an isoparametric approach to high order curvilinear boundary layer meshing abstract the generation of high order curvilinear meshes for complex three dimensional geometries is presently a challenging topic particularly for meshes used in simulations at high reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow in this paper we present a conceptually simple but very effective and modular method to address this issue we propose an isoparametric approach whereby a mesh containing a valid coarse discretization comprising of high order triangular prisms near walls is refined to obtain a finer prismatic or tetrahedral boundary layer mesh the validity of the prismatic mesh provides a suitable mapping that allows one to obtain very fine mesh resolutions across the thickness of the boundary layer we describe the method in detail for a high order approximation using modal basis functions discuss the requirements for the splitting method to produce valid prismatic and tetrahedral meshes and provide a sufficient criterion of validity in both cases by considering two complex aeronautical configurations we demonstrate how highly stretched meshes with sufficient resolution within the laminar sublayer can be generated to enable the simulation of flows with reynolds numbers of 10 6 and above

beyond color difference residual interpolation for color image demosaicking in this paper we propose residual interpolation ri as an alternative to color difference interpolation which is a widely accepted technique for color image demosaicking our proposed ri performs the interpolation in a residual domain where the residuals are differences between observed and tentatively estimated pixel values our hypothesis for the ri is that if image interpolation is performed in a domain with a smaller laplacian energy its accuracy is improved based on the hypothesis we estimate the tentative pixel values to minimize the laplacian energy of the residuals we incorporate the ri into the gradient based threshold free algorithm which is one of the state of the art bayer demosaicking algorithms experimental results demonstrate that our proposed demosaicking algorithm using the ri surpasses the state of the art algorithms for the kodak the imax and the beyond kodak data sets

optimized color filter arrays for sparse representation based demosaicking demosaicking is the problem of reconstructing a color image from the raw image captured by a digital color camera that covers its only imaging sensor with a color filter array cfa sparse representation based demosaicking has been shown to produce superior reconstruction quality however almost all existing algorithms in this category use the cfas which are not specifically optimized for the algorithms in this paper we consider optimally designing cfas for sparse representation based demosaicking where the dictionary is well chosen the fact that cfas correspond to the projection matrices used in compressed sensing inspires us to optimize cfas via minimizing the mutual coherence this is more challenging than that for traditional projection matrices because cfas have physical realizability constraints however most of the existing methods for minimizing the mutual coherence require that the projection matrices should be unconstrained making them inapplicable for designing cfas we consider directly minimizing the mutual coherence with the cfa s physical realizability constraints as a generalized fractional programming problem which needs to find sufficiently accurate solutions to a sequence of nonconvex nonsmooth minimization problems we adapt the redistributed proximal bundle method to address this issue experiments on benchmark images testify to the superiority of the proposed method in particular we show that a simple sparse representation based demosaicking algorithm with our specifically optimized cfa can outperform lssc 1 to the best of our knowledge it is the first sparse representation based demosaicking algorithm that beats lssc in terms of cpsnr

practical poissonian gaussian noise modeling and fitting for single image raw data we present a simple and usable noise model for the raw data of digital imaging sensors this signal dependent noise model which gives the pointwise standard deviation of the noise as a function of the expectation of the pixel raw data output is composed of a poissonian part modeling the photon sensing and gaussian part for the remaining stationary disturbances in the output data we further explicitly take into account the clipping of the data over and under exposure faithfully reproducing the nonlinear response of the sensor we propose an algorithm for the fully automatic estimation of the model parameters given a single noisy image experiments with synthetic images and with real raw data from various sensors prove the practical applicability of the method and the accuracy of the proposed model

adaptive filtering for color filter array demosaicking most digital still cameras acquire imagery with a color filter array cfa sampling only one color value for each pixel and interpolating the other two color values afterwards the interpolation process is commonly known as demosaicking in general a good demosaicking method should preserve the high frequency information of imagery as much as possible since such information is essential for image visual quality we discuss in this paper two key observations for preserving high frequency information in cfa demosaicking 1 the high frequencies are similar across three color components and 2 the high frequencies along the horizontal and vertical axes are essential for image quality our frequency analysis of cfa samples indicates that filtering a cfa image can better preserve high frequencies than filtering each color component separately this motivates us to design an efficient filter for estimating the luminance at green pixels of the cfa image and devise an adaptive filtering approach to estimating the luminance at red and blue pixels experimental results on simulated cfa images as well as raw cfa data verify that the proposed method outperforms the existing state of the art methods both visually and in terms of peak signal to noise ratio at a notably lower computational cost

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

robust untangling of curvilinear meshes this paper presents a technique that allows to untangle high order curvilinear meshes the technique makes use of unconstrained optimization where element jacobians are constrained to lie in a prescribed range through moving log barriers the untangling procedure starts from a possibly invalid curvilinear mesh and moves mesh vertices with the objective of producing elements that all have bounded jacobians bounds on jacobians are computed using the results of johnen et al 2012 2013 1 2 the technique is applicable to any kind of polynomial element for surface volume hybrid or boundary layer meshes a series of examples demonstrate both the robustness and the efficiency of the technique the final example involving a time explicit computation shows that it is possible to control the stable time step of the computation for curvilinear meshes through an alternative element deformation measure

optimizing the geometrical accuracy of curvilinear meshes this paper presents a method to generate valid high order meshes with optimized geometrical accuracy the high order meshing procedure starts with a linear mesh that is subsequently curved without taking care of the validity of the high order elements an optimization procedure is then used to both untangle invalid elements and optimize the geometrical accuracy of the mesh standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two dimensional meshes but they prove computationally too costly for optimization purposes a fast estimate of the geometrical accuracy based on taylor expansions of the curves is introduced an unconstrained optimization procedure based on this estimate is shown to yield significant improvements in the geometrical accuracy of high order meshes as measured by the standard hausdorff distance between the geometrical model and the mesh several examples illustrate the beneficial impact of this method on cfd solutions with a particular role of the enhanced mesh boundary smoothness

on discretely entropy stable weight adjusted discontinuous galerkin methods curvilinear meshes abstract we construct entropy conservative and entropy stable discontinuous galerkin dg discretizations for time dependent nonlinear hyperbolic conservation laws on curvilinear meshes the resulting schemes preserve a semi discrete quadrature approximation of a continuous global entropy inequality the proof requires the satisfaction of a discrete geometric conservation law which we enforce through an appropriate polynomial approximation we extend the construction of entropy conservative and entropy stable dg schemes to the case when high order curvilinear mass matrices are approximated using low storage weight adjusted approximations and describe how to retain global conservation properties under such an approximation for certain types of curvilinear meshes these weight adjusted approximations deliver optimal rates of convergence finally the high order accuracy local conservation and discrete conservation or dissipation of entropy for under resolved solutions are verified through numerical experiments for the compressible euler equations on triangular and tetrahedral meshes

universal demosaicking of color filter arrays a large number of color filter arrays cfas periodic or aperiodic have been proposed to reconstruct images from all different cfas and compare their imaging quality a universal demosaicking method is needed this paper proposes a new universal demosaicking method based on inter pixel chrominance capture and optimal demosaicking transformation it skips the commonly used step to estimate the luminance component at each pixel and thus avoids the associated estimation error instead we directly use the acquired cfa color intensity at each pixel as an input component two independent chrominance components are estimated at each pixel based on the inter pixel chrominance in the window which is captured with the difference of cfa color values between the pixel of interest and its neighbors two mechanisms are employed for the accurate estimation distance related and edge sensing weighting to reflect the confidence levels of the inter pixel chrominance components and pseudoinverse based estimation from the components in a window then from the acquired cfa color component and two estimated chrominance components the three primary colors are reconstructed by a linear color transform which is optimized for the least transform error our experiments show that the proposed method is much better than other published universal demosaicking methods

a geometric method for optimal design of color filter arrays a color filter array cfa used in a digital camera is a mosaic of spectrally selective filters which allows only one color component to be sensed at each pixel the missing two components of each pixel have to be estimated by methods known as demosaicking the demosaicking algorithm and the cfa design are crucial for the quality of the output images in this paper we present a cfa design methodology in the frequency domain the frequency structure which is shown to be just the symbolic dft of the cfa pattern one period of the cfa is introduced to represent images sampled with any rectangular cfas in the frequency domain based on the frequency structure the cfa design involves the solution of a constrained optimization problem that aims at minimizing the demosaicking error to decrease the number of parameters and speed up the parameter searching the optimization problem is reformulated as the selection of geometric points on the boundary of a convex polygon or the surface of a convex polyhedron using our methodology several new cfa patterns are found which outperform the currently commercialized and published ones experiments demonstrate the effectiveness of our cfa design methodology and the superiority of our new cfa patterns

mesh generation in curvilinear domains using high order elements the ability to construct suitable computational meshes is currently a significant limiting factor in the development of compact high order algorithms in very complex geometries compact high order algorithms such as spectral element or p type finite element techniques offer the potential of high accuracy if the solution is smooth and a well behaved mapping exists between the local sub domains and a standard region in this paper we address the problem of coupling high order algorithms with unstructured mesh generation and cad representation techniques we present three complementary strategies to alleviate the problem of generation of elemental regions with singular elemental mappings the first strategy investigates the influence of an anisometric parametric surface representation on the quality of high order unstructured meshes we show that a straightforward splitting of a standard linear mesh for use in a high order method can lead to the generation of distorted possibly invalid meshes even for simple computational domains such as cubes the second strategy uses hybrid meshes applying prismatic elements near curvilinear boundaries in the third and final strategy we investigate the use of curvature driven surface discretization to incorporate higher order information about the surface into the mesh generation using the computational reconstruction of the arterial bypass graft as an example computational domain we demonstrate how the combination of all three strategies leads to a valid high order discretization of the computational domain copyright 2001 john wiley sons ltd

on knudsen flows within thin tubes the dynamics of a test particle in an infinite tube is investigated it is proven that the evolution tends to that of a diffusion process as the radius of the tube decreases to zero this justifies the hypotheses underlying an experiment of clausing 1930

asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains we study stochastic billiards in infinite planar domains with curvilinear boundaries that is piecewise deterministic motion with randomness introduced via random reflections at the domain boundary physical motivation for the process originates with ideal gas models in the knudsen regime with particles reflecting off microscopically rough surfaces we classify the process into recurrent and transient cases we also give almost sure results on the long term behaviour of the location of the particle including a super diffusive rate of escape in the transient case a key step in obtaining our results is to relate our process to an instance of a one dimensional stochastic process with asymptotically zero drift for which we prove some new almost sure bounds of independent interest we obtain some of these bounds via an application of general semimartingale criteria also of some independent interest

curved boundary treatments for the discontinuous galerkin method applied to aeroacoustic propagation a discontinuous galerkin method is applied to unstructured grids to simulate aeroacoustic propagation modeled by the linearized euler equations on triangular and tetrahedral elements with straight edges the quadrature free form of the discontinuous galerkin method is used in addition to the classical linear treatment of wall boundaries two treatments involving a second order representation of the geometry are presented the simulation of acoustic scattering problems shows that the linear treatment can limit the accuracy at high order and demonstrates how the boundary treatment involving curved elements overcomes this restriction the benefits of higher order treatments are also assessed for more realistic geometries namely a high lift airfoil and an elliptical muffler

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

a new color filter array with optimal properties for noiseless and noisy color image acquisition digital color cameras acquire color images by means of a sensor on which a color filter array cfa is overlaid the bayer cfa dominates the consumer market but there has recently been a renewed interest for the design of cfas however robustness to noise is often neglected in the design though it is crucial in practice in this paper we present a new 2 3 periodic cfa which provides by construction the optimal tradeoff between robustness to aliasing chrominance noise and luminance noise moreover a simple and efficient linear demosaicking algorithm is described which fully exploits the spectral properties of the cfa practical experiments confirm the superiority of our design both in noiseless and noisy scenarios

demosaicking of noisy bayer sampled color images with least squares luma chroma demultiplexing and noise level estimation this paper adapts the least squares luma chroma demultiplexing lslcd demosaicking method to noisy bayer color filter array cfa images a model is presented for the noise in white balanced gamma corrected cfa images a method to estimate the noise level in each of the red green and blue color channels is then developed based on the estimated noise parameters one of a finite set of configurations adapted to a particular level of noise is selected to demosaic the noisy data the noise adaptive demosaicking scheme is called lslcd with noise estimation lslcd ne experimental results demonstrate state of the art performance over a wide range of noise levels with low computational complexity many results with several algorithms noise levels and images are presented on our companion web site along with software to allow reproduction of our results

nurbs enhanced finite element method nefem the development of nurbs enhanced finite element method nefem is revisited this technique allows a seamless integration of the cad boundary representation of the domain and the finite element method fem the importance of the geometrical model in finite element simulations is addressed and the benefits and potential of nefem are discussed and compared with respect to other curved finite element techniques

multiscale gradients based color filter array interpolation single sensor digital cameras use color filter arrays to capture a subset of the color data at each pixel coordinate demosaicing or color filter array cfa interpolation is the process of estimating the missing color samples to reconstruct a full color image in this paper we propose a demosaicing method that uses multiscale color gradients to adaptively combine color difference estimates from different directions the proposed solution does not require any thresholds since it does not make any hard decisions and it is noniterative although most suitable for the bayer cfa pattern the method can be extended to other mosaic patterns to demonstrate this we describe its application to the lukac cfa pattern experimental results show that it outperforms other available demosaicing methods by a clear margin in terms of cpsnr and s cielab measures for both mosaic patterns

training an active random field for real time image denoising many computer vision problems can be formulated in a bayesian framework based on markov random fields mrf or conditional random fields crf generally the mrf crf model is learned independently of the inference algorithm that is used to obtain the final result in this paper we observe considerable gains in speed and accuracy by training the mrf crf model together with a fast and suboptimal inference algorithm an active random field arf is defined as a combination of a mrf crf based model and a fast inference algorithm for the mrf crf model this combination is trained through an optimization of a loss function and a training set consisting of pairs of input images and desired outputs we apply the arf concept to image denoising using the fields of experts mrf together with a 1 4 iteration gradient descent algorithm for inference experimental validation on unseen data shows that the arf approach obtains an improved benchmark performance as well as a 1000 3000 times speedup compared to the fields of experts mrf using the arf approach image denoising can be performed in real time at 8 fps on a single cpu for a 256times256 image sequence with close to state of the art accuracy

geometrical validity of curvilinear finite elements in this paper we describe a way to compute accurate bounds on jacobian determinants of curvilinear polynomial finite elements our condition enables to guarantee that an element is geometrically valid i e that its jacobian determinant is strictly positive everywhere in its reference domain it also provides an efficient way to measure the distortion of curvilinear elements the key feature of the method is to expand the jacobian determinant using a polynomial basis built using bezier functions that has both properties of boundedness and positivity numerical results show the sharpness of our estimates