shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

predicting links based on knowledge dissemination in complex network abstract link prediction is the task of mining the missing links in networks or predicting the next vertex pair to be connected by a link a lot of link prediction methods were inspired by evolutionary processes of networks in this paper a new mechanism for the formation of complex networks called knowledge dissemination kd is proposed with the assumption of knowledge disseminating through the paths of a network accordingly a new link prediction method knowledge dissemination based link prediction kdlp is proposed to test kd kdlp characterizes vertex similarity based on knowledge quantity kq which measures the importance of a vertex through h index extensive numerical simulations on six real world networks demonstrate that kdlp is a strong link prediction method which performs at a higher prediction accuracy than four well known similarity measures including common neighbors local path index average commute time and matrix forest index furthermore based on the common conclusion that an excellent link prediction method reveals a good evolving mechanism the experiment results suggest that kd is a considerable network evolving mechanism for the formation of complex networks

dynamic contrast based quantization for lossy wavelet image compression this paper presents a contrast based quantization strategy for use in lossy wavelet image compression that attempts to preserve visual quality at any bit rate based on the results of recent psychophysical experiments using near threshold and suprathreshold wavelet subband quantization distortions presented against natural image backgrounds subbands are quantized such that the distortions in the reconstructed image exhibit root mean squared contrasts selected based on image subband and display characteristics and on a measure of total visual distortion so as to preserve the visual system s ability to integrate edge structure across scale space within a single unified framework the proposed contrast based strategy yields images which are competitive in visual quality with results from current visually lossless approaches at high bit rates and which demonstrate improved visual quality over current visually lossy approaches at low bit rates this strategy operates in the context of both nonembedded and embedded quantization the latter of which yields a highly scalable codestream which attempts to maintain visual quality at all bit rates a specific application of the proposed algorithm to jpeg 2000 is presented

vsnr a wavelet based visual signal to noise ratio for natural images this paper presents an efficient metric for quantifying the visual fidelity of natural images based on near threshold and suprathreshold properties of human vision the proposed metric the visual signal to noise ratio vsnr operates via a two stage approach in the first stage contrast thresholds for detection of distortions in the presence of natural images are computed via wavelet based models of visual masking and visual summation in order to determine whether the distortions in the distorted image are visible if the distortions are below the threshold of detection the distorted image is deemed to be of perfect visual fidelity vsnr infin and no further analysis is required if the distortions are suprathreshold a second stage is applied which operates based on the low level visual property of perceived contrast and the mid level visual property of global precedence these two properties are modeled as euclidean distances in distortion contrast space of a multiscale wavelet decomposition and vsnr is computed based on a simple linear sum of these distances the proposed vsnr metric is generally competitive with current metrics of visual fidelity it is efficient both in terms of its low computational complexity and in terms of its low memory requirements and it operates based on physical luminances and visual angle rather than on digital pixel values and pixel based dimensions to accommodate different viewing conditions

on the regularity of harmonic functions and spherical harmonic maps defined on lattices abstract a growth lemma for certain discrete symmetric laplacians defined on a lattice z d zd rd with spacing is proved the lemma implies a de giorgi theorem that the harmonic functions for these laplacians are equi holder continuous 0 these results are then applied to establish regularity properties for the harmonic maps defined on zd and taking values in an n dimensional sphere sn uniform in questions of the convergence 0 and the dirichlet problem for these discrete harmonic maps are also addressed

a visually weighted quantization scheme for image bandwidth compression at low data rates source encoding of images for bandwidth compression has become attractive in recent years because of decreasing hardware costs by combining the source encoding approach with transform coding techniques it is possible to obtain good image quality at low data rates the general aspects of such a system are presented the design of the quantizer for transform coefficients which is the major source of error associated with the compression process is considered using a visual fidelity criterion and subject to the constraint that the entropy of the quantizer be a prespecified quantity a visually weighted suboptimal quantization scheme is developed to take into account the relative importance of different transform coefficients to the human visual system

vertex similarity in networks we consider methods for quantifying the similarity of vertices in networks we propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar this leads to a self consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network we test our similarity measure on computer generated networks for which the expected results are known and on a number of real world networks

a mathematical analysis of the dct coefficient distributions for images over the past two decades there have been various studies on the distributions of the dct coefficients for images however they have concentrated only on fitting the empirical data from some standard pictures with a variety of well known statistical distributions and then comparing their goodness of fit the laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data yet to the best of our knowledge there has been no mathematical justification as to what gives rise to this distribution we offer a rigorous mathematical analysis using a doubly stochastic model of the images which not only provides the theoretical explanations necessary but also leads to insights about various other observations from the literature this model also allows us to investigate how certain changes in the image statistics could affect the dct coefficient distributions

synchronizability in complex ad hoc dynamical networks with accelerated growth recent research works have been pursued in connection with network synchronizability under various constraints for different topological structures and evolving mechanisms however the fundamental question of how the synchronizability of the networks relates to accelerated growth and ad hoc property in the evolving processes remains underexplored here we study the ad hoc dynamical models with accelerated growth where the total number of edges increases faster than linearly with network size by adopting three attachment mechanisms random rewired and preferential attachment we investigate the second largest eigenvalues and the ratios of the extremal eigenvalues of coupled matrices in the accelerated models with different evolving parameters for the new models we demonstrate the robustness and fragility of synchronization against random and specific attacks by numerical simulations we find that accelerated growth represents a convenient tool for improving the synchronizability of an evolving network furthermore we show that not only network synchronization but also topological periodicity has robustness and fragility against random failures and specifical removal of the nodes respectively in particular when ad hoc property is suggested in the evolving networks we find that the deletion of nodes is easier to change network synchronizability and robustness compared to the addition of nodes

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

rate bounds on ssim index of quantized images in this paper we derive bounds on the structural similarity ssim index as a function of quantization rate for fixed rate uniform quantization of image discrete cosine transform dct coefficients under the high rate assumption the space domain ssim index is first expressed in terms of the dct coefficients of the space domain vectors the transform domain ssim index is then used to derive bounds on the average ssim index as a function of quantization rate for uniform gaussian and laplacian sources as an illustrative example uniform quantization of the dct coefficients of natural images is considered we show that the ssim index between the reference and quantized images fall within the bounds for a large set of natural images further we show using a simple example that the proposed bounds could be very useful for rate allocation problems in practical image and video coding applications

asymptotic analysis of optimal fixed rate uniform scalar quantization studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean squared error mse when a symmetric source density with infinite support is sufficiently well behaved the optimal step size spl delta sub n for symmetric uniform scalar quantization decreases as 2 spl sigma n sup 1 v sup 1 1 6n sup 2 where n is the number of quantization levels spl sigma sup 2 is the source variance and v sup 1 spl middot is the inverse of v y y sup 1 spl int sub y sup spl infin p spl sigma sup 1 x x dx equivalently the optimal support length n spl delta sub n increases as 2 spl sigma v sup 1 1 6n sup 2 granular distortion is asymptotically well approximated by spl delta sub n sup 2 12 and the ratio of overload to granular distortion converges to a function of the limit spl tau spl equiv lim sub y spl rarr spl infin y sup 1 e x x y provided as usually happens that spl tau exists when it does its value is related to the number of finite moments of the source density an asymptotic formula for the overall distortion d sub n is obtained and spl tau 1 is both necessary and sufficient for the overall distortion to be asymptotically well approximated by spl delta sub n sup 2 12 applying these results to the class of two sided densities of the form b x sup spl beta e spl alpha x sup spl alpha which includes gaussian laplacian gamma and generalized gaussian it is found that spl tau 1 that spl delta sub n decreases as ln n sup 1 spl alpha n that d sub n is asymptotically well approximated by spl delta sub n sup 2 12 and decreases as ln n sup 2 spl alpha n sup 2 and that more accurate approximations to spl delta sub n are possible the results also apply to densities with one sided infinite support such as rayleigh and weibull and to densities whose tails are asymptotically similar to those previously mentioned

adaptive image coding with perceptual distortion control this paper presents a discrete cosine transform dct based locally adaptive perceptual image coder which discriminates between image components based on their perceptual relevance for achieving increased performance in terms of quality and bit rate the new coder uses a locally adaptive perceptual quantization scheme based on a tractable perceptual distortion metric our strategy is to exploit human visual masking properties by deriving visual masking thresholds in a locally adaptive fashion the derived masking thresholds are used in controlling the quantization stage by adapting the quantizer reconstruction levels in order to meet the desired target perceptual distortion the proposed coding scheme is flexible in that it can be easily extended to work with any subband based decomposition in addition to block based transform methods compared to existing perceptual coding methods the proposed perceptual coding method exhibits superior performance in terms of bit rate and distortion control coding results are presented to illustrate the performance of the presented coding scheme

pagerank beyond the web google s pagerank method was developed to evaluate the importance of web pages via their link structure the mathematics of pagerank however are entirely general and apply to any graph or network in any domain thus pagerank is now regularly used in bibliometrics social and information network analysis and for link prediction and recommendation it s even used for systems analysis of road networks as well as biology chemistry neuroscience and physics we ll see the mathematics and ideas that unite these diverse applications

a visual model weighted cosine transform for image compression and quality assessment utilizing a cosine transform in image compression has several recognized performance benefits resulting in the ability to attain large compression ratios with small quality loss also incorporation of a model of the human visual system into an image compression or quality assessment technique intuitively should and has often proven to improve performance clearly then it should prove highly beneficial to combine the image cosine transform with a visual model in the past combining these two has been hindered by a fundamental problem resulting from the scene alteration that is necessary for proper cosine transform utilization a new analytical solution to this problem taking the form of a straightforward multiplicative weighting function is developed in this paper this solution is readily applicable to image compression and quality assessment in conjunction with a visual model and the image cosine transform in the development relevant aspects of a human visual system model are discussed and a refined version of the mean square error quality assessment measure is given which should increase this measure s utility

design of linear equalizers optimized for the structural similarity index we propose an algorithm for designing linear equalizers that maximize the structural similarity ssim index between the reference and restored signals the ssim index has enjoyed considerable application in the evaluation of image processing algorithms algorithms however have not been designed yet to explicitly optimize for this measure the design of such an algorithm is nontrivial due to the nonconvex nature of the distortion measure in this paper we reformulate the nonconvex problem as a quasi convex optimization problem which admits a tractable solution we compute the optimal solution in near closed form with complexity of the resulting algorithm comparable to complexity of the linear minimum mean squared error mmse solution independent of the number of filter taps to demonstrate the usefulness of the proposed algorithm it is applied to restore images that have been blurred and corrupted with additive white gaussian noise as a special case we consider blur free image denoising in each case its performance is compared to a locally adaptive linear mse optimal filter we show that the images denoised and restored using the ssim optimal filter have higher ssim index and superior perceptual quality than those restored using the mse optimal adaptive linear filter through these results we demonstrate that a designing image processing algorithms and in particular denoising and restoration type algorithms can yield significant gains over existing in particular linear mmse based algorithms by optimizing them for perceptual distortion measures and b these gains may be obtained without significant increase in the computational complexity of the algorithm

boundary regularity and the dirichlet problem for harmonic maps in a previous paper 10 we developed an interior regularity theory for energy minimizing harmonic maps into riemannian manifolds in the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed dirichlet boundary condition we show that such maps are regular in a full neighborhood of the boundary assuming appropriate regularity on the manifolds the boundary and the data the reader may refer to theorem 2 7 for a statement of the precise result it is not surprising that the boundary regularity is actually stronger than the partial regularity we obtained for the interior this is due to the fact that there are no nontrivial smooth harmonic maps from hemispheres s which map the boundary s 9s to a point i j n 2 and is analogous to the fact that in certain cases we were able to obtain complete regularity in the interior many authors have worked on boundary regularity for this general type of problem we mention hildebrandt and widman 5 and hamilton 4 as having obtained important results specifically for harmonic maps morrey had obtained the boundary regularity for domain dimension n 2 in conjunction with his investigation of the plateau problem in riemannian manifolds 8 in 3 of this paper we observe that the direct method gives solvability of the dirichlet problem under reasonable hypotheses on the manifolds we give as an application an amusing proof of a theorem of sacks and uhlenbeck 9 on the existence of minimal 2 spheres representing the second homotopy group of a manifold the same method gives smooth harmonic representations for k n for a certain class of manifolds n these are characterized by the nonexistence of lower dimensional harmonic spheres whose homogeneous extensions are minimal see proposition 3 4 in the last section of the paper we discuss approximation of l maps by smooth maps we give a simple example of an l map from the three dimensional ball to the two sphere which is not an l limit of continuous maps we