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

roof edge preserving image smoothing based on mrfs a novel markov random field mrf model is proposed for roof edge as well as step edge preserving image smoothing image surfaces containing roof edges are represented by piecewise continuous polynomial functions governed by a few parameters piecewise smoothness constraint is imposed on these parameters rather than on the surface heights as is in traditional models for step edges in this way roof edges are preserved without the necessity to deal with unstable higher order derivatives

a de interlacing algorithm using markov random field model in this paper a motion compensated de interlacing algorithm using the markov random field mrf model is proposed the de interlacing problem is formulated as a maximum a posteriori map mrf problem the map solution is the one that minimizes an energy function which imposes discontinuity adaptive smoothness das spatial constraint on the de interlaced frame the edge direction information which is used to formulate the das constraint is implicitly indicated by weight vectors weights for 16 digitized directions generally large weights are assigned to along edge directions and relatively small weights are assigned to across edge directions as a local statistical based method the proposed weighting method should be more robust than traditional edge directed interpolation methods in deciding local edge directions the proposed algorithm is implemented by an iterative optimization process which guarantees convergence however a global optimal solution is not guaranteed due to computational complexity concern simulation results compare the proposed algorithm to other motion compensated de interlacing algorithms significant improvements of de interlaced edges are observed

regularization of wavelet approximations in this paper we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly spaced the approach can apply readily to many other statistical contexts various new penalty functions are proposed the hard thresholding and soft thresholding estimators of donoho and johnstone are specific members of nonlinear regularized wavelet estimators they correspond to the lower and upper envelopes of a class of the penalized least squares estimators necessary conditions for penalty functions are given for regularized estimators to possess thresholding properties oracle inequalities and universal thresholding parameters are obtained for a large class of penalty functions the sampling properties of nonlinear regularized wavelet estimators are established and are shown to be adaptively minimax to efficiently solve penalized least squares problems nonlinear regularized sobolev interpolators nrsi are proposed as initial estimators wh

space time simulation of intermittent rainfall with prescribed advection field adaptation of the turning band method 1 space time rainfall simulation is useful to study questions like for instance the propagation of rainfall measurement uncertainty in hydrological modeling this study adapts a classical gaussian field simulation technique the turning band method in order to produce sequences of rainfall fields satisfying three key features of actual precipitation systems i the skewed point distribution and the space time structure of nonzero rainfall nzr ii the average probability and the space time structure of intermittency and iii a prescribed advection field the acronym of our simulator is sampo for simulation of advected mesoscale precipitations and their occurrence sampo assembles various theoretical developments available from the literature the concept of backtrajectories introduces a priori any type of advection field in the heart of the turning band method tbm tbm outputs transformation into rainfall fields with a desired structure is controlled using chebyshev hermite polynomial expansion the intermittency taken as a binary process statistically independent of the nzr process allows the use of a common algorithm for both processes the 3 d simulation with a space time anisotropy captures important details of the precipitation kinematics summarized by the taylor velocity of both nzr and intermittency a case study based on high resolution weather radar data serves as an example of model inference illustrative simulations revisit some classical questions about rainfall variography like the influence of advection or intermittency they also show the combined role of taylor s and advection velocities

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

shape reconstruction on a varying mesh a central class of image understanding problems is concerned with reconstructing a shape from an incomplete data set such as fitting a surface to partially given contours a new theory for solving such problems is presented unlike the current heuristic methods the method used starts from fundamental principles that should be followed by any reconstruction method regardless of its mathematical or physical implementation a mathematical procedure which conforms to these principles is presented one major advantage of the method is the ability to handle shapes containing both smooth and sharp parts without using thresholds a sharp variation such as a corner requires a high resolution mesh for adequate representation while slowly varying sections can be represented with sparser mesh points unlike current methods this procedure fits the surface on a varying mesh the mesh is constructed automatically to be more dense at parts of the image that have more rapid variation analytical examples are given in simple cases followed by numerical experiments

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

on discontinuity adaptive smoothness priors in computer vision a variety of analytic and probabilistic models in connection with markov random fields mrfs have been proposed in the last decade for solving low level vision problems involving discontinuities this paper presents a systematic study of these models and defines a general discontinuity adaptive da mrf model by analyzing the euler equation associated with the energy minimization it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points which is determined by the a priori smoothness constraint encoded into the energy function an important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing this forms the basis on which a class of adaptive interaction functions aifs is defined the da model is defined in terms of the euler equation constrained by this class of aifs its solution is c sup 1 continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities because of the continuous nature it is stable to changes in parameters and data a good property for regularizing ill posed problems experimental results are shown

the equivalence of half quadratic minimization and the gradient linearization iteration a popular way to restore images comprising edges is to minimize a cost function combining a quadratic data fidelity term and an edge preserving possibly nonconvex regularization term mainly because of the latter term the calculation of the solution is slow and cumbersome half quadratic hq minimization multiplicative form was pioneered by geman and reynolds 1992 in order to alleviate the computational task in the context of image reconstruction with nonconvex regularization by promoting the idea of locally homogeneous image models with a continuous valued line process they reformulated the optimization problem in terms of an augmented cost function which is quadratic with respect to the image and separable with respect to the line process hence the name half quadratic since then a large amount of papers were dedicated to hq minimization and important results including edge preservation along with convex regularization and convergence have been obtained in this paper we show that hq minimization multiplicative form is equivalent to the most simple and basic method where the gradient of the cost function is linearized at each iteration step in fact both methods give exactly the same iterations furthermore connections of hq minimization with other methods such as the quasi newton method and the generalized weiszfeld s method are straightforward

an edge based algorithm for discontinuity adaptive color image smoothing abstract we present a new scheme to increase the performance of edge preserving image smoothing algorithm from the parameter tuning of a markov random field mrf function this method is based on an automatic control of the image smoothing strength in the mrf function in which the parameter control of the function depends on edge magnitude resulted from discontinuities of image intensity without any binary decision for the edge magnitude direct use of full edge magnitude could improve the performance of discontinuity preserving image smoothing technique

salt and pepper noise removal by median type noise detectors and detail preserving regularization this paper proposes a two phase scheme for removing salt and pepper impulse noise in the first phase an adaptive median filter is used to identify pixels which are likely to be contaminated by noise noise candidates in the second phase the image is restored using a specialized regularization method that applies only to those selected noise candidates in terms of edge preservation and noise suppression our restored images show a significant improvement compared to those restored by using just nonlinear filters or regularization methods only our scheme can remove salt and pepper noise with a noise level as high as 90

open loop equilibrium strategy for mean variance asset liability management portfolio selection problem with debt ratio abstract in this study we consider a time consistent mean variance asset liability management portfolio selection problem in which the liability is controllable the objective is to find an equilibrium investment strategy and an equilibrium debt ratio in the financial market consisting of one risk free asset and one risky asset by using forward backward stochastic differential equations fbsdes we derive a sufficient condition and a necessary condition for the open loop equilibrium strategies the uniqueness of the strategies is also provided furthermore to illustrate our results we provide numerical examples to show how the parameters impact on the equilibrium strategies and the corresponding efficient frontier

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

statistic based map image reconstruction from poisson data using gibbs priors a statistical method for selecting the gibbs parameter in map image restoration from poisson data using gibbs priors is presented the gibbs parameter determines the degree to which the prior influences the restoration the presented method yields a map restored image minimally influenced by the prior for which a statistic falls within an appropriate confidence interval the method assumes that a close approximation to the blurring function is known a simple iterative feedback algorithm is presented to statistically select the parameter as the map image restoration is being performed this algorithm is heuristically based on a model reference control formulation but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value the performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2 d and 3 d images

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

a tree structured markov random field model for bayesian image segmentation we present a new image segmentation algorithm based on a tree structured binary mrf model the image is recursively segmented in smaller and smaller regions until a stopping condition local to each region is met each elementary binary segmentation is obtained as the solution of a map estimation problem with the region prior modeled as an mrf since only binary fields are used and thanks to the tree structure the algorithm is quite fast and allows one to address the cluster validation problem in a seamless way in addition all field parameters are estimated locally allowing for some spatial adaptivity to improve segmentation accuracy a split and merge procedure is also developed and a spatially adaptive mrf model is used numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on flat mrf models and its performance in terms of segmentation accuracy and map smoothness is comparable or even superior

a markov model for blind image separation by a mean field em algorithm this paper deals with blind separation of images from noisy linear mixtures with unknown coefficients formulated as a bayesian estimation problem this is a flexible framework where any kind of prior knowledge about the source images and the mixing matrix can be accounted for in particular we describe local correlation within the individual images through the use of markov random field mrf image models these are naturally suited to express the joint pdf of the sources in a factorized form so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained our model also includes edge variables to preserve intensity discontinuities mrf models have been proved to be very efficient in many visual reconstruction problems such as blind image restoration and allow separation and edge detection to be performed simultaneously we propose an expectation maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix the sources and their edge maps we tested this procedure on both synthetic and real images in the fully blind case i e no prior information on mixing is exploited and found that a source model accounting for local autocorrelation is able to increase robustness against noise even space variant furthermore when the model closely fits the source characteristics independence is no longer a strict requirement and cross correlated sources can be separated as well

edge preserving image denoising and estimation of discontinuous surfaces in this paper we are interested in the problem of estimating a discontinuous surface from noisy data a novel procedure for this problem is proposed based on local linear kernel smoothing in which local neighborhoods are adapted to the local smoothness of the surface measured by the observed data the procedure can therefore remove noise correctly in continuity regions of the surface and preserve discontinuities at the same time since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects this procedure can be applied directly to image denoising numerical studies show that it works well in applications compared to some existing procedures

optimal estimation of contour properties by cross validated regularization the problem of estimating the properties of smooth continuous contours from discrete noisy samples is used as vehicle to demonstrate the robustness of cross validated regularization applied to a vision problem a method for estimation of contour properties based on smoothing spline approximations is presented generalized cross validation is to devise an automatic algorithm for finding the optimal value of the smoothing regularization parameter from the data the cross validated smoothing splines are then used to obtain optimal estimates of the derivatives of quantized contours experimental results are presented which demonstrate the robustness of the method applied to the estimation of curvature of quantized contours under variable scale rotation and partial occlusion these results suggest the application of generalized cross validation to other computer vision algorithms involving regularization

one dimensional regularization with discontinuities regularization is equivalent to fitting smoothing splines to the data so that efficient and reliable numerical algorithms exist for finding solutions however the results exhibit poor performance along edges and boundaries to cope with such anomalies a more general class of smoothing splines that preserve corners and discontinuities is studied cubic splines are investigated in detail since they are easy to implement and produce smooth curves near all data points except those marked as discontinuities or creases a discrete regularization method is introduced to locate corners and discontinuities in the data points before the continuous regularization is applied