generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

a priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient abstract we consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient such as f x u d u d 2 u c x u m x d u d u h x in a bounded domain with a dirichlet boundary condition here r c h l p p n 1 c 0 and the matrix m satisfies 0 1 i m 2 i recently this problem was studied in the coercive case c 0 where uniqueness of solutions can be expected and it was conjectured that the solution set is more complex for noncoercive equations this conjecture was verified in 2015 by arcoya de coster jeanjean and tanaka for equations in divergence form by exploiting the integral formulation of the problem here we show that similar phenomena occur for general even fully nonlinear equations in nondivergence form we use different techniques based on the maximum principle we develop a new method to obtain the crucial uniform a priori bounds which permit to us to use degree theory this method is based on basic regularity estimates such as half harnack inequalities and on a vazquez type strong maximum principle for our kind of equations

deformable contours modeling and extraction this paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images we propose a global contour model based on a stable and regenerative shape matrix which is invariant and unique under rigid motions combined with markov random field to model local deformations this yields prior distribution that exerts influence over a global model while allowing for deformations we then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model we discuss pertinent issues in shape training energy minimization line search strategies minimax regularization and initialization by generalized hough transform finally we present experimental results and compare its performance to rigid template matching

existence results for a class of nonlinear elliptic problems with p growth in the gradient abstract we prove the existence of bounded solutions for a class of nonlinear elliptic problems whose model is in the form div a x u du k 1 u du p k 2 u f u w 0 1 p l where a x b p b is a continuous monotone decreasing function and k1 and k2 are continuous monotone increasing functions

singular quasilinear equations with quadratic growth in the gradient without sign condition given a bounded domain in r n a nd af unctiona l q with q n 2 we study the existence of a positive solution for the quasilinear problem

parabolic equations with nonlinear singularities abstract we show the existence of positive solutions u l 2 0 t h 0 1 for nonlinear parabolic problems with singular lower order terms of the asymptote type more precisely we shall consider both semilinear problems whose model is u t u u 1 u f x t in 0 t u x 0 u 0 x in u x t 0 on 0 t and quasilinear problems having natural growth with respect to the gradient whose model is u t u u 2 u f x t in 0 t u x 0 u 0 x in u x t 0 on 0 t with 0 moreover we prove a comparison principle and as an application we study the asymptotic behavior of the solution as t goes to infinity

quasilinear elliptic problems with singular and homogeneous lower order terms abstract we deal with singular quasilinear elliptic equations namely u u x u q u q 1 f x in u 0 in u 0 on where is a bounded smooth domain of r n n 3 r 1 q 2 0 l and 0 f l p for some p n 2 we completely describe the set of values of the parameter for which the problem admits solution thus we study existence nonexistence and uniqueness of bounded weak solutions in both cases f 0 and f 0

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions in this paper we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

on a singular elliptic system with quadratic growth in the gradient abstract in this paper we deal with the following singular elliptic system u u 2 u p p q a x v q u p 2 u f x r n v v 2 v q p q a x u p v q 2 v g x r n where n 3 n 2 4 p q 1 and p q n 2 n 2 we show through the sub and supersolutions method the existence of a nonnegative solution for an approximated system the limit of the approximated solution is a positive solution in the case 0 p q and f g we prove the uniqueness of a solution among others we prove some existence and uniqueness results for some auxiliary problems by using the comparison principle a minimization method and with the help of nehari manifold the proofs rely on the concentration compactness principle

comparison of interpolating methods for image resampling when resampling an image to a new set of coordinates for example when rotating an image there is often a noticeable loss in image quality to preserve image quality the interpolating function used for the resampling should be an ideal low pass filter to determine which limited extent convolving functions would provide the best interpolation five functions were compared a nearest neighbor b linear c cubic b spline d high resolution cubic spline with edge enhancement a 1 and e high resolution cubic spline a 0 5 the functions which extend over four picture elements c d e were shown to have a better frequency response than those which extend over one a or two b pixels the nearest neighbor function shifted the image up to one half a pixel linear and cubic b spline interpolation tended to smooth the image the best response was obtained with the high resolution cubic spline functions the location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned and the response has the most smoothing when the resampled points are equidistant from the original coordinate points thus at the expense of some increase in computing time image quality can be improved by resampled using the high resolution cubic spline function as compared to the nearest neighbor linear or cubic b spline functions

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

object tracking in image sequences using point features this paper presents an object tracking technique based on the bayesian multiple hypothesis tracking mht approach two algorithms both based on the mht technique are combined to generate an object tracker the first mht algorithm is employed for contour segmentation the segmentation of contours is based on an edge map the segmented contours are then merged to form recognisable objects the second mht algorithm is used in the temporal tracking of a selected object from the initial frame an object is represented by key feature points that are extracted from it the key points mostly corner points are detected using information obtained from the edge map these key points are then tracked through the sequence to confirm the correctness of the tracked key points the location of the key points on the trajectory are verified against the segmented object identified in each frame if an acceptable number of key points lie on or near the contour of the object in a particular frame n th frame we conclude that the selected object has been tracked identified successfully in frame n

nonlinear elliptic equations with natural growth in the gradient and source terms in lorentz spaces abstract in this paper we consider the problem u w 0 1 p div a x u d u b x u d u h x u d u in d where div a x u d u is a leray lions operator which is defined on w 0 1 p with coercivity where the growth with respect to du of h x u d u is controlled by d u p and where b x u d u satisfies a similar growth condition but has the good sign the main feature of the problem is that the source terms belong to the lorentz space l n p when two smallness conditions are satisfied the second one depends on the behavior of b x u d u when u tends to infinity we prove the existence of a solution which further satisfies e p 1 u 1 w 0 1 p for every with 0 for some threshold 0 the key ingredient in the proof of the existence result is an a priori estimate which holds true for every solution to the problem which satisfies the above mentioned exponential regularity condition

physically based active shape models initialization and optimization in this paper we describe a new approach for 2 d object segmentation using an automatic method applied on images with problems as partial information overlapping objects many objects in a single scene severe noise conditions and locating objects with a very high degree of deformation we use a physically based shape model to obtain a deformable template which is defined on a canonical orthogonal coordinate system the proposed methodology works starting from the output of an edge detector which is processed to automatically obtain an approximation of the shape the final estimation of the shapes is obtained fitting a deformable template model which is defined on a learned surface of deformation results from biological images are presented

existence and uniqueness for several non linear elliptic problems arising in lubrication theory we consider the non linear elliptic equation a x p p b x p with positive dirichlet boundary data the coefficients a and b are taken from models used in lubrication theory andin particular are not d negative values of p we prove some general existence anduniqueness results for a family of mod els which extendrelatedresults in the literature these results allow us to prove existence uniqueness andpositivity of the solution to advanced compressible lubrication models such as the kinetic based fukui kaneko model and the second order slip model we also consider a spring like model of compliant foil compressible bearing andweaken some hypotheses of previous results on more classical mod els such as the standard reynolds model and the first order slip model

bayesian shape model for facial feature extraction and recognition abstract a facial feature extraction algorithm using the bayesian shape model bsm is proposed in this paper a full face model consisting of the contour points and the control points is designed to describe the face patch using which the warping normalization of the extracted face patch can be performed efficiently first the bsm is utilized to match and extract the contour points of a face in bsm the prototype of the face contour can be adjusted adaptively according to its prior distribution moreover an affine invariant internal energy term is introduced to describe the local shape deformations between the prototype contour in the shape domain and the deformable contour in the image domain thus both global and local shape deformations can be tolerated then the control points are estimated from the matching result of the contour points based on the statistics of the full face model finally the face patch is extracted and normalized using the piece wise affine triangle warping algorithm experimental results based on real facial feature extraction demonstrate that the proposed bsm facial feature extraction algorithm is more accurate and effective as compared to that of the active shape model asm

nonlinear fractional laplacian problems with nonlocal gradient terms let n 2 be a smooth bounded domain for s 1 2 1 we consider a problem of the form where 0 is a real parameter f belongs to a suitable lebesgue space and is a nonlocal gradient square term given by depending on the real parameter 0 we derive existence and non existence results the proof of our existence result relies on sharp calderon zygmund type regularity results for the fractional poisson equation with low integrability data we also obtain existence results for related problems involving different nonlocal diffusion terms

existence and uniqueness of solutions for a singular semilinear elliptic system abstract in this paper we study the existence and the uniqueness of solutions for the singular semilinear elliptic system u f x u 2 g x u 1 p 2 p q a x u p v 1 q x r n v f x v 2 g x v 1 q 2 p q a x u 1 p v q x r n where 0 p 1 and 0 q 1 we show the existence of a solution for an approximated system by using a perturbation method which eliminates the singularity and via variational methods the limit of the approximated solutions is a positive solution in the case g 0 p q and 1 2 p 1 we prove the uniqueness of solution the proofs rely on the concentration compactness principle

a robust snake implementation a dual active contour a conventional active contour formulation suffers difficulty in appropriate choice of an initial contour and values of parameters recent approaches have aimed to resolve these problems but can compromise other performance aspects to relieve the problem in initialization we use a dual active contour which is combined with a local shape model to improve the parameterization one contour expands from inside the target feature the other contracts from the outside the two contours are interlinked to provide a balanced technique with an ability to reject weak local energy minima

existence and non existence of solutions to elliptic equations with a general convection term in this paper we consider the nonlinear elliptic problem u u g u h x in u 0 on where is a smooth bounded domain of n 0 g is an arbitrary c 1 increasing function and h c 1 is non negative we completely analyse the existence and non existence of positive classical solutions in terms of the parameter we show that there exist solutions for every when 0 and the integral 1 g s d s or when 0 and the integral s g s d s conversely when the respective integrals converge and h is non trivial on existence depends on the size of moreover non existence holds for large our proofs mainly rely on comparison arguments and on the construction of suitable supersolutions in annuli our results include some cases where the function g is superquadratic and existence still holds without assuming any smallness condition on

rearrangement relatif dans les equations elliptiques quasi lineaires avec un second membre distribution application a un theoreme d existence et de regularite abstract in this paper we are concerned with quasilinear elliptic equations that is p au f u u t in r u w01 p l where a is an operator of leray lions type which is defined on w 0 1 p l 1 f is a non linear map having a suitable growth and t is a distribution of w 1 r r n p 1 and r p p 1 using the techniques of the relative rearrangement ann scuola norm sup pisa cl sci 4 in press we give a precise a priori estimate of the solution u of p in l norm these estimates allow us to prove an existence theorem for p and to get the holder continuity of the solution u

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

existence and nonexistence of solutions for singular quadratic quasilinear equations we study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient whose model is 8

on deformable models for visual pattern recognition this paper reviews model based methods for non rigid shape recognition these methods model match and classify non rigid shapes which are generally problematic for conventational algorithms using rigid models issues including model representation optimization criteria formulation model matching and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field this paper emphasizes on 2d deformable models their potential applications and future research directions particularly on deformable pattern classification are discussed

a coarse to fine deformable contour optimization framework this paper introduces a novel coarse to fine deformable contour optimization framework which is composed of two main components the first component uses scale space and information theories to produce a coarser representation of the input image to be used in a coarse to fine optimization scheme the employment of information theory ensures that maximal image information is propagated to the coarse images and employment of scale spaces provides a mechanism to change the image coarseness locally based on the deformable contour model definition the second component of this framework uses a novel combination of dynamic programming and gradient descent methods to optimize the contour energy on coarser representations and then use the obtained coarse contour positions in finer optimizations the motivation in using a combination of dynamic programming and gradient descent method is to take advantage of each method s efficiency and avoid their drawbacks in order to verify the performance of this framework we constructed a deformable contour model for the spatiotemporal tracking of closed contours and optimized the model energy under this framework experiments on this system performed using synthetic images and real world echocardiographic sequences demonstrated the effectiveness and practicality of this framework

fast and accurate edge based segmentation with no contour smoothing in 2 d real images we propose an edge based segmentation algorithm built on a new type of active contour which is fast has a low computational complexity and does not introduce unwanted smoothing on the retrieved contours the contours are always returned as closed chains of points resulting in a very useful base for subsequent shape representation techniques

an elliptic singular system with nonlocal boundary conditions abstract we study the existence of solutions for the nonlinear second order elliptic system u g u f x where g c r n s r n with s r n bounded using topological degree methods we prove an existence result under a geometric condition on g moreover we analyze the particular case of an isolated repulsive singularity under a nirenberg type condition we prove the existence of a sequence of solutions of appropriate approximated problems that converges to a generalized solution

some remarks on elliptic problems with critical growth in the gradient abstract in this work we analyze existence nonexistence multiplicity and regularity of solution to problem 1 u u u 2 f x in u 0 on where is a continuous nondecreasing positive function and f belongs to some suitable lebesgue spaces

two dimensional interpolation by generalized spline filters based on partial differential equation image models optimal image interpolation schemes based on partial differential equation pde models for the image signal are presented these schemes use the generalized spline interpolation approach minimum mean square error mmse is achieved given an image pde model and a finite set of the image data samples two new types of two dimensional 2 d interpolation techniques are presented for the implementation of these schemes these are the generalized cardinal spline digital filter and the generalized b spline interpolator computer simulations are described in addition to possessing a meaningful theoretical basis the results show a practical improvement of the approach presented over the existing schemes

a fast minimal path active contour model a new minimal path active contour model for boundary extraction is presented implementing the new approach requires four steps 1 users place some initial end points on or near the desired boundary through an interactive interface 2 a potential searching window is defined between two end points 3 a graph search method based on conic curves is used to search the boundary and 4 a wriggling procedure is used to calibrate the contour and reduce sensitivity of the search results on the selected initial end points the last three steps are performed automatically in the proposed approach the potential window systematically provides a new node connection for the later graph search which is different from the row by row and column by column methods used in the classical graph search furthermore this graph search also suggests ways to design a wriggling procedure to evolve the contour in the direction nearly perpendicular to itself by creating a list of displacement vectors in the potential window the proposed minimal path active contour model speeds up the search and reduces the metrication error frequently encountered in the classical graph search methods e g the dynamic programming minimal path dpmp method

a singular semilinear problem with dependence on the gradient abstract in the present paper we study the problem of finding classical and weak solutions for a semilinear elliptic equation involving a singular term and a nonlinearity depending on the gradient the approach we follow based on a suitable combination of sub supersolutions techniques and fixed point theory is not quite the same in the two cases and requires different kind of assumptions

some elliptic problems with singular natural growth lower order terms abstract in this paper we deal with a nonlinear elliptic problem whose model is u b d u 2 u f in u 0 on where b 0 and f 0 belongs to a lebesgue space we prove the existence of positive solutions in suitable sobolev spaces depending on f and b

an adaptive image interpolation algorithm for image video processing image interpolation is one of the key technologies in image video processing in this study a new adaptive image interpolation algorithm is proposed the objective of the proposed approach is to recover up sampled image frames from the corresponding decimated low resolution image frames in the proposed approach within each iteration two proposed nonlinear filters are utilized to iteratively generate high frequency components lost within the decimation procedure finally a post processing procedure is adopted to reduce the blocking artifacts within the interpolated images based on the experimental results obtained in this study in terms of the average psnrp peak signal to noise ratio in db and subjective measure of the quality of the interpolated images the interpolation results by the proposed approach are better than that by three existing interpolation approaches for comparison

on the sensitivity of the hough transform for object recognition object recognition from sensory data involves in part determining the pose of a model with respect to a scene a common method for finding an object s pose is the generalized hough transform which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters large clusters of similar transformations in that space are taken as evidence of a correct match a theoretical analysis of the behavior of such methods is presented the authors derive bounds on the set of transformations consistent with each pairing of data and model features in the presence of noise and occlusion in the image bounds are provided on the likelihood of false peaks in the parameter space as a function of noise occlusion and tessellation effects it is argued that haphazardly applying such methods to complex recognition tasks is risky as the probability of false positives can be very high

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality