nonlinear wavelet transforms for image coding via lifting we investigate central issues such as invertibility stability synchronization and frequency characteristics for nonlinear wavelet transforms built using the lifting framework the nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework we also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels preliminary compression results for model and real world images demonstrate the promise of our techniques

subpixel edge detection of color images by principal axis analysis and moment preserving principle this paper discusses a new approach for detecting edges with sub pixel accuracy in color images using the principal axis analysis and the moment preserving principle first the principal axis of the color vectors in a three dimensional space is obtained analytically for each image block based on the projection scores the direction of the line edge is obtained by analyzing the three dimensional principal axis of a color image block next by preserving some spatial color moments of the pixels of each square block analytic formulas are derived to extract the edge feature experiments on both synthetic and real images show that the accuracy of the proposed method is comparable to other color edge detectors the proposed algorithm can be performed very fast for real time applications with no need for special hardware

locally adaptive wavelet based image interpolation we describe a spatially adaptive algorithm for image interpolation the algorithm uses a wavelet transform to extract information about sharp variations in the low resolution image and then implicitly applies interpolation which adapts to the image local smoothness singularity characteristics the proposed algorithm yields images that are sharper compared to several other methods that we have considered in this paper better performance comes at the expense of higher complexity

on the role of exponential splines in image interpolation a sobolev reproducing kernel hilbert space approach to image interpolation is introduced the underlying kernels are exponential functions and are related to stochastic autoregressive image modeling the corresponding image interpolants can be implemented effectively using compactly supported exponential b splines a tight l2 upper bound on the interpolation error is then derived suggesting that the proposed exponential functions are optimal in this regard experimental results indicate that the proposed interpolation approach with properly tuned signal dependent weights outperforms currently available polynomial b spline models of comparable order furthermore a unified approach to image interpolation by ideal and nonideal sampling procedures is derived suggesting that the proposed exponential kernels may have a significant role in image modeling as well our conclusion is that the proposed sobolev based approach could be instrumental and a preferred alternative in many interpolation tasks

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

curvature interpolation method for image zooming we introduce a novel image zooming algorithm called the curvature interpolation method cim which is partial differential equation pde based and easy to implement in order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect the cim first evaluates the curvature of the low resolution image after interpolating the curvature to the high resolution image domain the cim constructs the high resolution image by solving a linearized curvature equation incorporating the interpolated curvature as an explicit driving force it has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and pde based methods of no curvature information various results are given to prove effectiveness and reliability of the new method

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

a theory of pseudoskeleton approximations abstract let an m n matrix a be approximated by a rank r matrix with an accuracy e we prove that it is possible to choose r columns and r rows of a forming a so called pseudoskeleton component which approximates a with o e r m n accuracy in the sense of the 2 norm on the way to this estimate we study the interconnection between the volume i e the determinant in the absolute value and the minimal singular value r of r r submatrices of an n r matrix with orthogonal columns we propose a lower bound better than one given by chandrasekaran and ipsen and by hong and pan for the maximum of r over all these submatrices and formulate a hypothesis on a tighter bound

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

estimators of tissue proportions from x ray ct images des estimateurs de proportions tissulaires sont obtenus a partir d images de tomographie numerisee par rayons x ils prennent en compte le fait que de nombreux pixels dans de telles images correspondent a des melanges de types tissulaires le probleme est suggere par une application supposant l estimation de poids des tissus chez le mouton l estimateur standard le compte du nombre de pixels dans un intervalle particuliers de valeurs est compare a l ajustement au maximum de vraisemblance d une distribution d un melange de pixels et a un estimateur des moments des simulations comme notre application montrent la superiorite de l estimateur des moments

fast image interpolation via random forests this paper proposes a two stage framework for fast image interpolation via random forests firf the proposed firf method gives high accuracy as well as requires low computation the underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low resolution image patch to high resolution image patch the firf framework consists of two stages stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image while stage 2 further refines the stage 1 interpolated image by varying the number of decision trees in the random forests and the number of stages applied the proposed firf method can realize computationally scalable image interpolation extensive experimental results show that the proposed firf 3 2 method achieves more than 0 3 db improvement in peak signal to noise ratio over the state of the art nonlocal autoregressive modeling narm method moreover the proposed firf 1 1 obtains similar or better results as narm while only takes its 0 3 computational time

comparison of interpolating methods for image resampling when resampling an image to a new set of coordinates for example when rotating an image there is often a noticeable loss in image quality to preserve image quality the interpolating function used for the resampling should be an ideal low pass filter to determine which limited extent convolving functions would provide the best interpolation five functions were compared a nearest neighbor b linear c cubic b spline d high resolution cubic spline with edge enhancement a 1 and e high resolution cubic spline a 0 5 the functions which extend over four picture elements c d e were shown to have a better frequency response than those which extend over one a or two b pixels the nearest neighbor function shifted the image up to one half a pixel linear and cubic b spline interpolation tended to smooth the image the best response was obtained with the high resolution cubic spline functions the location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned and the response has the most smoothing when the resampled points are equidistant from the original coordinate points thus at the expense of some increase in computing time image quality can be improved by resampled using the high resolution cubic spline function as compared to the nearest neighbor linear or cubic b spline functions

segment adaptive gradient angle interpolation we introduce a new edge directed interpolator based on locally defined straight line approximations of image isophotes spatial derivatives of image intensity are used to describe the principal behavior of pixel intersecting isophotes in terms of their slopes the slopes are determined by inverting a tridiagonal matrix and are forced to vary linearly from pixel to pixel within segments image resizing is performed by interpolating along the approximated isophotes the proposed method can accommodate arbitrary scaling factors provides state of the art results in terms of psnr as well as other quantitative visual quality metrics and has the advantage of reduced computational complexity that is directly proportional to the number of pixels

evolution equations for continuous scale morphological filtering multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges the authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous space multiscale morphological erosions dilations openings and closings these equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals the nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators generally taking the form of a nonlinear function of certain partial differential operators

fitting curves and surfaces with constrained implicit polynomials a problem which often arises while fitting implicit polynomials to 2d and 3d data sets is the following although the data set is simple the fit exhibits undesired phenomena such as loops holes extraneous components etc previous work tackled these problems by optimizing heuristic cost functions which penalize some of these topological problems in the fit the paper suggests a different approach to design parameterized families of polynomials whose zero sets are guaranteed to satisfy certain topological properties namely we construct families of polynomials with star shaped zero sets as well as polynomials whose zero sets are guaranteed not to intersect an ellipse circumscribing the data or to be entirely contained in such an ellipse this is more rigorous than using heuristics which may fail and result in pathological zero sets the ability to parameterize these families depends heavily on the ability to parameterize positive polynomials to achieve this we use some powerful results from real algebraic geometry

a fast high order algorithm for the solution of surface scattering problems basic implementation tests and applications we present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three dimensional space this algorithm evaluates scattered fields through fast high order solution of the corresponding boundary integral equation the high order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities the acceleration in turn results from use of a novel approach which based on high order two face equivalent source approximations reduces the evaluation of far interactions to evaluation of 3 d fast fourier transforms ffts this approach is faster and substantially more accurate and it runs on dramatically smaller memories than other fft and k space methods the present algorithm computes one matrix vector multiplication in o n6 5logn to o n4 3logn operations where n is the number of surface discretization points the latter estimate applies to smooth surfaces for which our high order algorithm provides accurate solutions with small values of n the former more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling further our approach exhibits super algebraic convergence it can be applied to smooth and nonsmooth scatterers and it does not suffer from accuracy breakdowns of any kind in this paper we introduce the main algorithmic components in our approach and we demonstrate its performance with a variety of numerical results in particular we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds

a note on cubic convolution interpolation we establish a link between classical osculatory interpolation and modern convolution based interpolation and use it to show that two well known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago we also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing

fast directional multilevel algorithms for oscillatory kernels this paper introduces a new directional multilevel algorithm for solving n body or n point problems with highly oscillatory kernels these systems often result from the boundary integral formulations of scattering problems and are difficult due to the oscillatory nature of the kernel and the non uniformity of the particle distribution we address the problem by first proving that the interaction between a ball of radius r and a well separated region has an approximate low rank representation as long as the well separated region belongs to a cone with a spanning angle of o 1 r and is at a distance which is at least o r 2 away from from the ball we then propose an efficient and accurate procedure which utilizes random sampling to generate such a separated low rank representation based on the resulting representations our new algorithm organizes the high frequency far field computation by a multidirectional and multiscale strategy to achieve maximum efficiency the algorithm performs well on a large group of highly oscillatory kernels our algorithm is proved to have o n log n computational complexity for any given accuracy when the points are sampled from a two dimensional surface we also provide numerical results to demonstrate these properties

improvements to image magnification the main limitation of state of the art magnifying techniques is that they do not introduce any new information to the original image this lack of information more precisely the absence of high spatial frequency components is responsible for the perceptible degradation of the enlarged image the idea underlying this work is to estimate the phases and frequencies of absent waveforms of absent frequencies from the original low resolution image and then to synthesize them in the high resolution image the developed technique takes advantage of sub pixel edge estimations from the low resolution image to direct the subsequent polynomial interpolation step to improve perceptible image quality the n degree polynomial interpolating curve is user controllable allowing both sharp and smooth edges to be synthesized the proposed approach has been applied both to gray level images and to color images

image interpolation by adaptive 2 d autoregressive modeling and soft decision estimation the challenge of image interpolation is to preserve spatial details we propose a soft decision interpolation technique that estimates missing pixels in groups rather than one at a time the new technique learns and adapts to varying scene structures using a 2 d piecewise autoregressive model the model parameters are estimated in a moving window in the input low resolution image the pixel structure dictated by the learnt model is enforced by the soft decision estimation process onto a block of pixels including both observed and estimated the result is equivalent to that of a high order adaptive nonseparable 2 d interpolation filter this new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods and it produces the best results so far over a wide range of scenes in both psnr measure and subjective visual quality edges and textures are well preserved and common interpolation artifacts blurring ringing jaggies zippering etc are greatly reduced

watersnakes energy driven watershed segmentation the watershed algorithm from mathematical morphology is powerful for segmentation however it does not allow incorporation of a priori information as segmentation methods that are based on energy minimization in particular there is no control of the smoothness of the segmentation result in this paper we show how to represent watershed segmentation as an energy minimization problem using the distance based definition of the watershed line a priori considerations about smoothness can then be imposed by adding the contour length to the energy function this leads to a new segmentation method called watersnakes integrating the strengths of watershed segmentation and energy based segmentation experimental results show that when the original watershed segmentation has noisy boundaries or wrong limbs attached to the object of interest the proposed method overcomes those drawbacks and yields a better segmentation

image interpolation via regularized local linear regression the linear regression model is a very attractive tool to design effective image interpolation schemes some regression based image interpolation algorithms have been proposed in the literature in which the objective functions are optimized by ordinary least squares ols however it is shown that interpolation with ols may have some undesirable properties from a robustness point of view even small amounts of outliers can dramatically affect the estimates to address these issues in this paper we propose a novel image interpolation algorithm based on regularized local linear regression rllr starting with the linear regression model where we replace the ols error norm with the moving least squares mls error norm leads to a robust estimator of local image structure to keep the solution stable and avoid overfitting we incorporate the l2 norm as the estimator complexity penalty moreover motivated by recent progress on manifold based semi supervised learning we explicitly consider the intrinsic manifold structure by making use of both measured and unmeasured data points specifically our framework incorporates the geometric structure of the marginal probability distribution induced by unmeasured samples as an additional local smoothness preserving constraint the optimal model parameters can be obtained with a closed form solution by solving a convex optimization problem experimental results on benchmark test images demonstrate that the proposed method achieves very competitive performance with the state of the art interpolation algorithms especially in image edge structure preservation

high resolution local structure constrained image upsampling with the development of ultra high resolution display devices the visual perception of fine texture details is becoming more and more important a method of high quality image upsampling with a low cost is greatly needed in this paper we propose a fast and efficient image upsampling method that makes use of high resolution local structure constraints the average local difference is used to divide a bicubic interpolated image into a sharp edge area and a texture area and these two areas are reconstructed separately with specific constraints for reconstruction of the sharp edge area a high resolution gradient map is estimated as an extra constraint for the recovery of sharp and natural edges for the reconstruction of the texture area a high resolution local texture structure map is estimated as an extra constraint to recover fine texture details these two reconstructed areas are then combined to obtain the final high resolution image the experimental results demonstrated that the proposed method recovered finer pixel level texture details and obtained top level objective performance with a low time cost compared with state of the art methods

a parallel directional fast multipole method this paper introduces a parallel directional fast multipole method fmm for solving n body problems with highly oscillatory kernels with a focus on the helmholtz kernel in three dimensions this class of oscillatory kernels requires a more restrictive low rank criterion than that of the low frequency regime and thus effective parallelizations must adapt to the modified data dependencies we propose a simple partition at a fixed level of the octree and show that if the partitions are properly balanced between p processes the overall runtime is essentially mathcal o n log n p p by the structure of the low rank criterion we are able to avoid communication at the top of the octree we demonstrate the effectiveness of our parallelization on several challenging models

adaptive image resizing based on continuous domain stochastic modeling we introduce an adaptive continuous domain modeling approach to texture and natural images the continuous domain image is assumed to be a smooth function and we embed it in a parameterized sobolev space we point out a link between sobolev spaces and stochastic auto regressive models and exploit it for optimally choosing sobolev parameters from available pixel values to this aim we use exact continuous to discrete mapping of the auto regressive model that is based on symmetric exponential splines the mapping is computationally efficient and we exploit it for maximizing an approximated gaussian likelihood function we account for non gaussian levy type processes by deriving a more robust estimator that is based on the sample auto correlation sequence both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria experimental image resizing results indicate that the auto correlation criterion can cope better with non gaussian processes and model mismatch our work demonstrates the importance of the auto correlation function in adaptive image interpolation and image modeling tasks and we believe it is instrumental in other image processing tasks as well

arranging and interpolating sparse unorganized feature points with geodesic circular arc a novel method to reconstruct object boundaries with geodesic circular arc is proposed in this paper within this framework an energy of circular arc spline is utilized to simultaneously arrange and interpolate each member in the set of sparse unorganized feature points from the desired boundaries a general form for a family of parametric circular arc spline is firstly derived and followed by a novel method of arranging these feature points by minimizing an energy term depending on the circular arc spline configuration defined on these feature points with regard to the fact that the energy function is usually nonconvex and nondifferentiable at its critical points an improved scheme of particle swarm optimizer is given to find the minimum for the energy in this paper with this improved scheme each pair of neighboring feature points along the boundaries of the desired objects are picked out from the set of sparse unorganized feature points and the corresponding directional chord tangent angles are computed simultaneously to finish interpolation we show experimentally and comparatively that the proposed method can perform effectively to restrict leakage on weak boundaries and premature convergence on long concave boundaries besides it has good noise robustness and can as well extract multiple and open boundaries

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes

multiscale semilocal interpolation with antialiasing aliasing is a common artifact in low resolution lr images generated by a downsampling process recovering the original high resolution image from its lr counterpart while at the same time removing the aliasing artifacts is a challenging image interpolation problem since a natural image normally contains redundant similar patches the values of missing pixels can be available at texture relevant lr pixels based on this we propose an iterative multiscale semilocal interpolation method that can effectively address the aliasing problem the proposed method estimates each missing pixel from a set of texture relevant semilocal lr pixels with the texture similarity iteratively measured from a sequence of patches of varying sizes specifically in each iteration top texture relevant lr pixels are used to construct a data fidelity term in a maximum a posteriori estimation and a bilateral total variation is used as the regularization term experimental results compared with existing interpolation methods demonstrate that our method can not only substantially alleviate the aliasing problem but also produce better results across a wide range of scenes both in terms of quantitative evaluation and subjective visual quality

wideband fast kernel independent modeling of large multiscale structures via nested equivalent source approximation we propose a wideband fast kernel independent modeling of large multiscale structures we employ a nested equivalent source approximation nesa to compress the dense system matrix the nesa was introduced by these authors for low and moderate frequency problems smaller than a few wavelengths here we introduce a high frequency nesa algorithm and propose a hybrid version with extreme wideband properties the equivalent sources of the wideband nesa wnesa are obtained by an inverse source process enforcing equivalence of radiated fields on suitably defined testing surfaces in the low frequency region the nesa is used unmodified with a complexity of mathcal o n in the high frequency region in order to obtain a fixed rank matrix compression we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size and the nesa testing surfaces are defined as the boundaries of the pyramids this results in a directional nested low rank fixed rank approximation with mathcal o n log n computational complexity that is kernel independent overall the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low frequency nesa for multiscale problems numerical results and discussions demonstrate the validity of the proposed work

an adaptable k nearest neighbors algorithm for mmse image interpolation we propose an image interpolation algorithm that is nonparametric and learning based primarily using an adaptive k nearest neighbor algorithm with global considerations through markov random fields the empirical nature of the proposed algorithm ensures image results that are data driven and hence reflect ldquoreal worldrdquo images well given enough training data the proposed algorithm operates on a local window using a dynamic k nearest neighbor algorithm where k differs from pixel to pixel small for test points with highly relevant neighbors and large otherwise based on the neighbors that the adaptable k provides and their corresponding relevance measures a weighted minimum mean squared error solution determines implicitly defined filters specific to low resolution image content without yielding to the limitations of insufficient training additionally global optimization via single pass markov approximations similar to cited nearest neighbor algorithms provides additional weighting for filter generation the approach is justified in using a sufficient quantity of training per test point and takes advantage of image properties for in depth analysis we compare to existing methods and draw parallels between intuitive concepts including classification and ideas introduced by other nearest neighbor algorithms by explaining manifolds in low and high dimensions

nonlinear image upsampling method based on radial basis function interpolation in this paper we present a novel edge directed upsampling method based on radial basis function rbf interpolation in order to remove artifacts such as blurred edges or blocking effects we suggest a nonlinear method capable of taking edge information into account the resampling evaluation is determined according to the edge orientation the proposed scheme is as simple to implement as linear methods but it demonstrates improved visual quality by preserving the edge features better than the classical linear interpolation methods the algorithm is compared with some well known linear schemes as well as recently developed nonlinear schemes the resulting images demonstrate the new algorithm s ability to magnify an image while preserving the edge features

contrast guided image interpolation in this paper a contrast guided image interpolation method is proposed that incorporates contrast information into the image interpolation process given the image under interpolation four binary contrast guided decision maps cdms are generated and used to guide the interpolation filtering through two sequential stages 1 the 45 and 135 cdms for interpolating the diagonal pixels and 2 the 0 and 90 cdms for interpolating the row and column pixels after applying edge detection to the input image the generation of a cdm lies in evaluating those nearby non edge pixels of each detected edge for re classifying them possibly as edge pixels this decision is realized by solving two generalized diffusion equations over the computed directional variation dv fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges respectively the amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge the diffused dv fields are then thresholded for yielding the binary cdms respectively therefore the decision bands with variable widths will be created on each cdm the two cdms generated in each stage will be exploited as the guidance maps to conduct the interpolation process for each declared edge pixel on the cdm a 1 d directional filtering will be applied to estimate its associated to be interpolated pixel along the direction as indicated by the respective cdm otherwise a 2 d directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non edge pixel extensive simulation results have clearly shown that the proposed contrast guided image interpolation is superior to other state of the art edge guided image interpolation methods in addition the computational complexity is relatively low when compared with existing methods hence it is fairly attractive for real time image applications

a map based image interpolation method via viterbi decoding of markov chains of interpolation functions a new method of image resolution up conversion image interpolation based on maximum a posteriori sequence estimation is proposed instead of making a hard decision about the value of each missing pixel we estimate the missing pixels in groups at each missing pixel of the high resolution hr image we consider an ensemble of candidate interpolation methods interpolation functions the interpolation functions are interpreted as states of a markov model in other words the proposed method undergoes state transitions from one missing pixel position to the next accordingly the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing hr pixel positions we derive a parameter free probabilistic model for this to be estimated sequence of interpolation functions then we solve the estimation problem using a trellis representation and the viterbi algorithm using directional interpolation functions and sequence estimation techniques we classify the new algorithm as an adaptive directional interpolation using soft decision estimation techniques experimental results show that the proposed algorithm yields images with higher or comparable peak signal to noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations

shape based interpolation of multidimensional grey level images shape based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object it accomplishes this by first applying a distance transform to the data this results in the creation of a grey level data set in which the value at each point represents the minimum distance from that point to the surface of the object by convention points inside the object are assigned positive values points outside are assigned negative values this distance transformed data set is then interpolated using linear or higher order interpolation and is then thresholded at a distance value of zero to produce the interpolated binary data set here the authors describe a new method that extends shape based interpolation to grey level input data sets this generalization consists of first lifting the n dimensional n d image data to represent it as a surface or equivalently as a binary image in an n 1 dimensional n 1 d space the binary shape based method is then applied to this image to create an n 1 d binary interpolated image finally this image is collapsed inverse of lifting to create the n d interpolated grey level data set the authors have conducted several evaluation studies involving patient computed tomography ct and magnetic resonance mr data as well as mathematical phantoms they all indicate that the new method produces more accurate results than commonly used grey level linear interpolation methods although at the cost of increased computation

enlargement or reduction of digital images with minimum loss of information the purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary noninteger scaling factors in our formulation the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and spl delta respectively the change of scale is achieved by determining the spline with step size spl delta that provides the closest approximation of the original signal in the l sub 2 norm we show that this approximation can be computed in three steps i a digital prefilter that provides the b spline coefficients of the input signal ii a resampling using an expansion formula with a modified sampling kernel that depends explicitly on spl delta and iii a digital postfilter that maps the result back into the signal domain we provide explicit formulas for n 0 1 and 3 and propose solutions for the efficient implementation of these algorithms we consider image processing examples and show that the present method compares favorably with standard interpolation techniques finally we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity

fast directional algorithms for the helmholtz kernel this paper presents a new directional multilevel algorithm for solving n body or n point problems with highly oscillatory kernels we address the problem by first proving that the interaction between a ball of radius r and a well separated region has an approximate low rank representation as long as the well separated region belongs to a cone with a spanning angle of o 1 r and is at a distance which is at least o r 2 away from the ball based on this representation our algorithm organizes the high frequency computation using a multidirectional and multiscale strategy our algorithm is proved to have an optimal o nlogn computational complexity for any given accuracy when the points are sampled from a two dimensional surface

image zooming method using edge directed moving least squares interpolation based on exponential polynomials this paper presents a nonlinear image interpolation algorithm the suggested method is based on the moving least squares mls projection technique but introduces a fundamental modification the algebraic polynomial based mls methods provide very satisfactory results however the associated approximation space is shift and scale invariant so that it cannot be adjusted according to the characteristic of a given data as a result when upsampling images it has a limitation in producing sharp edges such that edges are often blurred in the magnified images to recover sharper edges we need to reduce smoothing parameter or adapt a new parameter sharpening the edges motivated by this observations we propose a novel mls method governed by a set of exponential polynomials with tension parameters such that they can be tuned to the characteristic of given data moreover for a better match to the local structures around the edges the suggested algorithm uses weights which consider the edge orientation numerical results are presented and compared visually and by using some quantitative fidelity measures psnr epsnr ssim and fsim to the bicubic spline interpolation and other recently developed nonlinear methods the results demonstrate the new algorithm s ability to magnify an image while preserving edge features

interpolation dependent image downsampling traditional methods for image downsampling commit to remove the aliasing artifacts however the influences on the quality of the image interpolated from the downsampled one are usually neglected to tackle this problem in this paper we propose an interpolation dependent image downsampling idid where interpolation is hinged to downsampling given an interpolation method the goal of idid is to obtain a downsampled image that minimizes the sum of square errors between the input image and the one interpolated from the corresponding downsampled image utilizing a least squares algorithm the solution of idid is derived as the inverse operator of upsampling we also devise a content dependent idid for the interpolation methods with varying interpolation coefficients numerous experimental results demonstrate the viability and efficiency of the proposed idid

markov random field model based edge directed image interpolation this paper presents an edge directed image interpolation algorithm in the proposed algorithm the edge directions are implicitly estimated with a statistical based approach in opposite to explicit edge directions the local edge directions are indicated by length 16 weighting vectors implicitly the weighting vectors are used to formulate geometric regularity gr constraint smoothness along edges and sharpness across edges and the gr constraint is imposed on the interpolated image through the markov random field mrf model furthermore under the maximum a posteriori mrf framework the desired interpolated image corresponds to the minimal energy state of a 2 d random field given the low resolution image simulated annealing methods are used to search for the minimal energy state from the state space to lower the computational complexity of mrf a single pass implementation is designed which performs nearly as well as the iterative optimization simulation results show that the proposed mrf model based edge directed interpolation method produces edges with strong geometric regularity compared to traditional methods and other edge directed interpolation methods the proposed method improves the subjective quality of the interpolated edges while maintaining a high psnr level

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

a new orientation adaptive interpolation method we propose an isophote oriented orientation adaptive interpolation method the proposed method employs an interpolation kernel that adapts to the local orientation of isophotes and the pixel values are obtained through an oriented bilinear interpolation we show that by doing so the curvature of the interpolated isophotes is reduced and thus zigzagging artifacts are largely suppressed analysis and experiments show that images interpolated using the proposed method are visually pleasing and almost artifact free

edge forming methods for color image zooming this paper introduces edge forming schemes for image zooming of color images by general magnification factors in order to remove reduce artifacts arising in image interpolation such as image blur and the checkerboard effect an edge forming method is suggested to be applied as a postprocess of standard interpolation methods the method is based on nonconvex nonlinear partial differential equations the equations are carefully discretized incorporating numerical schemes of anisotropic diffusion to be able to form reliable edges satisfactorily the alternating direction implicit adi method is employed for an efficient simulation of the model it has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 adi iterations various results are given to show th effectiveness and reliability of the algorithm

an edge guided image interpolation algorithm via directional filtering and data fusion preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high resolution image from a low resolution counterpart we propose a new edge guided nonlinear interpolation technique through directional filtering and data fusion for a pixel to be interpolated two observation sets are defined in two orthogonal directions and each set produces an estimate of the pixel value these directional estimates modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square error estimation lmmse technique into a more robust estimate using the statistics of the two observation sets we also present a simplified version of the lmmse based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

orthogonal distance fitting of implicit curves and surfaces dimensional model fitting finds its applications in various fields of science and engineering and is a relevant subject in computer machine vision and coordinate metrology in this paper we present two new fitting algorithms distance based and coordinate based algorithm for implicit surfaces and plane curves which minimize the square sum of the orthogonal error distances between the model feature and the given data points each of the two algorithms has its own advantages and is to be purposefully applied to a specific fitting task considering the implementation and memory space cost and possibilities of observation weighting by the new algorithms the model feature parameters are grouped and simultaneously estimated in terms of form position and rotation parameters the form parameters determine the shape of the model feature and the position rotation parameters describe the rigid body motion of the model feature the proposed algorithms are applicable to any kind of implicit surface and plane curve in this paper we also describe algorithm implementation and show various examples of orthogonal distance fit

warped distance for space variant linear image interpolation the problem of image interpolation using linear techniques is dealt with in this paper conventional space invariant methods are revisited and changed into space variant ones by introducing the concept of the warped distance among the pixels of an image a better perceptual rendition of the image details is obtained in this way this effect is proved both via the evaluation of the response to an idealized sigmoidal edge model and with experiments on real world images the computational costs of the proposed approach are very small when compared to those of state of the art nonlinear interpolation operators

a general methodology for the determination of 2d bodies elastic deformation invariants application to the automatic identification of parasites a novel methodology is introduced here that exploits 2d images of arbitrary elastic body deformation instances so as to quantify mechanoelastic characteristics that are deformation invariant determination of such characteristics allows for developing methods offering an image of the undeformed body general assumptions about the mechanoelastic properties of the bodies are stated which lead to two different approaches for obtaining bodies deformation invariants one was developed to spot a deformed body s neutral line and its cross sections while the other solves deformation pdes by performing a set of equivalent image operations on the deformed body images both of these processes may furnish a body undeformed version from its deformed image this was confirmed by obtaining the undeformed shape of deformed parasites cells protozoa fibers and human lips in addition the method has been applied to the important problem of parasite automatic classification from their microscopic images to achieve this we first apply the previous method to straighten the highly deformed parasites and then apply a dedicated curve classification method to the straightened parasite contours it is demonstrated that essentially different deformations of the same parasite give rise to practically the same undeformed shape thus confirming the consistency of the introduced methodology finally the developed pattern recognition method classifies the unwrapped parasites into six families with an accuracy rate of 97 6 percent

an adaptive image interpolation algorithm for image video processing image interpolation is one of the key technologies in image video processing in this study a new adaptive image interpolation algorithm is proposed the objective of the proposed approach is to recover up sampled image frames from the corresponding decimated low resolution image frames in the proposed approach within each iteration two proposed nonlinear filters are utilized to iteratively generate high frequency components lost within the decimation procedure finally a post processing procedure is adopted to reduce the blocking artifacts within the interpolated images based on the experimental results obtained in this study in terms of the average psnrp peak signal to noise ratio in db and subjective measure of the quality of the interpolated images the interpolation results by the proposed approach are better than that by three existing interpolation approaches for comparison