unified framework for anisotropic interpolation and smoothing of diffusion tensor images to enhance the performance of diffusion tensor imaging dti based fiber tractography this study proposes a unified framework for anisotropic interpolation and smoothing of dti data the critical component of this framework is an anisotropic sigmoid interpolation kernel which is adaptively modulated by the local image intensity gradient profile the adaptive modulation of the sigmoid kernel permits image smoothing in homogeneous regions and meanwhile guarantees preservation of structural boundaries the unified scheme thus allows piece wise smooth continuous and boundary preservation interpolation of dti data so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure the new interpolation method is compared with conventional interpolation methods on the basis of fiber tracking from synthetic and in vivo dti data which demonstrates the effectiveness of this unified framework

scale selection for anisotropic diffusion filter by markov random field model the selection of stopping time i e scale significantly affects the performance of anisotropic diffusion filter for image denoising this paper designs a markov random field mrf scale selection model which selects scales for image segments then the denoised image is the composition of segments at their optimal scales in the scale space firstly statistics based scale selection criteria are proposed for image segments then we design a scale selection energy function in the mrf framework by considering the scale coherence between neighboring segments a segment based noise estimation algorithm is also developed to estimate the noise statistics efficiently experiments show that the performance of mrf scale selection model is much better than the previous global scale selection schemes combined with this scale selection model the anisotropic diffusion filter is comparable to or even outperform the state of the art denoising methods in performance

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

an advanced and adaptive mathematical function for an efficient anisotropic image filtering image de noising and enhancement are becoming increasingly widespread anisotropic diffusion is one of the greatest techniques that are used to remove noise of the image while keeping the important information unvaried nevertheless it suffers from many drawbacks such as the image blurring this work is concerned with a new anisotropic diffusion approach founded on an innovative mathematical function for noise reducing and edge preserving the entire contribution can be observed from the experimental results which have shown that the new proposed anisotropic scheme is not only able to remove the noise efficiently but also to preserve the content in the denoised image

modelling fingerprint ridge orientation using legendre polynomials the estimation of fingerprint ridge orientation is an essential step in every automatic fingerprint verification system the importance of ridge orientation can be deflected from the fact that it is inevitably used for detecting describing and matching fingerprint features such as minutiae and singular points in this paper we propose a novel method for fingerprint ridge orientation modelling using legendre polynomials one of the main problems it addresses is smoothing orientation data while preserving details in high curvature areas especially singular points we show that singular points which result in a discontinuous orientation field can be modelled by the zero poles of legendre polynomials the models parameters are obtained in a two staged optimization procedure another advantage of the proposed method is a very compact representation of the orientation field using only 56 coefficients we have carried out extensive experiments using a state of the art fingerprint matcher and a singular point detector moreover we compared the proposed method with other state of the art fingerprint orientation estimation algorithms we can report significant improvements in both singular point detection and matching rates

denoising enhancing images on elastic manifolds the conflicting demands for simultaneous low pass and high pass processing required in image denoising and enhancement still present an outstanding challenge although a great deal of progress has been made by means of adaptive diffusion type algorithms to further advance such processing methods and algorithms we introduce a family of second order in time partial differential equations these equations describe the motion of a thin elastic sheet in a damping environment they are also derived by a variational approach in the context of image processing the new operator enables better edge preservation in denoising applications by offering an adaptive lowpass filter which preserves high frequency components in the pass band better than the adaptive diffusion filter while offering slower error propagation across edges we explore the action of this powerful operator in the context of image processing and exploit for this purpose the wealth of knowledge accumulated in physics and mathematics about the action and behavior of this operator the resulting methods are further generalized for color and or texture image processing by embedding images in multidimensional manifolds a specific application of the proposed new approach to superresolution is outlined

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

a new clustering algorithm with multiple runs of iterative procedures abstract the k means clustering algorithm is well known and widely used recently an alternative algorithm based on an earlier idea duda and hart pattern classification and scene analysis 1973 ismail and kamel pattern recognition 22 75 89 1989 has been proposed in comprehensive experiments we verify that this alternative is superior to k means both techniques suffer from the complexity of the cost function surface they are descending and a consequent inclination to fall into poor local minima a popular solution to this problem is to rerun the chosen iterative procedure from many randomly chosen starting positions saving the best we introduce here an alternative strategy to form the starting position for such a multiple run which consists of perturbing an existing result in an attempt to improve its poor aspects this controlled configuration change has comparable complexity with random initialisation but usually produces superior clustering results comprehensive experiments confirm this result

nonlinear scale space with spatially varying stopping time a general scale space algorithm is presented for denoising signals and images with spatially varying dominant scales the process is formulated as a partial differential equation with spatially varying time the proposed adaptivity is semi local and is in conjunction with the classical gradient based diffusion coefficient designed to preserve edges the new algorithm aims at maximizing a local snr measure of the denoised image it is based on a generalization of a global stopping time criterion presented recently by the author and colleagues most notably the method works well also for partially textured images and outperforms any selection of a global stopping time given an estimate of the noise variance the procedure is automatic and can be applied well to most natural images

hyperconnected attribute filters based on k flat zones in this paper we present a new method for attribute filtering combining contrast and structural information using hyperconnectivity based on k flat zones we improve the ability of attribute filters to retain internal details in detected objects simultaneously we improve the suppression of small unwanted detail in the background we extend the theory of attribute filters to hyperconnectivity and provide a fast algorithm to implement the new method the new version is only marginally slower than the standard max tree algorithm for connected attribute filters and linear in the number of pixels or voxels it is two orders of magnitude faster than anisotropic diffusion the method is implemented in the form of a filtering rule suitable for handling both increasing size and nonincreasing shape attributes we test this new framework on nonincreasing shape filters on both 2d images from astronomy document processing and microscopy and 3d ct scans and show increased robustness to noise while maintaining the advantages of previous methods

iterative parameter choice and multigrid methods for anisotropic diffusion denoising anisotropic diffusion methods are well known for giving good qualitative results for image denoising this paper gives a review of the anisotropic diffusion methodology and its application to image denoising we propose a fixed point iteration using a multigrid solver to solve a regularized anisotropic diffusion equation which is not only well posed but also has a nontrivial steady state solution a new regularization parameter choice method brent ncp combining brent s method and the normalized cumulative periodogram information of the misfit is also introduced we test our algorithm on several common test images with different noise levels the experimental results demonstrate the effectiveness of the anisotropic diffusion with a multigrid approach and the broad applicability of the brent ncp parameter choice algorithm

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

an efficient color quantization based on generic roughness measure color quantization is a process to compress image color space while minimizing visual distortion the quantization based on preclustering has low computational complexity but cannot guarantee quantization precision the quantization based on postclustering can produce high quality quantization results however it has to traverse image pixels iteratively and suffers heavy computational burden its computational complexity was not reduced although the revised versions have improved the precision in the work of color quantization balancing quantization quality and quantization complexity is always a challenging point in this paper a two stage quantization framework is proposed to achieve this balance in the first stage high resolution color space is initially compressed to a condensed color space by thresholding roughness indices instead of linear compression we propose generic roughness measure to generate the delicate segmentation of image color in this way it causes less distortion to the image in the second stage the initially compressed colors are further clustered to a palette using weighted rough k means to obtain final quantization results our objective is to design a postclustering quantization strategy at the color space level rather than the pixel level applying the quantization in the precisely compressed color space the computational cost is greatly reduced meanwhile the quantization quality is maintained the substantial experimental results validate the high efficiency of the proposed quantization method which produces high quality color quantization while possessing low computational complexity

efficient diffusion coefficient for image denoising diffusion coefficient has an important role in the performance of partial differential equation pde based image denoising techniques commonly the classical perona malik pm diffusion coefficient is widely used in pde based noise removal algorithms in this paper pm diffusion coefficient is analyzed regarding to its flux based on the analysis pm flux for regions where the gradient magnitude is higher than smoothing threshold may lead to undesirable blurring effect and edge displacement to address these issues the image is divided into three segments based on the gradient magnitude regions where the gradient is lower than the smoothing threshold regions where the gradient is between the smoothing threshold and inflection point of flux and regions where the gradient magnitude is higher than inflection point we define the conditions that should be considered in these three segments then a diffusion coefficient satisfying all these conditions is computed experimental results confirm the performance of the proposed method with regard to peak signal to noise ratio psnr mean structural similarity mssim universal quality index uqi visual information fidelity vif feature similarity fsim information content weighted ssim iw ssim and visual quality

the perona malik paradox the perona malik equation is a formally ill posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable after discussing the background of this parad

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

hierarchical super resolution based inpainting this paper introduces a novel framework for examplar based inpainting it consists in performing first the inpainting on a coarse version of the input image a hierarchical super resolution algorithm is then used to recover details on the missing areas the advantage of this approach is that it is easier to inpaint low resolution pictures than high resolution ones the gain is both in terms of computational complexity and visual quality however to be less sensitive to the parameter setting of the inpainting method the low resolution input picture is inpainted several times with different configurations results are efficiently combined with a loopy belief propagation and details are recovered by a single image super resolution algorithm experimental results in a context of image editing and texture synthesis demonstrate the effectiveness of the proposed method results are compared to five state of the art inpainting methods

salem sets in local fields the fourier restriction phenomenon and the hausdorff young inequality abstract we establish the existence of salem sets in the ring of integers of any local field and study the fourier restriction phenomenon on such sets optimal extension of the hausdorff young inequality initially attained for the torus by g mockenhaupt and w ricker is also established in the local field setting

anisotropic diffusion with generalized diffusion coefficient function for defect detection in low contrast surface images in this paper an anisotropic diffusion model with a generalized diffusion coefficient function is presented for defect detection in low contrast surface images and especially aims at material surfaces found in liquid crystal display lcd manufacturing a defect embedded in a low contrast surface image is extremely difficult to detect because the intensity difference between the unevenly illuminated background and the defective region is hardly observable and no clear edges are present between the defect and its surroundings the proposed anisotropic diffusion model provides a generalized diffusion mechanism that can flexibly change the curve of the diffusion coefficient function it adaptively carries out a smoothing process for faultless areas and performs a sharpening process for defect areas in an image an entropy criterion is proposed as the performance measure of the diffused image and then a stochastic evolutionary computation algorithm particle swarm optimization pso is applied to automatically determine the best parameter values of the generalized diffusion coefficient function experimental results have shown that the proposed method can effectively and efficiently detect small defects in various low contrast surface images

noise driven anisotropic diffusion filtering of mri a new filtering method to remove rician noise from magnetic resonance images is presented this filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for mri as the speckle reducing anisotropic diffusion did for ultrasound images the parameters of the filter are automatically chosen from the estimated noise this property improves the convergence rate of the diffusion while preserving contours leading to more robust and intuitive filtering the partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations this new filter combines volumetric planar and linear components of the local image structure the numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented in the experiments the new filter leads to the best results

segmentation and shape tracking of whole fluorescent cells based on the chan vese model we present a fast and robust approach to tracking the evolving shape of whole fluorescent cells in time lapse series the proposed tracking scheme involves two steps first coherence enhancing diffusion filtering is applied on each frame to reduce the amount of noise and enhance flow like structures second the cell boundaries are detected by minimizing the chan vese model in the fast level set like and graph cut frameworks to allow simultaneous tracking of multiple cells over time both frameworks have been integrated with a topological prior exploiting the object indication function the potential of the proposed tracking scheme and the advantages and disadvantages of both frameworks are demonstrated on 2 d and 3 d time lapse series of rat adipose derived mesenchymal stem cells and human lung squamous cell carcinoma cells respectively

cyclic schemes for pde based image analysis we investigate a class of efficient numerical algorithms for many partial differential equations pdes in image analysis they are applicable to parabolic or elliptic pdes that have bounded coefficients and lead to space discretisations with symmetric matrices our schemes are easy to implement and well suited for parallel implementations on gpus since they are based on the explicit diffusion scheme in the parabolic case and the jacobi method in the elliptic case by supplementing these methods with cyclically varying time step sizes or relaxation parameters we achieve efficiency gains of several orders of magnitude we call the resulting algorithms fast explicit diffusion fed and fast jacobi fj methods to achieve a good compromise between efficiency and accuracy we show that one should use parameter cycles that result from factorisations of box filters for these cycles we establish stability results in the euclidean norm our schemes perform favourably in a number of applications including isotropic nonlinear diffusion filters with widely varying diffusivities as well as anisotropic diffusion methods for image filtering inpainting and regularisation in computer vision moreover they are equally suited for higher dimensional problems as well as higher order pdes and they can also be interpreted as efficient first order methods for smooth optimisation problems

a new interpretation and improvement of the nonlinear anisotropic diffusion for image enhancement the purpose of the article is to give an analysis of the anisotropic diffusion ad and propose adaptive nonlinear filtering based on a judicious choice of the conductance function cf and the edgeness threshold a new undesirable effect which we call the pinhole effect may result when ad is introduced for the first time a robust solution to this effect is proposed and evaluated through experimental data the evolution of the diffused signal is analyzed through a physical model using the optical flow technique oft the overall strategy is evaluated through experimental results obtained on synthetic and actual images

a novel non local means image denoising method based on grey theory in this paper a novel non local means image denoising method called grey theory applied in non local means gnlm is proposed different from previous works our method is based on grey theory the advantage of grey theory is its flexibility in handling complex scenes the grey relational analysis needs fewer testing samples but can achieve a better performance therefore we analyze the structure similarity by grey relation of coefficients set similar weight function accordingly and propose an efficient non local means this new method solves the parameter setting problem encountered by traditional non local means methods and reduces the computational complexity experimental results validate our proposed method it removes noise well and is efficient in capturing details especially edges and corners this leads to a state of the art denoising performance the performance is equivalent and sometimes surpasses recently published leading alternative denoising methods new method solves the parameter setting problem encountered by traditional methods the grey relational analysis needs fewer testing samples but can achieve a better performance efficient in capturing details especially edges and corners

an algorithm for competitive learning in clustering problems abstract competitive learning is one of the algorithms for clustering based on the least sum of squares criterion however competitive learning has a problem of serious decline of learning ability from lack of competition when one unit monopolizes all input vectors this problem must be avoided using an additional algorithm this paper presents an algorithm which makes competitive learning give a good approximate solution for clustering the results using our method are better than previous studies this paper also presents a parameter optimization of competitive learning using anova analysis of variance using anova helps to optimize a parameter condition systematically

explicit salem sets in r2 abstract we construct explicit i e non random examples of salem sets in r 2 of dimension s for every 0 s 2 in particular we give the first explicit examples of salem sets in r 2 of dimension 0 s 1 this extends a theorem of kaufman

orientation matching minimization for image denoising and inpainting in this paper we propose an orientation matching functional minimization for image denoising and image inpainting following the two step tv stokes algorithm rahman et al in scale space and variational methods in computer vision pp 473 482 springer heidelberg 2007 tai et al in image processing based on partial differential equations pp 3 22 springer heidelberg 2006 bertalmio et al in proc conf comp vision pattern rec pp 355 362 2001 a regularized tangential vector field with zero divergence condition is first obtained then a novel approach to reconstruct the image is proposed instead of finding an image that fits the regularized normal direction from the first step we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction this functional yields a new nonlinear partial differential equation pde for reconstructing denoised and inpainted images the equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field providing reconstructed images which have sharp edges and smooth regions the additive operator splitting aos scheme is used for discretizing euler lagrange equations we present the results of various numerical experiments that illustrate the improvements obtained with the new functional

adaptive smoothing respecting feature directions accurate extraction of the image feature directions is essential to image smoothing and other image processing tasks we show that the gradient based feature direction extraction method can be very erroneous the gradient is too local and it cannot detect oscillations we have developed two new methods the hessian method an approach using higher order differentiations and the gabor 1946 method an approach using space frequency analysis

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

variational segmentation of vector valued images with gradient vector flow in this paper we extend the gradient vector flow field for robust variational segmentation of vector valued images rather than using scalar edge information we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4d gradient vector flow equation to reduce the contribution of noise in the structure tensor image channels are weighted according to a blind estimator of contrast the method is applied to biological volume delineation in dynamic pet imaging and validated on realistic monte carlo simulations of numerical phantoms as well as on real images

estimation of optimal pde based denoising in the snr sense this paper is concerned with finding the best partial differential equation based denoising process out of a set of possible ones we focus on either finding the proper weight of the fidelity term in the energy minimization formulation or on determining the optimal stopping time of a nonlinear diffusion process a necessary condition for achieving maximal snr is stated based on the covariance of the noise and the residual part we provide two practical alternatives for estimating this condition by observing that the filtering of the image and the noise can be approximated by a decoupling technique with respect to the weight or time parameters our automatic algorithm obtains quite accurate results on a variety of synthetic and natural images including piecewise smooth and textured ones we assume that the statistics of the noise were previously estimated no a priori knowledge regarding the characteristics of the clean image is required a theoretical analysis is carried out where several snr performance bounds are established for the optimal strategy and for a widely used method wherein the variance of the residual part equals the variance of the noise

a global sparse gradient based coupled system for image denoising abstract we consider a coupled system for image denoising which consists of an anisotropic diffusion equation and a global sparse gradient model gsg the global sparse gradient model is used to estimate the edge map from the noisy image accurately and robustly the anisotropic diffusion process is guided by the edge map furthermore we prove the existence and uniqueness of the solutions of the coupled system with dirichlet initial boundary value problem finally comparing with the edge indicators based on local methods experimental results demonstrate that our proposed method has the state of the art performance among the pde based anisotropic diffusion approaches both in objective measurement and visual evaluation

automatic segmentation of mitochondria in em data using pairwise affinity factorization and graph based contour searching in this paper we investigate the segmentation of closed contours in subcellular data using a framework that primarily combines the pairwise affinity grouping principles with a graph partitioning contour searching approach one salient problem that precluded the application of these methods to large scale segmentation problems is the onerous computational complexity required to generate comprehensive representations that include all pairwise relationships between all pixels in the input data to compensate for this problem a practical solution is to reduce the complexity of the input data by applying an over segmentation technique prior to the application of the computationally demanding strands of the segmentation process this approach opens the opportunity to build specific shape and intensity models that can be successfully employed to extract the salient structures in the input image which are further processed to identify the cycles in an undirected graph the proposed framework has been applied to the segmentation of mitochondria membranes in electron microscopy data which are characterized by low contrast and low signal to noise ratio the algorithm has been quantitatively evaluated using two datasets where the segmentation results have been compared with the corresponding manual annotations the performance of the proposed algorithm has been measured using standard metrics such as precision and recall and the experimental results indicate a high level of segmentation accuracy

revisiting the relationship between adaptive smoothing and anisotropic diffusion with modified filters anisotropic diffusion has been known to be closely related to adaptive smoothing and discretized in a similar manner this paper revisits a fundamental relationship between two approaches it is shown that adaptive smoothing and anisotropic diffusion have different theoretical backgrounds by exploring their characteristics with the perspective of normalization evolution step size and energy flow based on this principle adaptive smoothing is derived from a second order partial differential equation pde not a conventional anisotropic diffusion via the coupling of fick s law with a generalized continuity equation where a source or sink exists which has not been extensively exploited we show that the source or sink is closely related to the asymmetry of energy flow as well as the normalization term of adaptive smoothing it enables us to analyze behaviors of adaptive smoothing such as the maximum principle and stability with a perspective of a pde ultimately this relationship provides new insights into application specific filtering algorithm design by modeling the source or sink in the pde we introduce two specific diffusion filters the robust anisotropic diffusion and the robust coherence enhancing diffusion as novel instantiations which are more robust against the outliers than the conventional filters

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

contrast enhancement by nonlinear diffusion filtering to enhance the visual quality of an image that is degraded by uneven light an effective method is to estimate the illumination component and compress it some previous methods have either defects of halo artifacts or contrast loss in the enhanced image due to incorrect estimation in this paper we discuss this problem and propose a novel method to estimate the illumination the illumination is obtained by iteratively solving a nonlinear diffusion equation during the diffusion process surround suppression is embedded in the conductance function to specially enhance the diffusive strength in textural areas of the image the proposed estimation method has the following two merits 1 the boundary areas are preserved in the illumination and thus halo artifacts are prevented and 2 the textural details are preserved in the reflectance to not suffer from illumination compression which contributes to the contrast enhancement in the result experimental results show that the proposed algorithm achieves excellent performance in artifact removal and local contrast enhancement

a scheme with discrete maximum principle and optimized rotation invariance for coherence enhancing diffusion abstract experiments show that the widely employed 3 3 stencil schemes for the coherence enhancing diffusion neither provide acceptable rotational invariance nor do they satisfy the maximum minimum principle at a discrete level we address the problem of rotation invariance by proposing a new 3 3 stencil scheme this scheme also lacks in the discrete maximum principle an enforcement of the discrete maximum principle is presented using a repair technique extensive numerical simulations confirmed the advantage of the repaired scheme over the existing 3 3 stencil schemes in terms of rotational invariance and discrete maximum principle

nonlinear image filtering with edge and corner enhancement the authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion the method is designed to enhance not only edges but corners and t junctions as well the method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges such a process is ill posed making the results depend strongly on how the algorithm differs from the diffusion process two ways of modifying the equations using simulations on a variable grid are studied

on the choice of the parameters for anisotropic diffusion in image processing anisotropic diffusion filtering is highly dependent on some crucial parameters such as the conductance function the gradient threshold parameter and the stopping time of the iterative process the various alternative options at each stage of the algorithm are examined and evaluated and the best choice is selected an automatic stopping criterion is proposed that takes into consideration the quality of the preserved edges as opposed to just the level of smoothing achieved the proposed scheme is evaluated with the help of real and simulated images and compared with other state of the art schemes using objective criteria

flux based anisotropic diffusion applied to enhancement of 3 d angiogram we present a new approach to anisotropic diffusion based on a multidirectional diffusion flux the diffusion flux is decomposed in an orthogonal basis effectively enabling enhancement of contours as well as diffusion along the contours to this end we have selected a three dimensional basis that depicts the directions of principal curvature and has an interesting interpretation in the context of the vessels the diffusion function associated to each vector of the basis depends on the first order derivative of the intensity in this direction instead of the traditional norm of the smoothed gradient accordingly we present the results of a restoration of computed tomography data of the liver

a variational formulation for fingerprint orientation modeling orientation pattern is an important feature for characterizing fingerprint and plays critical roles in fingerprint recognition and fingerprint classification this paper proposes a framework for modeling the fingerprint orientation field based on the variational principle where the orientation pattern can be estimated through solving the associated euler lagrange equation compared with existing methods our proposed method has the following features firstly it does not require any prior information about the structure of the acquired fingerprint such as location of singular point s secondly it explicitly provides freedom for modeling the singularity in the orientation field thirdly it has less number of parameters comparison has been made with respect to state of the arts in fingerprint orientation modeling in terms of modeling accuracy fingerprint enhancement and singular point detection advantages of the proposed method are demonstrated

image deblurring in the presence of impulsive noise consider the problem of image deblurring in the presence of impulsive noise standard image deconvolution methods rely on the gaussian noise model and do not perform well with impulsive noise the main challenge is to deblur the image recover its discontinuities and at the same time remove the impulse noise median based approaches are inadequate because at high noise levels they induce nonlinear distortion that hampers the deblurring process distinguishing outliers from edge elements is difficult in current gradient based edge preserving restoration methods the suggested approach integrates and extends the robust statistics line process half quadratic and anisotropic diffusion points of view we present a unified variational approach to image deblurring and impulse noise removal the objective functional consists of a fidelity term and a regularizer data fidelity is quantified using the robust modified l 1 norm and elements from the mumford shah functional are used for regularization we show that the mumford shah regularizer can be viewed as an extended line process it reflects spatial organization properties of the image edges that do not appear in the common line process or anisotropic diffusion this allows to distinguish outliers from edges and leads to superior experimental results

tubular structure segmentation based on minimal path method and anisotropic enhancement we present a new interactive method for tubular structure extraction the main application and motivation for this work is vessel tracking in 2d and 3d images the basic tools are minimal paths solved using the fast marching algorithm this allows interactive tools for the physician by clicking on a small number of points in order to obtain a minimal path between two points or a set of paths in the case of a tree structure our method is based on a variant of the minimal path method that models the vessel as a centerline and surface this is done by adding one dimension for the local radius around the centerline the crucial step of our method is the definition of the local metrics to minimize we have chosen to exploit the tubular structure of the vessels one wants to extract to built an anisotropic metric the designed metric is well oriented along the direction of the vessel admits higher velocity on the centerline and provides a good estimate of the vessel radius based on the optimally oriented flux this measure is required to be robust against the disturbance introduced by noise or adjacent structures with intensity similar to the target vessel we obtain promising results on noisy synthetic and real 2d and 3d images and we present a clinical validation

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

a class of nonlocal tensor telegraph diffusion equations applied to coherence enhancement abstract in this paper we propose a nonlocal tensor telegraph diffusion equation which could be applied to enhancement of coherent flow like structures the telegraph diffusion equation interpolates between diffusion equation and wave equation which lead to a mixed behaviour of diffusion and wave propagation and thus it can preserve edges in a highly oscillatory region replacing scalar valued diffusivity function by diffusion tensor enables real anisotropic diffusion processes which may reveal advantages to enhance the flow like structures in addition the nonlocal technique makes our model robust to noise the existence uniqueness and stability of the solution of our model are proved in this paper the experimental results indicate superiority of the proposed model over the existing methods

graph spectral image smoothing using the heat kernel a new method for smoothing both gray scale and color images is presented that relies on the heat diffusion equation on a graph we represent the image pixel lattice using a weighted undirected graph the edge weights of the graph are determined by the gaussian weighted distances between local neighboring windows we then compute the associated laplacian matrix the degree matrix minus the adjacency matrix anisotropic diffusion across this weighted graph structure with time is captured by the heat equation and the solution i e the heat kernel is found by exponentiating the laplacian eigensystem with time image smoothing is accomplished by convolving the heat kernel with the image and its numerical implementation is realized by using the krylov subspace technique the method has the effect of smoothing within regions but does not blur region boundaries we also demonstrate the relationship between our method standard diffusion based pdes fourier domain signal processing and spectral clustering experiments and comparisons on standard images illustrate the effectiveness of the method