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

shape from texture and contour by weak isotropy abstract a unified framework for shape from texture and contour is proposed it is based on the assumption that the surface markings are not systematically compressed or formally that they are weakly isotropic the weak isotropy principle is based on analysis of the directional statistics of the projected surface markings it builds on several previous theories in particular by witkin 25 and kanatani 15 it extends these theories in various ways most notably to perspective projection the theory also provides an exact solution to an estimation problem earlier solved approximately by kanatani the weak isotropy principle leads to a computationally efficient algorithm wisp for estimation of surface orientation wisp uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initial approximate estimate in a single step in certain simple cases this first estimate is exact and in experiments with natural images it is typically within 5 of the final estimate furthermore a proof is given that a rotationally symmetric contour of order three or higher is weakly isotropic hence the wisp algorithm will without modification recover the orientation of any such contour from a perspective view of it

a general goodness of fit test for markov and hidden markov models markov models are a convenient and useful method of estimating transition rates between levels of a categorical response variable such as a disease stage which changes over time in medical applications the response variable is typically observed at irregular intervals a pearson type goodness of fit test for such models was proposed by aguirre hernandez and farewell statist med 2002 21 1899 1911 but this test is not applicable in the common situation where the process includes an absorbing state such as death for which the time of entry is known precisely nor when the data include censored state observations this paper presents a modification to the pearson type test to allow for these cases an extension of the method to allow for the class of hidden markov models where the response variable is subject to misclassification error is given the method is applied to data on cardiac allograft vasculopathy in post heart transplant patients

shape from texture estimation isotropy and moments a theory is proposed for the interpretation of 3d textures with oriented elements it builds on two previous theories a statistical one due to witkin and kanatani s buffon transform we show that the statistical estimation of orientation of a textured plane is one of a general family of optimal backprojection problems which also includes maximal compactness general uniqueness and convergence results are obtained for an efficient algorithm employing second moment feedback this framework greatly enhances the usefulness of surface orientation estimation for texture in two ways first an error distribution is derived for the estimator and this is crucial for integration of shape information second hypotheses about intrinsic texture statistics can be verified by a 2 test which if failed warns that the orientation estimator is not to be believed finally it is argued that these results suggest a general moment tensor approach to analysis of 3d texture

shape from regular patterns niis paper describes an aigoritlitr1 to obtaitl local surface orierltatiorr frofti the apparetlt surface pattertl distortion in an image we propose a spherical projection to model perspctiue imaging a trtappitlg is debtled based of1 the measurement of the local distortions of a repeated known rexture pattern due io the image projection 77tis mapping maps an apparent shape on the image sphere lo a locus of possible surface orienrations on the gaussian sphere an ireratiw constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation 7lis algorithm can recover local surface orientation as well as interpolate surjace orientations where no information is auailable xis algorithm is applied to a real image ro demonstrate its perfontlance

a new normalized relatively stable lattice structure this paper proposes a new lattice filter structure that has the following properties when the filter is linear time invariant lti it is equivalent to the celebrated gray markel lattice when the lattice parameters vary with time it sustains arbitrary rates of time variations without sacrificing a prescribed degree of stability provided that the lattice coefficients are magnitude bounded in a region where all lti lattices have the same degree of stability we also show that the resulting ltv lattice obeys an energy contraction condition this structure thus generalizes the normalized gray markel lattice which has similar properties but only with respect to stability as opposed to relative stability

planar surface orientation from texture spatial frequencies abstract this paper presents a computational model and a practical algorithm for determining the three dimensional orientation of a planar surface from visual texture information the model consists of three parts 1 a local spatial frequency based texture representation 2 a model describing the projection of surface texture to image texture and 3 a solution of the texture projection model for the surface orientation under an assumption of surface texture homogeneity the algorithm first measures the dominant frequency at each image point using three wavelet like transforms and then finds the surface orientation that minimizes the variance of the image frequencies backprojections the algorithm is tested on photographs of real world surfaces exhibiting an average accuracy of better than 3 in slant and 4 in tilt the current model and algorithm are more accurate yet substantially simpler than earlier versions of this approach

robust relative stability of time invariant and time varying lattice filters we consider the relative stability of time invariant and time varying unnormalized lattice filters first we consider a set of lattice filters whose reflection parameters spl alpha sub i obey spl alpha sub i spl les spl delta sub i and provide necessary and sufficient conditions on the spl delta sub i that guarantee that each time invariant lattice in the set has poles inside a circle of prescribed radius 1 spl rho 1 spl rho

shape from texture general principle abstract the 3d shape of a textured surface is recovered from its projected image on the assumption that the texture is homogeneously distributed our method does not require recognition of the structure regularity periodicity parallelism orthogonality etc of the texture distribution first the homogeneity of a discrete texture is precisely defined in terms of the theory of distributions next distortion of the observed texture due to perspective projection is described in terms of the first fundamental form expressed as a function of the image coordinates based on this result the 3d recovery equations for determining the surface shape are derived for both planar and curved surfaces some numerical schemes for solving these equations are proposed ambiguity in the interpretation of curved surfaces is also analyzed finally some numerical examples for synthetic data are presented and our method is compared with other existing methods

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

shape from periodic texture using the eigenvectors of local affine distortion shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly without the need for iterative numerical optimization we work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks the key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces in particular the leading eigenvector points in the tilt direction although not as geometrically transparent the direction of the second eigenvector can be used to estimate the slant direction the required affine distortion matrices are computed using the correspondences between spectral peaks established on the basis of their energy ordering we apply the method to a variety of real world and synthetic imagery

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

direct estimation of shape from texture witkin 1981 has proposed a maximum likelihood ml estimator of surface orientation based on the observed directional bias of projected texture elements however a drawback of this procedure is that the estimate is only defined indirectly in terms of a set of nonlinear equations an alternative method is proposed which allows an estimate of the surface orientation to be computed directly in a single step from certain simple statistics of the image data we also show that this direct estimate allows witkin s ml estimate to be computed to within 0 05 degrees in only two or three iterative steps the performance of the new estimator is demonstrated experimentally and compared to that of the ml estimator using both synthetic data and real gray level images

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

a mixed model for two state markov processes under panel observation many chronic medical conditions can be meaningfully characterized in terms of a two state stochastic process here we consider the problem in which subjects make transitions among two such states in continuous time but are only observed at discrete irregularly spaced time points that are possibly unique to each subject data arising from such an observation scheme are called panel data and methods for related analyses are typically based on markov assumptions the purpose of this article is to present a conditionally markov model that accommodates subject to subject variation in the model parameters by the introduction of random effects we focus on a particular random effects formulation that generates a closed form expression for the marginal likelihood the methodology is illustrated by application to a data set from a parasitic field infection survey

a note on the stability of linear discrete systems and lyapunov method in a publication by y p harn and c t chen 1 a proof of a discrete stability test by using the lyapunov method was given in this note the main results obtained by the author in this direction in 1965 6 7 and the extensions and applications obtained partially with other authors since then and published in different journals 8 10 are surveyed the similarity to the results in 1 is obvious

adaptive scale filtering a general method for obtaining shape from texture introduces adaptive scale filtering a general method for deriving shape from texture under perspective projection without recourse to prior segmentation of the image into geometric texture elements texels and without thresholding of filtered images if texels on a given surface can be identified in an image then the orientation of that surface can be obtained however there is no general characterization of texels for arbitrary textures furthermore even if the size and shape of texels on the surface is invariant with regard to position perspective projection ensures that the size and shape of the corresponding image texels vary by orders of magnitude commencing with an initial set f sub o of identical image filters adaptive scale filtering iteratively derives a set f sub n which contains a unique filter for each image position each element of f sub n is tuned to the three dimensional structure of the surface that is all image filters in f sub n back project to an identical shape and size on the surface thus image texels of various sizes but associated with a single spatial scale on the surface can be identified in different parts of the image when combined with conventional shape from texture methods edges derived using f sub n provide accurate estimates of surface orientation results for planar surfaces are presented

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

exponential asymptotic stability of time varying inverse prediction error filters it is a classical result of linear prediction theory that as long as the minimum prediction error variance is nonzero the transfer function of the optimum linear prediction error filter for a stationary process is minimum phase and therefore its inverse is exponentially stable here extensions of this result to the case of nonstationary processes are investigated in that context the filter becomes time varying and the concept of transfer function ceases to make sense nevertheless we prove that under mild condition on the input process the inverse system remains exponentially stable we also consider filters obtained in a deterministic framework and show that if the time varying coefficients of the predictor are computed by means of the recursive weighted least squares algorithm then its inverse remains exponentially stable under a similar set of conditions

alignment using distributions of local geometric properties we describe a framework for aligning images without needing to establish explicit feature correspondences we assume that the geometry between the two images can be adequately described by an affine transformation and develop a framework that uses the statistical distribution of geometric properties of image contours to estimate the relevant transformation parameters the estimates obtained using the proposed method are robust to illumination conditions sensor characteristics etc since image contours are relatively invariant to these changes moreover the distributional nature of our method alleviates some of the common problems due to contour fragmentation occlusion clutter etc we provide empirical evidence of the accuracy and robustness of our algorithm finally we demonstrate our method on both real and synthetic images including multisensor image pairs

stereo matching as a nearest neighbor problem we propose a representation of images called intrinsic curves that transforms stereo matching from a search problem into a nearest neighbor problem intrinsic curves are the paths that a set of local image descriptors trace as an image scanline is traversed from left to right intrinsic curves are ideally invariant with respect to disparity stereo correspondence then becomes a trivial lookup problem in the ideal case we also show how to use intrinsic curves to match real images in the presence of noise brightness bias contrast fluctuations moderate geometric distortion image ambiguity and occlusions in this case matching becomes a nearest neighbor problem even for very large disparity values

isoperimetric normalization of planar curves this paper presents an algorithm for transforming closed planar curves into a canonical form independent of the viewpoint from which the original image of the contour was taken the transformation that takes the contour to its canonical form is a member of the projective group pgl 2 chosen because pgl 2 contains all possible transformations of a plane curve under central projection onto another plane the scheme relies on solving computationally an isoperimetric problem in which a transformation is sought which maximises the area of a curve given unit perimeter in the case that the transformation is restricted to the affine subgroup there is a unique extremising transformation for any piecewise smooth closed curve uniqueness holds almost always even for curves that are not closed in the full projective case isoperimetric normalization is well defined only for closed curves we have found computational counterexamples for which there is more than one extremal transformation numerical algorithms are described and demonstrated both for the affine and the projective cases once a canonical curve is obtained its isoperimetric area can be regarded as an invariant descriptor of shape

fundamental limitations on projective invariants of planar curves in this paper some fundamental limitations of projective invariants of non algebraic planar curves are discussed it is shown that all curves within a large class can be mapped arbitrarily close to a circle by projective transformations it is also shown that arbitrarily close to each of a finite number of closed planar curves there is one member of a set of projectively equivalent curves thus a continuous projective invariant on closed curves is constant this also limits the possibility of finding so called projective normalisation schemes for closed planar curves

a pearson type goodness of fit test for stationary and time continuous markov regression models markov regression models describe the way in which a categorical response variable changes over time for subjects with different explanatory variables frequently it is difficult to measure the response variable on equally spaced discrete time intervals here we propose a pearson type goodness of fit test for stationary markov regression models fitted to panel data a parametric bootstrap algorithm is used to study the distribution of the test statistic the proposed technique is applied to examine the fit of a markov regression model used to identify markers for disease progression in psoriatic arthritis

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

the analysis of asthma control under a markov assumption with use of covariates in studies of disease states and their relation to evolution data on the state are usually obtained at in frequent time points during follow up moreover in many applications there are measured covariates on each individual under study and interest centres on the relationship between these covariates and the disease evolution we developed a continuous time markov model with use of time dependent covariates and a markov model with piecewise constant intensities to model asthma evolution methods to estimate the effect of covariates on transition intensities to test the assumption of time homogeneity and to assess goodness of fit are proposed we apply these methods to asthma control we consider a three state model and we discuss in detail the analysis of asthma control evolution copyright 2003 john wiley sons ltd