Techniques for augmenting the visualisation of dynamic raster surfaces

Despite their aesthetic appeal and condensed nature, dynamic raster surface representations such as a temporal series of a landform and an attribute series of a socio-economic attribute of an area, are often criticised for the lack of an effective information delivery and interactivity.In this work, we readdress some of the earlier raised reasons for these limitations -information-laden quality of surface datasets, lack of spatial and temporal continuity in the original data, and a limited scope for a real-time interactivity. We demonstrate with examples that the use of four techniques namely the re-expression of the surfaces as a framework of morphometric features, spatial generalisation, morphing, graphic lag and brushing can augment the visualisation of dynamic raster surfaces in temporal and attribute series

Segmentation of Loops from Coronal EUV Images

We present a procedure which extracts bright loop features from solar EUV images. In terms of image intensities, these features are elongated ridge-like intensity maxima. To discriminate the maxima, we need information about the spatial derivatives of the image intensity. Commonly, the derivative estimates are strongly affected by image noise. We therefore use a regularized estimation of the derivative which is then used to interpolate a discrete vector field of ridge points ``ridgels'' which are positioned on the ridge center and have the intrinsic orientation of the local ridge direction. A scheme is proposed to connect ridgels to smooth, spline-represented curves which fit the observed loops. Finally, a half-automated user interface allows one to merge or split, eliminate or select loop fits obtained form the above procedure. In this paper we apply our tool to one of the first EUV images observed by the SECCHI instrument onboard the recently launched STEREO spacecraft. We compare the extracted loops with projected field lines computed from almost-simultaneously-taken magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated using a linear force-free field model. This comparison allows one to verify faint and spurious loop connections produced by our segmentation tool and it also helps to prove the quality of the magnetic-field model where well-identified loop structures comply with field-line projections. We also discuss further potential applications of our tool such as loop oscillations and stereoscopy.Comment: 13 pages, 9 figures, Solar Physics, online firs

A Dynamically Adaptive Sparse Grid Method for Quasi-Optimal Interpolation of Multidimensional Analytic Functions

In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to construct an interpolant in space that corresponds to the "best $M$-terms" based on sharp a priori estimate of polynomial coefficients. In the past, SG methods have been successful in achieving this, with a traditional construction that relies on the solution to a Knapsack problem: only the most profitable hierarchical surpluses are added to the SG. However, this approach requires additional sharp estimates related to the size of the analytic region and the norm of the interpolation operator, i.e., the Lebesgue constant. Instead, we present an iterative SG procedure that adaptively refines an estimate of the region and accounts for the effects of the Lebesgue constant. Our approach does not require any a priori knowledge of the analyticity or operator norm, is easily generalized to both affine and non-affine analytic functions, and can be applied to sparse grids build from one dimensional rules with arbitrary growth of the number of nodes. In several numerical examples, we utilize our dynamically adaptive SG to interpolate quantities of interest related to the solutions of parametrized elliptic and hyperbolic PDEs, and compare the performance of our quasi-optimal interpolant to several alternative SG schemes

Surprises in High-Dimensional Ridgeless Least Squares Interpolation

Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum $\ell_2$ norm (``ridgeless'') interpolation in high-dimensional least squares regression. We consider two different models for the feature distribution: a linear model, where the feature vectors $x_i \in {\mathbb R}^p$ are obtained by applying a linear transform to a vector of i.i.d.\ entries, $x_i = \Sigma^{1/2} z_i$ (with $z_i \in {\mathbb R}^p$); and a nonlinear model, where the feature vectors are obtained by passing the input through a random one-layer neural network, $x_i = \varphi(W z_i)$ (with $z_i \in {\mathbb R}^d$, $W \in {\mathbb R}^{p \times d}$ a matrix of i.i.d.\ entries, and $\varphi$ an activation function acting componentwise on $W z_i$). We recover -- in a precise quantitative way -- several phenomena that have been observed in large-scale neural networks and kernel machines, including the "double descent" behavior of the prediction risk, and the potential benefits of overparametrization.Comment: 68 pages; 16 figures. This revision contains non-asymptotic version of earlier results, and results for general coefficient

Curved Gabor Filters for Fingerprint Image Enhancement

Gabor filters play an important role in many application areas for the enhancement of various types of images and the extraction of Gabor features. For the purpose of enhancing curved structures in noisy images, we introduce curved Gabor filters which locally adapt their shape to the direction of flow. These curved Gabor filters enable the choice of filter parameters which increase the smoothing power without creating artifacts in the enhanced image. In this paper, curved Gabor filters are applied to the curved ridge and valley structure of low-quality fingerprint images. First, we combine two orientation field estimation methods in order to obtain a more robust estimation for very noisy images. Next, curved regions are constructed by following the respective local orientation and they are used for estimating the local ridge frequency. Lastly, curved Gabor filters are defined based on curved regions and they are applied for the enhancement of low-quality fingerprint images. Experimental results on the FVC2004 databases show improvements of this approach in comparison to state-of-the-art enhancement methods

A synoptic comparison of the MHD and the OPAL equations of state

A detailed comparison is carried out between two popular equations of state (EOS), the Mihalas-Hummer-Dappen (MHD) and the OPAL equations of state, which have found widespread use in solar and stellar modeling during the past two decades. They are parts of two independent efforts to recalculate stellar opacities; the international Opacity Project (OP) and the Livermore-based OPAL project. We examine the difference between the two equations of state in a broad sense, over the whole applicable rho-T range, and for three different chemical mixtures. Such a global comparison highlights both their differences and their similarities. We find that omitting a questionable hard-sphere correction, tau, to the Coulomb interaction in the MHD formulation, greatly improves the agreement between the MHD and OPAL EOS. We also find signs of differences that could stem from quantum effects not yet included in the MHD EOS, and differences in the ionization zones that are probably caused by differences in the mechanisms for pressure ionization. Our analysis do not only give a clearer perception of the limitations of each equation of state for astrophysical applications, but also serve as guidance for future work on the physical issues behind the differences. The outcome should be an improvement of both equations of state.Comment: 33 pages, 26 figures. Corrected discussion of Basu & Antia, 2004, ApJ, 606, L85-L8