Degree Of Smoothness Research Articles

Optimization of Breast Tomosynthesis Visualization through 3D Volume Rendering.

3D volume rendering may represent a complementary option in the visualization of Digital Breast Tomosynthesis (DBT) examinations by providing an understanding of the underlying data at once. Rendering parameters directly influence the quality of rendered images. The purpose of this work is to study the influence of two of these parameters (voxel dimension in z direction and sampling distance) on DBT rendered data. Both parameters were studied with a real phantom and one clinical DBT data set. The voxel size was changed from 0.085 × 0.085 × 1.0 mm3 to 0.085 × 0.085 × 0.085 mm3 using ten interpolation functions available in the Visualization Toolkit library (VTK) and several sampling distance values were evaluated. The results were investigated at 90º using volume rendering visualization with composite technique. For phantom quantitative analysis, degree of smoothness, contrast-to-noise ratio, and full width at half maximum of a Gaussian curve fitted to the profile of one disk were used. Additionally, the time required for each visualization was also recorded. Hamming interpolation function presented the best compromise in image quality. The sampling distance values that showed a better balance between time and image quality were 0.025 mm and 0.05 mm. With the appropriate rendering parameters, a significant improvement in rendered images was achieved.

WAVELET-BASED FEATURE EXTRACTION FOR MORTALITY PROJECTION

AbstractWavelet theory is known to be a powerful tool for compressing and processing time series or images. It consists in projecting a signal on an orthonormal basis of functions that are chosen in order to provide a sparse representation of the data. The first part of this article focuses on smoothing mortality curves by wavelets shrinkage. A chi-square test and a penalized likelihood approach are applied to determine the optimal degree of smoothing. The second part of this article is devoted to mortality forecasting. Wavelet coefficients exhibit clear trends for the Belgian population from 1965 to 2015, they are easy to forecast resulting in predicted future mortality rates. The wavelet-based approach is then compared with some popular actuarial models of Lee–Carter type estimated fitted to Belgian, UK, and US populations. The wavelet model outperforms all of them.

Groupwise Non-Rigid Registration with Deep Learning: An Affordable Solution Applied to 2D Cardiac Cine MRI Reconstruction.

Groupwise image (GW) registration is customarily used for subsequent processing in medical imaging. However, it is computationally expensive due to repeated calculation of transformations and gradients. In this paper, we propose a deep learning (DL) architecture that achieves GW elastic registration of a 2D dynamic sequence on an affordable average GPU. Our solution, referred to as dGW, is a simplified version of the well-known U-net. In our GW solution, the image that the other images are registered to, referred to in the paper as template image, is iteratively obtained together with the registered images. Design and evaluation have been carried out using 2D cine cardiac MR slices from 2 databases respectively consisting of 89 and 41 subjects. The first database was used for training and validation with 66.6–33.3% split. The second one was used for validation (50%) and testing (50%). Additional network hyperparameters, which are—in essence—those that control the transformation smoothness degree, are obtained by means of a forward selection procedure. Our results show a 9-fold runtime reduction with respect to an optimization-based implementation; in addition, making use of the well-known structural similarity (SSIM) index we have obtained significative differences with dGW with respect to an alternative DL solution based on Voxelmorph.

High-quality vascular modeling and modification with implicit extrusion surfaces for blood flow computations

Background and ObjectiveHigh-quality vascular modeling is crucial for blood flow simulations, i.e., computational fluid dynamics (CFD). As without an accurate geometric representation of the smooth vascular surface, it is impossible to make meaningful blood flow simulations. The purpose of this work is to develop high-quality vascular modeling and modification method for blood flow computations. MethodsWe develop a new technique for the accurate geometric modeling and modification of vasculatures using implicit extrusion surfaces (IES). In the proposed method, the skeleton of the vascular structure is subdivided into short curve segments, each of which is then represented implicitly locally as the intersection of two mutually orthogonal implicit surfaces defined by distance functions. A set of contour points is extracted and fitted with an implicit curve for accurately specifying the vessel cross-section profile, which is then extruded locally along the skeleton to fill the gaps between two vascular tube cross sections. We also present a new implicit geometric editing technique to modify the constructed vascular model with pathology for virtual stenting. ResultsExperimental results and validations show that accurate vascular models with highly smooth surfaces can be generated by the proposed method. In addition, we conduct some blood flow simulations to indicate the effectiveness of proposed method for hemodynamic simulations. ConclusionsThe proposed technique can achieve precise geometric models of vasculatures with any required degree of smoothness for reliable blood flow simulations.

Reproducible Evaluation of Diffusion MRI Features for Automatic Classification of Patients with Alzheimer's Disease.

Diffusion MRI is the modality of choice to study alterations of white matter. In past years, various works have used diffusion MRI for automatic classification of Alzheimer's disease. However, classification performance obtained with different approaches is difficult to compare because of variations in components such as input data, participant selection, image preprocessing, feature extraction, feature rescaling (FR), feature selection (FS) and cross-validation (CV) procedures. Moreover, these studies are also difficult to reproduce because these different components are not readily available. In a previous work (Samper-González et al. 2018), we propose an open-source framework for the reproducible evaluation of AD classification from T1-weighted (T1w) MRI and PET data. In the present paper, we first extend this framework to diffusion MRI data. Specifically, we add: conversion of diffusion MRI ADNI data into the BIDS standard and pipelines for diffusion MRI preprocessing and feature extraction. We then apply the framework to compare different components. First, FS has a positive impact on classification results: highest balanced accuracy (BA) improved from 0.76 to 0.82 for task CN vs AD. Secondly, voxel-wise features generally gives better performance than regional features. Fractional anisotropy (FA) and mean diffusivity (MD) provided comparable results for voxel-wise features. Moreover, we observe that the poor performance obtained in tasks involving MCI were potentially caused by the small data samples, rather than by the data imbalance. Furthermore, no extensive classification difference exists for different degree of smoothing and registration methods. Besides, we demonstrate that using non-nested validation of FS leads to unreliable and over-optimistic results: 5% up to 40% relative increase in BA. Lastly, with proper FR and FS, the performance of diffusion MRI features is comparable to that of T1w MRI. All the code of the framework and the experiments are publicly available: general-purpose tools have been integrated into the Clinica software package ( www.clinica.run ) and the paper-specific code is available at: https://github.com/aramis-lab/AD-ML .

Stable-by-Design Kinematic Control Based on Optimization

This article presents a new kinematic control paradigm for redundant robots based on optimization. The general approach takes into account convex objective functions with inequality constraints and a specific equality constraint resulting from a Lyapunov function, which ensures closed-loop stability by design. Furthermore, we tackle an important particular case by using a convex combination of quadratic and $l_{1}$ -norm objective functions, making possible for the designer to choose different degrees of sparseness and smoothness in the control inputs. We provide a pseudoanalytical solution to this optimization problem and validate the approach by controlling the center of mass of the humanoid robot HOAP3.

BUFFER‐STOCK SAVING AND HOUSEHOLDS' RESPONSE TO INCOME SHOCKS

AbstractWe exploit information on the joint dynamics of household labor income, consumption, and wealth in the Italian Survey of Household Income and Wealth to structurally estimate a buffer‐stock saving model. We compare the degree of consumption smoothing implied by the model to the corresponding empirical estimates based on the same data set. We estimate that Italian households smooth 12% of permanent income shocks in the data that is comparable to the model counterpart of 11% . This result contrasts with existing evidence, and our own findings in this article, of substantially more consumption smoothing in U.S. data.

On a question of Pietch

The main result is that a finite dimensional normed space embeds isometrically in $\ell_p$ if and only if it has a discrete Levy $p$-representation. This provides an alternative answer to a question raised by Pietch, and as a corollary, a simple proof of the fact that unless $p$ is an even integer, the two-dimensional Hilbert space $\ell_2^2$ is not isometric to a subspace of $\ell_p$. The situation for $\ell_q^2$ with $q\neq 2$ turns out to be much more restrictive. The main result combined with a result of Dor provides a proof of the fact that if $q\neq 2$ then $\ell_q^2$ is not isometric to a subspace of $\ell_p$ unless $q=p$. Further applications concerning restrictions on the degree of smoothness of finite dimensional subspaces of $\ell_p$ are included as well.

Feature-Temporal Semi-Supervised Extreme Learning Machine for Robotic Terrain Classification

Robotic terrain classification refers to the ability that a field robot could identify the traversing terrains autonomously under as little human supervision as possible. Such a task could be achieved by semi-supervised learning which works in the premise of smoothness assumption in the feature space. However, we found that the feature smoothness assumption cannot be fully satisfied (i.e., there is no apparent low-density region in the feature space) in the robotic terrain classification, which motivates us to propose the feature-temporal semi-supervised extreme learning machine (FT-S2ELM). With introducing the feature-temporal similarity matrix, the accuracy of the classifier trained by semi-supervised learning increases significantly. Furthermore, considering the uncertainty in determining the smoothness degree (i.e., the free parameters of similarity matrix), we introduce an automatic approach to find the optimal graph Laplacian, thus increasing the safety. The proposed method is verified experimentally on the data gathered by a micro tracked robot.

Skeletonization via dual of shape segmentation

Curve skeletons of 3D objects are central to many geometry analysis tasks in the field of computer graphics. A desirable skeleton has to meet at least four requirements: (1) topologically homotopic to the primitive shape, (2) truly well-centred, (3) feature preserving and (4) has a reasonable degree of smoothness. There are at least a couple of difficulties with skeletonization. On the one hand, finding the “best” skeleton is related to visual perception, to some extent, and thus hard to be completely solved by a pure geometric technique. On the other hand, how to exactly characterize the centredness of a skeleton, without a pre-computed medial axis surface, still remains challenging.Due to the fact that skeletons are able to encode the overall structure, a skeleton has been used to guide segmentation of a shape, which implies that there exists a dual relationship between segmentation and skeletonization. Based on the underlying duality, we propose to generate skeletons from a reliable segmentation result that is more easily available by deep learning or alternative techniques. In implementation, we first extract a collection of samples and then compute the Voronoi diagram restricted in the volume w.r.t. those samples, followed by transforming the clipped Voronoi diagram into a graph G. We further equip each edge in G with a centredness score. The user-specific segmentation result is then used to decompose G into a set of subgraphs Gi=1k. The next task is to compute the Steiner tree for each subgraph while requiring that the Steiner trees of two adjacent parts Gi and Gj must be linked together. The global structure of the final skeleton inherits the proximity configuration of the user-specific segmentation, and thus is topologically homotopic to the primitive shape. At the same time, the centredness of the final skeleton is taken into full consideration by maximizing the overall centredness score. We also integrate the other two requirements carefully into our algorithmic framework. We conduct extensive experiments to evaluate the new approach in terms of the above-mentioned aspects. The experimental results show that our approach has an obvious advantage over the state-of-the-arts. As a by-product of our algorithm, users can obtain skeletons with different levels of details by editing the segmentation configurations.

Regularity of the Density of States of Random Schrödinger Operators

In this paper we solve a long standing open problem for Random Schrödinger operators on $$L^2({\mathbb {R}}^d)$$ with i.i.d single site random potentials. We allow a large class of free operators, including magnetic potential, however our method of proof works only for the case when the random potentials satisfy a complete covering condition. We require that the supports of the random potentials cover $${\mathbb {R}}^d$$ and the bump functions that appear in the random potentials form a partition of unity. For such models, we show that the Density of States (DOS) is m times differentiable in the part of the spectrum where exponential localization is valid, if the single site distribution has compact support and has Hölder continuous $$m+1$$ st derivative. The required Hölder continuity depends on the fractional moment bounds satisfied by appropriate operator kernels. Our proof of the Random Schrödinger operator case is an extensions of our proof for Anderson type models on $$\ell ^2(\mathbb {G})$$ , $$\mathbb {G}$$ a countable set, with the property that the cardinality of the set of points at distance N from any fixed point grows at some rate in $$N^\alpha , \alpha >0$$ . This condition rules out the Bethe lattice, where our method of proof works but the degree of smoothness also depends on the localization length, a result we do not present here. Even for these models the random potentials need to satisfy a complete covering condition. The Anderson model on the lattice for which regularity results were known earlier also satisfies the complete covering condition.

On measures that improve $L^q$ dimension under convolution

The L^q dimensions, for 1 < q < \infty , quantify the degree of smoothness of a measure. We study the following problem on the real line: when does the L^q dimension improve under convolution? This can be seen as a variant of the well-known L^p -improving property. Our main result asserts that uniformly perfect measures (which include Ahlfors-regular measures as a proper subset) have the property that convolving with them results in a strict increase of the L^q dimension. We also study the case q = \infty , which corresponds to the supremum of the Frostman exponents of the measure. We obtain consequences for repeated convolutions and for the box dimension of sumsets. Our results are derived from an inverse theorem for the L^q norms of convolutions due to the second author.

ANCF curvature continuity: application to soft and fluid materials

The continuity of the position-vector gradients at the nodal points of a finite element mesh does not always ensure the continuity of the gradients at the element interfaces. Discontinuity of the gradients at the interface not only adversely affects the quality of the simulation results, but can also lead to computer models that do not properly represent realistic physical system behaviors, particularly in the case of soft and fluid material applications. In this study, the absolute nodal coordinate formulation (ANCF) finite elements are used to define general curvature-continuity conditions that allow for eliminating or minimizing the discontinuity of the position gradients at the element interface. For the ANCF solid element, with four-node surfaces, it is shown that continuity of the gradients tangent to an arbitrary point on a surface is ensured as the result of the continuity of the gradients at the nodal points. The general ANCF continuity conditions are applicable to both reference-configuration straight and curved geometries. These conditions are formulated without the need for using the computer-aided-design knot vector and knot multiplicity, which do not account properly for the concept of system degrees of freedom. The ANCF curvature-continuity conditions are written in terms of constant geometric coefficients obtained using the matrix of position-vector gradients that defines the reference-configuration geometry. The formulation of these conditions is demonstrated using the ANCF fully parameterized three-dimensional solid and tetrahedral elements, which employ a complete set of position gradients as nodal coordinates. Numerical results are presented in order to examine the effect of applying the curvature-continuity conditions on achieving a higher degree of smoothness at the element interfaces in the case of soft and fluid materials.

Deformation of Milnor algebras

We investigate deformations of Milnor algebras of smooth homogeneous polynomials, and prove in particular that any smooth degree $d$ homogeneous polynomial in $n+1$ variables that is not of Sebastiani-Thom type is determined by the degree $k$ homogeneous component of its Jacobian ideal for any $d-1\leq k\leq (n+1)(d-2)$. Our results generalize the previous result on the reconstruction of a homogeneous polynomial from its Jacobian ideal.

Estimation of gas record alteration in very low-accumulation ice cores

Abstract. We measured the methane mixing ratios of enclosed air in five ice core sections drilled on the East Antarctic Plateau. Our work aims to study two effects that alter the recorded gas concentrations in ice cores: layered gas trapping artifacts and firn smoothing. Layered gas trapping artifacts are due to the heterogeneous nature of polar firn, where some strata might close early and trap abnormally old gases that appear as spurious values during measurements. The smoothing is due to the combined effects of diffusive mixing in the firn and the progressive closure of bubbles at the bottom of the firn. Consequently, the gases trapped in a given ice layer span a distribution of ages. This means that the gas concentration in an ice layer is the average value over a certain period of time, which removes the fast variability from the record. Here, we focus on the study of East Antarctic Plateau ice cores, as these low-accumulation ice cores are particularly affected by both layering and smoothing. We use high-resolution methane data to test a simple trapping model reproducing the layered gas trapping artifacts for different accumulation conditions typical of the East Antarctic Plateau. We also use the high-resolution methane measurements to estimate the gas age distributions of the enclosed air in the five newly measured ice core sections. It appears that for accumulations below 2 cm ice equivalent yr−1 the gas records experience nearly the same degree of smoothing. We therefore propose to use a single gas age distribution to represent the firn smoothing observed in the glacial ice cores of the East Antarctic Plateau. Finally, we used the layered gas trapping model and the estimation of glacial firn smoothing to quantify their potential impacts on a hypothetical 1.5-million-year-old ice core from the East Antarctic Plateau. Our results indicate that layering artifacts are no longer individually resolved in the case of very thinned ice near the bedrock. They nonetheless contribute to slight biases of the measured signal (less than 10 ppbv and 0.5 ppmv in the case of methane using our currently established continuous CH4 analysis and carbon dioxide, respectively). However, these biases are small compared to the dampening experienced by the record due to firn smoothing.

Estimation of Wavelet Coherence of Seismic Ground Motions

ABSTRACTThe relation between the nonstationary seismic ground motions at two sites is often characterized using lagged coherence and phase spectrum. Their evaluation is most often carried out using ordinary Fourier analysis (i.e., without windowing) by assuming that they are time invariant. In the present study, the assessment of time-varying coherence is carried out based on the auto- and cross-wavelet power spectrum. The coherence is expressed in terms of lagged wavelet coherence and wavelet phase spectrum. For the analysis, the generalized Morse wavelets are employed, and the ground-motion records for several events from dense arrays located in Taiwan are used. It was shown that without adequate smoothing in scale and time, the obtained lagged wavelet coherence varies drastically in time and frequency (i.e., scale). A parametric analysis shows that the estimated coherence is sensitive to the degree of smoothing. The results of the lagged wavelet coherence and wavelet phase spectrum are time varying and frequency varying. This is in contrast with the time-invariant lagged coherence and phase spectrum assumed for the amplitude modulated evolutionary stochastic process. It is inferred from the results that the use of a time-varying coherence should be considered for seismic ground motions modeled as nonstationary processes.

Resting-state networks of the neonate brain identified using independent component analysis.

Resting-state functional magnetic resonance imaging (rs-fMRI) has been successfully used to probe the intrinsic functional organization of the brain and to study brain development. Here, we implemented a combination of individual and group independent component analysis (ICA) of FSL on a 6-min resting-state data set acquired from 21 naturally sleeping term-born (age 26±6.7 d), healthy neonates to investigate the emerging functional resting-state networks (RSNs). In line with the previous literature, we found evidence of sensorimotor, auditory/language, visual, cerebellar, thalmic, parietal, prefrontal, anterior cingulate as well as dorsal and ventral aspects of the default-mode-network. Additionally, we identified RSNs in frontal, parietal, and temporal regions that have not been previously described in this age group and correspond to the canonical RSNs established in adults. Importantly, we found that careful ICA-based denoising of fMRI data increased the number of networks identified with group-ICA, whereas the degree of spatial smoothing did not change the number of identified networks. Our results show that the infant brain has an established set of RSNs soon after birth.

Average inflation targeting and interest-rate smoothing

We study the welfare implication of average inflation targeting as a simple interest-rate rule, in which the monetary authority adjusts its short-term policy rate in response to the output gap as well as average inflation deviation from its target instead of reacting to the contemporaneous inflation rate as in a Taylor-type rule. We find that the welfare improvement achieved by switching to average inflation targeting from a standard Taylor rule is modest with a high degree of interest-rate smoothing, whereas it is significant without interest-rate smoothing. We show that average inflation targeting is welfare-improving in the same way as interest-rate smoothing by making the conduct of monetary policy history-dependent. Thus, the high degree of monetary policy inertia in the estimated interest-rate rules in many advanced economies implies that the welfare gain from adopting the average inflation targeting rule would be minimal.

On denoising satellite altimeter measurements for high-resolution geophysical signal analysis

Abstract Satellite radar altimeter observations are key to advanced studies in ocean dynamics, particularly those focusing on mesoscale processes. To resolve scales below about 100 km, because altimeter measurements are often characterized by a low signal-to-noise ratio (SNR), low-pass filtering or least-squares curve fitting is generally applied to smooth the data before analysis. Here, we present an alternative method. It is based on Empirical Mode Decomposition (EMD) developed to analyze non-stationary and non-linear processes, which adaptively projects a signal on a basis of empirical AM/FM functions called Intrinsic Modulation Functions (IMFs). Applied to a Gaussian noise signal, the EMD provides a set of IMFs with a predictable distribution of noise energy that can be exploited by wavelet-inspired threshold methods to provide an efficient approach to data denoising. The EMD method performs a local analysis of the SNR, does not require a priori assumptions about the underlying geophysical signal, e.g., its degree of smoothness or its compliance with a particular mathematical framework. The signal is simply assumed to be the sum of a piecewise-smooth deterministic part and a stochastic part. The proposed EMD-based denoising approach is therefore well suited for mapping non-linear features, such as strong gradients, and extreme values without significant smoothing. Using Jason-2, Cryosat-2, and Saral/AltiKa significant wave height measurements, the method provides an effective means of mapping overlooked geophysical variability of sea state at scales between about 100 km and 25 km, a range largely impacted by low SNR. Below 25 km, a spectral hump caused by inhomogeneities in the altimeter footprint essentially dominates the signal. In addition, the EMD method provides a consistent approach for long-term noise analysis and monitoring under global and local conditions. The proposed method is a step forward that will enable better exploitation of the unique set of altimeter observations that now covers more than 25 years.

Trend filtering – II. Denoising astronomical signals with varying degrees of smoothness

ABSTRACTTrend filtering – first introduced into the astronomical literature in Paper I of this series – is a state-of-the-art statistical tool for denoising 1D signals that possess varying degrees of smoothness. In this work, we demonstrate the broad utility of trend filtering to observational astronomy by discussing how it can contribute to a variety of spectroscopic and time-domain studies. The observations we discuss are (1) the Lyman-α (Lyα) forest of quasar spectra; (2) more general spectroscopy of quasars, galaxies, and stars; (3) stellar light curves with planetary transits; (4) eclipsing binary light curves; and (5) supernova light curves. We study the Lyα forest in the greatest detail – using trend filtering to map the large-scale structure of the intergalactic medium along quasar-observer lines of sight. The remaining studies share broad themes of: (1) estimating observable parameters of light curves and spectra; and (2) constructing observational spectral/light-curve templates. We also briefly discuss the utility of trend filtering as a tool for 1D data reduction and compression.