stage precisely achieves desirable segmentation result for inhomogeneous image segmentation. Two stage segmentation technique not only increases the accuracy but also eliminates the problem of initial contour existed in traditional local segmentation methods. The energy function of the proposed method uses both global and local terms incorporated with compacted geodesic edge term in an additive fashion which uses image gradient information to delineate obscured boundaries of objects inside an image. A Gaussian kernel is adapted for the regularization of the level set function and to avoid an expensive re-initialization. The experiments were carried out on synthetic and real images. Quantitative validations were performed on Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) 2015 and PH2 skin lesion database. The visual and quantitative comparisons will demonstrate the efficiency of the proposed method.

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##### Enhanced fluidity liquid chromatography of inulin fructans using ternary solvent strength and selectivity gradients

- Analytica chimica acta
- Published almost 2 years ago
- Discuss

The value of exploring selectivity and solvent strength ternary gradients in enhanced fluidity liquid chromatography (EFLC) is demonstrated for the separation of inulin-type fructans from chicory. Commercial binary pump systems for supercritical fluid chromatography only allow for the implementation of ternary solvent strength gradients which can be restrictive for the separation of polar polymeric analytes. In this work, a custom system was designed to extend the capability of EFLC to allow tuning of selectivity or solvent strength in ternary gradients. Gradient profiles were evaluated using the Berridge function (RF1), normalized resolution product (NRP), and gradient peak capacity (Pc). Selectivity gradients provided the separation of more analytes over time. The RF1 function showed favor to selectivity gradients with comparable Pc to that of solvent strength gradients. NRP did not strongly correlate with Pc or RF1 score. EFLC with the hydrophilic interaction chromatography, HILIC, separation mode was successfully employed to separate up to 47 fructan analytes in less than 25 min using a selectivity gradient.