the monogenic signal this paper introduces a two dimensional 2 d generalization of the analytic signal this novel approach is based on the riesz transform which is used instead of the hilbert transform the combination of a 2 d signal with the riesz transformed one yields a sophisticated 2 d analytic signal the monogenic signal the approach is derived analytically from irrotational and solenoidal vector fields based on local amplitude and local phase an appropriate local signal representation that preserves the split of identity i e the invariance equivariance property of signal decomposition is presented this is one of the central properties of the one dimensional 1 d analytic signal that decomposes a signal into structural and energetic information we show that further properties of the analytic signal concerning symmetry energy allpass transfer function and orthogonality are also preserved and we compare this with the behavior of other approaches for a 2 d analytic signal as a central topic of this paper a geometric phase interpretation that is based on the relation between the 1 d analytic signal and the 2 d monogenic signal established by the radon 1986 transform is introduced possible applications of this relationship are sketched and references to other applications of the monogenic signal are given

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

local surface shape estimation of 3 d textured surfaces using gaussian markov random fields and stereo windows the problem of extracting the local shape information of a 3 d texture surface from a single 2 d image by tracking the perceived systematic deformations the texture undergoes by virtue of being present on a 3 d surface and by virtue of being imaged is examined the surfaces of interest are planar and developable surfaces the textured objects are viewed as originating by laying a rubber planar sheet with a homogeneous parent texture on it onto the objects the homogeneous planar parent texture is modeled by a stationary gaussian markov random field gmrf a probability distribution function for the texture data obtained by projecting the planar parent texture under a linear camera model is derived which is an explicit function of the parent gmrf parameters the surface shape parameters and the camera geometry the surface shape parameter estimation is posed as a maximum likelihood estimation problem a stereo windows concept is introduced to obtain a unique and consistent parent texture from the image data that under appropriate transformations yields the observed texture in the image the theory is substantiated by experiments on synthesized as well as real images of textured surfaces

3 d shape from a shaded and textural surface image a new 3d texture model is developed by considering the scene image as the superposition of a random texture image on a smooth shaded image the whole image is analyzed using a patch by patch process each patch is assumed to be a tilted and slanted texture plane a modified reflectance map function is applied to describe the deterministic part and the fractional differencing periodic model is chosen to describe the random texture because of its good performance in texture synthesis and its ability to represent the coarseness and the pattern of the surface at the same time an orthographical projection technique is developed to deal with this particular random model which has a nonisotropically distributed texture pattern for estimating the parameter a hybrid method that uses both the least square and the maximum likelihood estimates is applied directly to the given intensity function by using these parameters the synthesized image is obtained and used to reconstruct the original image

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

improved methods of estimating shape from shading using the light source coordinate system abstract this paper develops improved methods of estimating local surface orientation from shading information with the aid of a coordinate system having one axis in the assumed direction of the light source in this system the surface tilt is related to the direction of the gray level gradient at the given point an alternative formulation of the surface slant probability density is developed that takes the discrete nature of digital images into account and that yields a better estimate of the light source direction

multiresolution moment filters theory and applications we introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales when the window function satisfies a two scale relation we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet like algorithm we show that b splines are well suited window functions because in addition to being refinable they are positive symmetric separable and very nearly isotropic gaussian shape we present three applications of these multiscale local moments the first is a feature extraction method for detecting and characterizing elongated structures in images the second is a noise reduction method which can be viewed as a multiscale extension of savitzky golay filtering the third is a multiscale optical flow algorithm that uses a local affine model for the motion field extending the lucas kanade optical flow method the results obtained in all cases are promising

identifying regional cardiac abnormalities from myocardial strains using nontracking based strain estimation and spatio temporal tensor analysis myocardial strain is a critical indicator of many cardiac diseases and dysfunctions the goal of this paper is to extract and use the myocardial strain pattern from tagged magnetic resonance imaging mri to identify and localize regional abnormal cardiac function in human subjects in order to extract the myocardial strains from the tagged images we developed a novel nontracking based strain estimation method for tagged mri this method is based on the direct extraction of tag deformation and therefore avoids some limitations of conventional displacement or tracking based strain estimators based on the extracted spatio temporal strain patterns we have also developed a novel tensor based classification framework that better conserves the spatio temporal structure of the myocardial strain pattern than conventional vector based classification algorithms in addition the tensor based projection function keeps more of the information of the original feature space so that abnormal tensors in the subspace can be back projected to reveal the regional cardiac abnormality in a more physically meaningful way we have tested our novel methods on 41 human image sequences and achieved a classification rate of 87 80 the regional abnormalities recovered from our algorithm agree well with the patient s pathology and clinical image interpretation and provide a promising avenue for regional cardiac function analysis

multiresolution monogenic signal analysis using the riesz laplace wavelet transform the monogenic signal is the natural 2d counterpart of the 1d analytic signal we propose to transpose the concept to the wavelet domain by considering a complexified version of the riesz transform which has the remarkable property of mapping a real valued primary wavelet basis of l2 r2 into a complex one the riesz operator is also steerable in the sense that it give access to the hilbert transform of the signal along any orientation having set those foundations we specify a primary polyharmonic spline wavelet basis of l2 r2 that involves a single mexican hat like mother wavelet laplacian of a b spline the important point is that our primary wavelets are quasi isotropic they behave like multiscale versions of the fractional laplace operator from which they are derived which ensures steerability we propose to pair these real valued basis functions with their complex riesz counterparts to specify a multiresolution monogenic signal analysis this yields a representation where each wavelet index is associated with a local orientation an amplitude and a phase we give a corresponding wavelet domain method for estimating the underlying instantaneous frequency we also provide a mechanism for improving the shift and rotation invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect reconstruction filterbanks we illustrate the specific feature extraction capabilities of the representation and present novel examples of wavelet domain processing in particular a robust tensor based analysis of directional image patterns the demodulation of interferograms and the reconstruction of digital holograms

rotation invariant texture classification using a complete space frequency model a method of rotation invariant texture classification based on a complete space frequency model is introduced a polar analytic form of a two dimensional 2 d gabor wavelet is developed and a multiresolution family of these wavelets is used to compute information conserving microfeatures from these microfeatures a micromodel which characterizes spatially localized amplitude frequency and directional behavior of the texture is formed the essential characteristics of a texture sample its macrofeatures are derived from the estimated selected parameters of the micromodel classification of texture samples is based on the macromodel derived from a rotation invariant subset of macrofeatures in experiments comparatively high correct classification rates were obtained using large sample sets

long correlation image models for textures with circular and elliptical correlation structures a class of random field model having long correlation characteristics is introduced unlike earlier approaches in long correlation models the correlation structure is isotropic or elliptical in this new class of random field model the new model has an advantage of modeling diverse real textures with less than five model parameters further the model parameters match with intuitive attributes of textures such as smoothness pattern size elongation or orientation of patterns the new long correlation models are based on the fractional differencing of a two dimensional 2 d autoregressive polynomial defined by eight symmetric neighbors and they are either persistent or periodic models depending whether the roots of the polynomial are real or imaginary a comprehensive three step algorithm for parameter estimation is developed and the statistical properties of the estimators are also discussed the validity of the new model in modeling textures is tested by synthesizing images from manually selected parameters as well as parameters estimated from real textures it is shown that an image with desired attributes can be synthesized by selecting proper values of the parameters further it is shown that the models introduced can be used in modeling wide range of textures by synthesizing images resembling real textures from estimated parameters

shape from texture without boundaries we describe a shape from texture method that constructs an estimate of surface geometry using only the deformation of individual texture elements our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of elements the method assumes that surface texture elements are drawn from a number of different types each of fixed shape neither the shape of the elements nor the number of types need be known in advance we show that with this assumption and assuming a generic scaled orthographic view and texture each type of texture element can be reconstructed in a frontal coordinate system from image instances interest point methods supply a method of simultaneously obtaining instances of each texture element automatically and defining each type of element furthermore image instances that have been marked in error can be identified and ignored using the expectation maximization algorithm a further em procedure yields a surface reconstruction and a relative irradiance map from the data we provide numerous examples of reconstructions for images of real scenes show a comparison between our reconstruction and range maps and demonstrate that the reconstructions display geometric and irradiance phenomena that can be observed in the original image

where and why local shading analysis works an apparent contradiction in the shape from shading literature is examined although practical experience suggests that shape can be inferred from the local analysis of shading mathematical analyses support the opposite a criterion for exact surface recovery is derived and it is shown that as a result of surface geometry elliptic hyperbolic and doubly curved surfaces could be recovered to reasonable accuracy provided that surface curvature and or foreshortening were limited in other words by relaxing the requirement that surfaces be recovered exactly it is found that local analysis of shading can provide useful descriptions of shape as evidenced by the results presented

synthesis and estimation of random fields using long correlation models random field models have arisen in important applications in many diverse fields including image synthesis and analysis the automatic description and processing of images is limited by the types of underlying models that are hypothesized for the image hence new random field models and associated techniques are developed the new class of models includes the traditional simultaneous autoregressive and moving average models but extends these to comprise a substantially larger new class thus new image textures are representable with convenient small order parameterizations in particular representations with significant correlations between distant locations are achieved the algorithms for synthesis and estimation however require only about the same amount of time as the classical models the development is facilitated by a new mathematical formulation suitable for problems involving high dimensional transformations

robust image modeling techniques with an image restoration application a robust parameter estimation algorithm for a nonsymmetric half plane nshp autoregressive model where the driving noise is a mixture of a gaussian and an outlier process is presented the convergence of the estimation algorithm is proved an algorithm to estimate parameters and original image intensity simultaneously from the impulse noise corrupted image where the model governing the image is not available is also presented the robustness of the parameter estimates is demonstrated by simulation finally an algorithm to restore realistic images is presented the entire image generally does not obey a simple image model but a small portion e g 8 8 of the image is assumed to obey an nshp model the original image is divided into windows and the robust estimation algorithm is applied for each window the restoration algorithm is tested by comparing it to traditional methods on several different images

gauge transformation of the third kind for u 1 invariant coupled schrodinger equations we consider a large class of canonical coupled nonlinear schrodinger equations invariant over the action of the u 1 group the most general nonlinearity is taken into account through a matrix that without loss of generality can be separated into the sum of a hermitian matrix and an anti hermitian matrix the u 1 symmetry implies the existence of a set of continuity equations for the conserved densities where the corresponding currents have in general a nonlinear structure for this class of coupled schrodinger equations we introduce a nonlinear gauge transformation which changes the nonlinear matrix into another one purely hermitian consequently the currents are transformed in the standard bilinear form generalization to noncanonical systems is also discussed some examples are presented to illustrate the applicability of the method

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

classification via sparse representation of steerable wavelet frames on grassmann manifold application to target recognition in sar image automatic target recognition has been widely studied over the years yet it is still an open problem the main obstacle consists in extended operating conditions e g depression angle change configuration variation articulation and occlusion to deal with them this paper proposes a new classification strategy we develop a new representation model via the steerable wavelet frames the proposed representation model is entirely viewed as an element on grassmann manifolds to achieve target classification we embed grassmann manifolds into an implicit reproducing kernel hilbert space rkhs where the kernel sparse learning can be applied specifically the mappings of training sample in rkhs are concatenated to form an overcomplete dictionary it is then used to encode the counterpart of query as a linear combination of its atoms by designed grassmann kernel function it is capable to obtain the sparse representation from which the inference can be reached the novelty of this paper comes from 1 the development of representation model by the set of directional components of riesz transform 2 the quantitative measure of similarity for proposed representation model by grassmann metric and 3 the generation of global kernel function by grassmann kernel extensive comparative studies are performed to demonstrate the advantage of proposed strategy

myocardial motion estimation from medical images using the monogenic signal we present a method for the analysis of heart motion from medical images the algorithm exploits monogenic signal theory recently introduced as an n dimensional generalization of the analytic signal the displacement is computed locally by assuming the conservation of the monogenic phase over time a local affine displacement model is considered to account for typical heart motions as contraction expansion and shear a coarse to fine b spline scheme allows a robust and effective computation of the model s parameters and a pyramidal refinement scheme helps to handle large motions robustness against noise is increased by replacing the standard point wise computation of the monogenic orientation with a robust least squares orientation estimate given its general formulation the algorithm is well suited for images from different modalities in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption this paper evaluates the method s feasibility on two emblematic cases cardiac tagged magnetic resonance and cardiac ultrasound in order to quantify the performance of the proposed method we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known a comparison is presented with state of the art methods for cardiac motion analysis on the data considered these conventional approaches are outperformed by the proposed algorithm a recent global optical flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison with respect to the latter the proposed framework provides along with higher accuracy superior robustness to noise and a considerably shorter computation time

estimation of myocardial strain and contraction phase from cine mri using variational data assimilation this paper presents a new method to estimate left ventricle deformations using variational data assimilation that combines image observations from cine mri and a dynamic evolution model of the heart the main contribution of the model is that it embeds parameters modeling the contraction relaxation process it estimates myocardial motion and contraction parameters simultaneously providing accurate complementary information for diagnosis the method was applied to synthetic datasets with known ground truth motion and to 47 patients mri datasets acquired at three slice locations base mid ventricle and apex radial and circumferential strain components were compared to those obtained with a reference tag tracking software exhibiting good agreement with intraclass correlation coefficients icc above 0 8 results were also evaluated against wall motion score indices used to assess cardiac kinetics in clinical practice the assimilation process overcame issues caused by temporal artifacts as a result of the dynamic model compared to using the observation term alone moreover we found that the new dynamic model consisting of a piecewise transport model acting independently on systole and diastole performed better than the standard continuous transport model which oversmooths temporal variations estimated strain and contraction parameters significantly correlated to clinical scores making them promising features for diagnosing not only hypokinesia but also dyskinesia

estimation of orientation of a textured planar surface using projective equations and separable analysis with m channel wavelet decomposition estimation of the orientation of a textured planar surface is one of the basic tasks in the area of shape from texture for the solution of this task many successful approaches were proposed in this paper we have examined a few unaddressed questions first is there a mathematical formulation that relates the spectral characteristics of the texture pattern and the orientation of an inclined planar surface in a polar coordinate system second is there a good wavelet based approach that produces an accurate estimate of the orientation angle of the textured planar surface by analyzing the spectral behavior of one single uncalibrated image to answer these questions at first we present the formulation of a texture projective equation which relates the depth and orientation of an inclined planar surface in a polar coordinate system with the spectral properties of its image texture a suitable imaging geometry has been considered to enable separable analysis of the effect of inclination of the texture surface next a method for shape from texture is presented based on discrete wavelet analysis to estimate the orientation of the planar surface this approach although designed mainly for m channel wavelets is also applicable for dyadic wavelet analysis texture characteristics in the subbands of wavelet decomposition are analyzed using scalograms and quantitatively evaluated based on texture projective equations the proposed method of estimation of the orientation of a planar texture surface is evaluated using a set of simulated and real world textured images

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

the visual interpretation of surface contours this article examines the computational problems underlying the 3 d interpretation of surface contours a surface contour is the image of a curve across a physical surface such as the edge of a shadow cast across a surface a gloss contour wrinkle seam or pigmentation marking surface contours by and large are not as restricted as occluding contours and therefore pose a more difficult interpretation problem nonetheless we are adept at perceiving a definite 3 d surface from even simple line drawings e g graphical depictions of continuous functions of two variables the solution of a specific surface shape comes by assuming that the physical curves are particularly restricted in their geometric relationship to the underlying surface these geometric restrictions are examined

on the imaging of fractal surfaces an analysis is presented of the imaging of surfaces modeled by fractal brownian elevation functions of the sort used in computer graphics it is shown that if lambertian reflectance modest surface slopes and the absence of occlusions and self shadowing are assumed a fractal surface with fourier power spectrum proportional to f sup beta produces an image with power spectrum proportional to f sup 2 beta here f is the spatial frequency and beta is related to the fractional dimension value this allows one to use the spectral falloff of the images to predict the fractal dimension of the surface

spatio temporal nonrigid registration for ultrasound cardiac motion estimation we propose a new spatio temporal elastic registration algorithm for motion reconstruction from a series of images the specific application is to estimate displacement fields from two dimensional ultrasound sequences of the heart the basic idea is to find a spatio temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame the key feature of our method is the use of a semi local spatio temporal parametric model for the deformation using splines and the reformulation of the registration task as a global optimization problem the scale of the spline model controls the smoothness of the displacement field our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness we evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package together with a realistic cardiac motion model we compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency finally we applied the algorithm to the regional analysis of the left ventricle displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments thereby illustrating the clinical applicability of our method

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

orbital stability of solitary waves for kundu equation abstract in this paper we consider the kundu equation which is not a standard hamiltonian system the abstract orbital stability theory proposed by grillakis et al 1987 1990 cannot be applied directly to study orbital stability of solitary waves for this equation motivated by the idea of guo and wu 1995 we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for kundu equation since kundu equation is more complex than the derivative schrodinger equation we utilize some techniques to overcome some difficulties in this paper it should be pointed out that the results obtained in this paper are more general than those obtained by guo and wu 1995 we present a sufficient condition under which solitary waves are orbitally stable for 2 c 3 s 2 0 while guo and wu 1995 only considered the case 2 c 3 s 2 0 we obtain the results on orbital stability of solitary waves for the derivative schrodinger equation given by colin and ohta 2006 as a corollary in this paper furthermore we obtain orbital stability of solitary waves for chen lee lin equation and gerdjikov ivanov equation respectively

myocardial motion analysis from b mode echocardiograms the quantitative assessment of cardiac motion is a fundamental concept to evaluate ventricular malfunction we present a new optical flow based method for estimating heart motion from two dimensional echocardiographic sequences to account for typical heart motions such as contraction expansion and shear we analyze the images locally by using a local affine model for the velocity in space and a linear model in time the regional motion parameters are estimated in the least squares sense inside a sliding spatiotemporal b spline window robustness and spatial adaptability is achieved by estimating the model parameters at multiple scales within a coarse to fine multiresolution framework we use a wavelet like algorithm for computing b spline weighted inner products and moments at dyadic scales to increase computational efficiency in order to characterize myocardial contractility and to simplify the detection of myocardial dysfunction the radial component of the velocity with respect to a reference point is color coded and visualized inside a time varying region of interest the algorithm was first validated on synthetic data sets that simulate a beating heart with a speckle like appearance of echocardiograms the ability to estimate motion from real ultrasound sequences was demonstrated by a rotating phantom experiment the method was also applied to a set of in vivo echocardiograms from an animal study motion estimation results were in good agreement with the expert echocardiographic reading

on the integrability of the extended nonlinear schrodinger equation and the coupled extended nonlinear schrodinger equations we consider the extended nonlinear schr enls equation which governs the propagation of nonlinear optical fields in a fibre with higher order effects such as higher order dispersion and self steepening we show that the enls equation does not pass the painlev test similarly we claim that the coupled enls equations and n coupled enls equations which govern the simultaneous propagation of two and more nonlinear fields in optical fibres are also not integrable from the painlev e analysis point of view

detection of surface orientation and motion from texture by a stereoogical technique abstract a new approach is given to detect the surface orientation and motion from the texture on the surface by making use of a mathematical principle called stereology information about the surface orientation is contained in features computed by scanning the image by parallel lines and counting the number of intersections with the curves of the texture a synthetic example is given to illustrate the technique this scheme can also detect surface motions relative to the viewer by computing features of its texture at one time and a short time later the motion is specified by explicit formulae of the computed features

propagation of dark solitons in a system of coupled higher order nonlinear schrodinger equations in this paper we consider the higher order linear and nonlinear effects in optics and analyse a coupled system of higher order nonlinear schrodinger equations to identify the conditions for dark soliton propagation through painleve analysis to supplement the known bright soliton conditions we also construct the explicit lax pair and the hirota bilinear form is used to generate one and two dark solitons

texture boundary detection based on the long correlation model the problem of detecting texture boundaries without assuming any knowledge on the number of regions or the types of textures is considered texture boundaries are often regarded as better features than intensity edges because a large class of images can be considered a composite of several different texture regions an algorithm is developed that detects texture boundaries at reasonably high resolution without assuming any prior knowledge on the texture composition of the image the algorithm utilizes the long correlation texture model with a small number of parameters to characterize textures the parameters of the model are estimated by a least squares method in the frequency domain the existence and the location of texture boundary is estimated by the maximum likelihood method the algorithm is applied to several different images and its performance is shown by examples experimental results show that the algorithm successfully detects texture boundaries without knowing the number of types of textures in the image

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow