decomposition tables for experiments ii two one randomizations we investigate structure for pairs of randomizations that do not follow each other in a chain these are unrandomized inclusive independent coincident or double randomizations this involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment we show how to establish the decomposition table giving the sources of variation their relationships and their degrees of freedom so that competing designs can be evaluated this leads to recommendations for when the different types of multiple randomization should be used

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

robust soft decision interpolation using weighted least squares soft decision adaptive interpolation sai provides a powerful framework for image interpolation the robustness of sai can be further improved by using weighted least squares estimation instead of least squares estimation in both of the parameter estimation and data estimation steps to address the mismatch issue of geometric duality during parameter estimation the residuals prediction errors are weighted according to the geometric similarity between the pixel of interest and the residuals the robustness of data estimation can be improved by modeling the weights of residuals with the well known bilateral filter experimental results show that there is a 0 25 db increase in peak signal to noise ratio psnr for a sample set of natural images after the suggested improvements are incorporated into the original sai the proposed algorithm produces the highest quality in terms of psnr and subjective quality among sophisticated algorithms in the literature

three new tests of independence that differentiate models of risky decision making this paper tests new independence properties to compare three models of risky decision making according to the rank affected multiplicative ram weights model all three properties should be satisfied according to the transfer of attention exchange tax model two should be satisfied and one can be violated however according to cumulative prospect theory cpt all three properties will be violated if the probability weighting function is nonlinear although cpt is flexible enough to accommodate violations of these properties its predicted violations based on previously estimated parameters failed to materialize in 14 choices for which the cpt model disagreed with tax cpt correctly predicted the modal choice in only one case and tax predicted the modal choice in the other 13 new versions of three other paradoxes were also tested and found to refute cpt

linear interpolation revitalized we present a simple original method to improve piecewise linear interpolation with uniform knots we shift the sampling knots by a fixed amount while enforcing the interpolation property we determine the theoretical optimal shift that maximizes the quality of our shifted linear interpolation surprisingly enough this optimal value is nonzero and close to 1 5 we confirm our theoretical findings by performing several experiments a cumulative rotation experiment and a zoom experiment both show a significant increase of the quality of the shifted method with respect to the standard one we also observe that in these results we get a quality that is similar to that of the computationally more costly high quality cubic convolution

single image super resolution using local geometric duality and non local similarity super resolution sr from a single image plays an important role in many computer vision applications it aims to estimate a high resolution hr image from an input low resolution lr image to ensure a reliable and robust estimation of the hr image we propose a novel single image sr method that exploits both the local geometric duality gd and the non local similarity of images the main principle is to formulate these two typically existing features of images as effective priors to constrain the super resolved results in consideration of this principle the robust soft decision interpolation method is generalized as an outstanding adaptive gd agd based local prior to adaptively design weights for the agd prior a local non smoothness detection method and a directional standard deviation based weights selection method are proposed after that the agd prior is combined with a variational framework based non local prior furthermore the proposed algorithm is speeded up by a fast gd matrices construction method which primarily relies on the selective pixel processing the extensive experimental results verify the effectiveness of the proposed method compared with several state of the art sr algorithms

rectangular lattice designs efficiency factors and analysis rectangular lattice designs are shown to be generally balanced with respect to a particular decomposition of the treatment space efficiency factors are calculated and the analysis including recovery of interblock information is outlined the ideas are extended to rectangular lattice designs with an extra blocking factor

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

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

the bounded rationality of probability distortion in decision making under risk dmr participants choices are based on probability values systematically different from those that are objectively correct similar systematic distortions are found in tasks involving relative frequency judgments jrf these distortions limit performance in a wide variety of tasks and an evident question is why do we systematically fail in our use of probability and relative frequency information we propose a bounded log odds model blo of probability and relative frequency distortion based on three assumptions 1 log odds probability and relative frequency are mapped to an internal log odds scale 2 boundedness the range of representations of probability and relative frequency are bounded and the bounds change dynamically with task and 3 variance compensation the mapping compensates in part for uncertainty in probability and relative frequency values we compared human performance in both dmr and jrf tasks to the predictions of the blo model as well as 11 alternative models each missing one or more of the underlying blo assumptions factorial model comparison the blo model and its assumptions proved to be superior to any of the alternatives in a separate analysis we found that blo accounts for individual participants data better than any previous model in the dmr literature we also found that subject to the boundedness limitation participants choice of distortion approximately maximized the mutual information between objective task relevant values and internal values a form of bounded rationality

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

economic decision making compared with an equivalent motor task there is considerable evidence that human economic decision making deviates from the predictions of expected utility theory eut and that human performance conforms to eut in many perceptual and motor decision tasks it is possible that these results reflect a real difference in decision making in the 2 domains but it is also possible that the observed discrepancy simply reflects typical differences in experimental design we developed a motor task that is mathematically equivalent to choosing between lotteries and used it to compare how the same subject chose between classical economic lotteries and the same lotteries presented in equivalent motor form in experiment 1 we found that subjects are more risk seeking in deciding between motor lotteries in experiment 2 we used cumulative prospect theory to model choice and separately estimated the probability weighting functions and the value functions for each subject carrying out each task we found no patterned differences in how subjects represented outcome value in the motor and the classical tasks however the probability weighting functions for motor and classical tasks were markedly and significantly different those for the classical task showed a typical tendency to overweight small probabilities and underweight large probabilities and those for the motor task showed the opposite pattern of probability distortion this outcome also accounts for the increased risk seeking observed in the motor tasks of experiment 1 we conclude that the same subject distorts probability but not value differently in making identical decisions in motor and classical form

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

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

hallucinating face in the dct domain in this paper we propose a novel learning based face hallucination framework built in the dct domain which can produce a high resolution face image from a single low resolution one the problem is formulated as inferring the dct coefficients in frequency domain instead of estimating pixel intensities in spatial domain our study shows that dc coefficients can be estimated fairly accurately by simple interpolation based methods ac coefficients which contain the information of local features of face image cannot be estimated well using interpolation a simple but effective learning based inference model is proposed to infer the ac coefficients experiments have been conducted to demonstrate the effectiveness of the proposed method in producing high quality hallucinated face 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

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

super resolution of images based on local correlations an adaptive two step paradigm for the super resolution of optical images is developed in this paper the procedure locally projects image samples onto a family of kernels that are learned from image data first an unsupervised feature extraction is performed on local neighborhood information from a training image these features are then used to cluster the neighborhoods into disjoint sets for which an optimal mapping relating homologous neighborhoods across scales can be learned in a supervised manner a super resolved image is obtained through the convolution of a low resolution test image with the established family of kernels results demonstrate the effectiveness of the approach

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

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

addendum b spline interpolation in medical image processing analyzes b spline interpolation techniques of degree 2 4 and 5 with respect to all criteria that have been applied to evaluate various interpolation schemes in a recently published survey on image interpolation in medical imaging lehmann et al 1999 it is shown that high degree b spline interpolation has superior fourier properties smallest interpolation error and reasonable computing times therefore high degree b splines are preferable interpolators for numerous applications in medical image processing particularly if high precision is required if no aliasing occurs this result neither depends on the geometric transform applied for the tests nor the actual content of images

pairwise operator learning for patch based single image super resolution motivated by the fact that image patches could be inherently represented by matrices single image super resolution is treated as a problem of learning regression operators in a matrix space in this paper the regression operators that map low resolution image patches to high resolution image patches are generally defined by the left and right multiplication operators the pairwise operators are respectively used to extract the raw and column information of low resolution image patches for recovering high resolution estimations the patch based regression algorithm possesses three favorable properties first the proposed super resolution algorithm is efficient during both training and testing because image patches are treated as matrices second the data storage requirement of the optimal pairwise operator is far less than most popular single image super resolution algorithms because only two small sized matrices need to be stored last the super resolution performance is competitive with most popular single image super resolution algorithms because both raw and column information of image patches is considered experimental results show the efficiency and effectiveness of the proposed patch based single image super resolution algorithm

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

what is an analysis of variance the analysis of variance is usually regarded as being concerned with sums of squares of numbers and independent quadratic forms of random variables in this paper an alternative interpretation is discussed for certain classes of dispersion models for finite or infinite arrays of random variables a form of generalized spectral analysis is described and its intuitive meaning explained the analysis gives a spectral decomposition of each dispersion in the class incorporating an analysis of the common variance and an associated orthogonal decomposition of each of the random variables one by product of this approach is a clear understanding of the similarity between the spectral decomposition for second order stationary processes and the familiar linear models with random effects

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

multiple randomizations discussion multitiered experiments are characterized by involving multiple randomizations in a sense that we make explicit we compare and contrast six types of multiple randomizations using a wide range of examples and discuss their use in designing experiments we outline a system of describing the randomizations in terms of sets of objects their associated tiers and the factor nesting using randomization diagrams which give a convenient and readily assimilated summary of an experiment s randomization we also indicate how to formulate a randomization based mixed model for the analysis of data from such experiments

estimability of variance components when all model matrices commute abstract this paper deals with estimability of variance components in mixed models when all model matrices commute in this situation it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators if in addition the family of possible variance covariance matrices forms an orthogonal block structure then there are the same number of variance components as strata and the variance components are all estimable if and only if there are non zero residual degrees of freedom in each stratum we investigate the case where the family of possible variance covariance matrices while still commutative no longer forms an orthogonal block structure now the variance components may or may not all be estimable but there is no clear link with residual degrees of freedom whether or not they are all estimable there may or may not be uniformly best unbiased quadratic estimators of those that are estimable examples are given to demonstrate all four possibilities

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

bayesian model selection for group studies bayesian model selection bms is a powerful method for determining the most likely among a set of competing hypotheses about the mechanisms that generated observed data bms has recently found widespread application in neuroimaging particularly in the context of dynamic causal modelling dcm however so far combining bms results from several subjects has relied on simple fixed effects metrics e g the group bayes factor gbf that do not account for group heterogeneity or outliers in this paper we compare the gbf with two random effects methods for bms at the between subject or group level these methods provide inference on model space using a classical and bayesian perspective respectively first a classical frequentist approach uses the log model evidence as a subject specific summary statistic this enables one to use analysis of variance to test for differences in log evidences over models relative to inter subject differences we then consider the same problem in bayesian terms and describe a novel hierarchical model which is optimised to furnish a probability density on the models themselves this new variational bayes method rests on treating the model as a random variable and estimating the parameters of a dirichlet distribution which describes the probabilities for all models considered these probabilities then define a multinomial distribution over model space allowing one to compute how likely it is that a specific model generated the data of a randomly chosen subject as well as the exceedance probability of one model being more likely than any other model using empirical and synthetic data we show that optimising a conditional density of the model probabilities given the log evidences for each model over subjects is more informative and appropriate than both the gbf and frequentist tests of the log evidences in particular we found that the hierarchical bayesian approach is considerably more robust than either of the other approaches in the presence of outliers we expect that this new random effects method will prove useful for a wide range of group studies not only in the context of dcm but also for other modelling endeavours e g comparing different source reconstruction methods for eeg meg or selecting among competing computational models of learning and decision making

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

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

decomposition tables for experiments i a chain of randomizations one aspect of evaluating the design for an experiment is the discovery of the relationships between subspaces of the data space initially we establish the notation and methods for evaluating an experiment with a single randomization starting with two structures or orthogonal decompositions of the data space we describe how to combine them to form the overall decomposition for a single randomization experiment that is structure balanced the relationships between the two structures are characterized using efficiency factors the decomposition is encapsulated in a decomposition table then for experiments that involve multiple randomizations forming a chain we take several structures that pairwise are structure balanced and combine them to establish the form of the orthogonal decomposition for the experiment in particular it is proven that the properties of the design for such an experiment are derived in a straightforward manner from those of the individual designs we show how to formulate an extended decomposition table giving the sources of variation their relationships and their degrees of freedom so that competing designs can be evaluated

image superresolution using support vector regression a thorough investigation of the application of support vector regression svr to the superresolution problem is conducted through various frameworks prior to the study the svr problem is enhanced by finding the optimal kernel this is done by formulating the kernel learning problem in svr form as a convex optimization problem specifically a semi definite programming sdp problem an additional constraint is added to reduce the sdp to a quadratically constrained quadratic programming qcqp problem after this optimization investigation of the relevancy of svr to superresolution proceeds with the possibility of using a single and general support vector regression for all image content and the results are impressive for small training sets this idea is improved upon by observing structural properties in the discrete cosine transform dct domain to aid in learning the regression further improvement involves a combination of classification and svr based techniques extending works in resolution synthesis this method termed kernel resolution synthesis uses specific regressors for isolated image content to describe the domain through a partitioned look of the vector space thereby yielding good results

analysis of variance tables based on experimental structure a stepwise procedure for obtaining the experimental structure for a particular experiment is presented together with rules for deriving the analysis of variance table from that structure the procedure involves the division of the factors into groups and is essentially a generalization of the method of nelder 1965 proceedings of the royal society series a 283 147 162 1965 proceedings of the royal society series a 283 163 178 to what are termed multi tiered experiments the proposed method is illustrated for a wine tasting experiment

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

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

novel example based method for super resolution and denoising of medical images in this paper we propose a novel example based method for denoising and super resolution of medical images the objective is to estimate a high resolution image from a single noisy low resolution image with the help of a given database of high and low resolution image patch pairs denoising and super resolution in this paper is performed on each image patch for each given input low resolution patch its high resolution version is estimated based on finding a nonnegative sparse linear representation of the input patch over the low resolution patches from the database where the coefficients of the representation strongly depend on the similarity between the input patch and the sample patches in the database the problem of finding the nonnegative sparse linear representation is modeled as a nonnegative quadratic programming problem the proposed method is especially useful for the case of noise corrupted and low resolution image experimental results show that the proposed method outperforms other state of the art super resolution methods while effectively removing noise

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

an iterative growing and pruning algorithm for classification tree design a critical issue in classification tree design obtaining right sized trees i e trees which neither underfit nor overfit the data is addressed instead of stopping rules to halt partitioning the approach of growing a large tree with pure terminal nodes and selectively pruning it back is used a new efficient iterative method is proposed to grow and prune classification trees this method divides the data sample into two subsets and iteratively grows a tree with one subset and prunes it with the other subset successively interchanging the roles of the two subsets the convergence and other properties of the algorithm are established theoretical and practical considerations suggest that the iterative free growing and pruning algorithm should perform better and require less computation than other widely used tree growing and pruning algorithms numerical results on a waveform recognition problem are presented to support this view

a belief based account of decision under uncertainty we develop a belief based account of decision under uncertainty this model predicts decisions under uncertainty from i judgments of probability which are assumed to satisfy support theory and ii decisions under risk which are assumed to satisfy prospect theory in two experiments subjects evaluated uncertain prospects and assessed the probability of the respective events study 1 involved the 1995 professional basketball playoffs study 2 involved the movement of economic indicators in a simulated economy the results of both studies are consistent with the belief based account but violate the partition inequality implied by the classical theory of decision under uncertainty

fast dct based spatial domain interpolation of blocks in images an efficient method is presented to restore a block in an image using a reduced set of border pixels the basic assumption is that if the set of pixels consisting of the missing block and its border pixels is transformed by the dct the high frequency coefficients obtained can be set to zero a system of linear equations results whose solution yields approximations for the values of the lost pixels in this interpolation scheme only eight border pixels are used in the computation of any missing pixel simulation results show that the approach generally outperforms alternative methods at a smaller computational cost

on learning vector valued functions in this letter we provide a study of learning in a hilbert space of vectorvalued functions we motivate the need for extending learning theory of scalar valued functions by practical considerations and establish some basic results for learning vector valued functions that should prove useful in applications specifically we allow an output space y to be a hilbert space and we consider a reproducing kernel hilbert space of functions whose values lie in y in this setting we derive the form of the minimal norm interpolant to a finite set of data and apply it to study some regularization functionals that are important in learning theory we consider specific examples of such functionals corresponding to multiple output regularization networks and support vector machines for both regression and classification finally we provide classes of operator valued kernels of the dot product and translation invariant type

fast acquisition and reconstruction of optical coherence tomography images via sparse representation in this paper we present a novel technique based on compressive sensing principles for reconstruction and enhancement of multi dimensional image data our method is a major improvement and generalization of the multi scale sparsity based tomographic denoising msbtd algorithm we recently introduced for reducing speckle noise our new technique exhibits several advantages over msbtd including its capability to simultaneously reduce noise and interpolate missing data unlike msbtd our new method does not require an a priori high quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions this novel image restoration method which we termed sparsity based simultaneous denoising and interpolation sbsdi utilizes sparse representation dictionaries constructed from previously collected datasets we tested the sbsdi algorithm on retinal spectral domain optical coherence tomography images captured in the clinic experiments showed that the sbsdi algorithm qualitatively and quantitatively outperforms other state of the art methods

learning the kernel matrix with semidefinite programming kernel based learning algorithms work by embedding the data into a euclidean space and then searching for linear relations among the embedded data points the embedding is performed implicitly by specifying the inner products between each pair of points in the embedding space this information is contained in the so called kernel matrix a symmetric and positive semidefinite matrix that encodes the relative positions of all points specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space classical model selection problems in machine learning in this paper we show how the kernel matrix can be learned from data via semidefinite programming sdp techniques when applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm using the labeled part of the data one can learn an embedding also for the unlabeled part the similarity between test points is inferred from training points and their labels importantly these learning problems are convex so we obtain a method for learning both the model class and the function without local minima furthermore this approach leads directly to a convex method for learning the 2 norm soft margin parameter in support vector machines solving an important open problem

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework