local part chamfer matching for shape based object detection chamfer matching is one of the elegant and powerful tools for shape based detection in cluttered images however the chamfer matching methods including oriented chamfer matching ocm and directional chamfer matching dcm tend to produce bad detections due to deformation of object shapes and cluttering in the scene to improve detection accuracy of these chamfer matching methods we propose local part oriented chamfer matching lpocm and local part directional chamfer matching lpdcm first shape templates and discriminative contour fragments are learned and then a shape representation is built using a markov random field mrf finally the template detection in an input image is formulated as an inference in the mrf experimental results for benchmark datasets including ethz shape classes inria horses and weizmann horses clearly demonstrate that the proposed lpocm and lpdcm significantly improve the detection accuracy of ocm and dcm without sacrificing much time efficiency highlightswe proposed two novel deformable chamfer matching methods based on orientation chamfer matching ocm and directional chamfer matching dcm respectively docm and ddcm can be implemeted easily and have great values on practice

weak lower semicontinuity of polyconvex integrals multiple integrals with polyconvex integrands are studied on the class of all sense preserving diffeomorphisms from w 1 p r n where is an open subset of r n they are proved to be sequentially weakly lower semicontinuous if 1 p n 1 an example is presented showing that a similar result is not valid if p n 1

regularity for double phase variational problems we prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases according to the zero set of a modulating coefficient a cdot the model case is given by the functional w mapsto int dw p a x dw q rm d x where q p and a cdot geqq 0

regularity of relaxed minimizers of quasiconvex variational integrals with p q growth we consider autonomous integrals f u int omega f du rm d x quad rm for u mathbb r n supset omega to mathbb r n in the multidimensional calculus of variations where the integrand f is a strictly quasiconvex c2 function satisfying the p q growth conditions gamma a p leqq f a leqq gamma 1 a q quad rm for every a in mathbb r nn with exponents 1 p leqq q infty

bag of contour fragments for robust shape classification shape representation is a fundamental problem in computer vision current approaches to shape representation mainly focus on designing low level shape descriptors which are robust to rotation scaling and deformation of shapes in this paper we focus on mid level modeling of shape representation we develop a new shape representation called bag of contour fragments bcf inspired by classical bag of words bow model in bcf a shape is decomposed into contour fragments each of which is then individually described using a shape descriptor e g the shape context descriptor and encoded into a shape code finally a compact shape representation is built by pooling shape codes in the shape shape classification with bcf only requires an efficient linear svm classifier in our experiments we fully study the characteristics of bcf show that bcf achieves the state of the art performance on several well known shape benchmarks and can be applied to real image classification problem highlightsa new shape representation is proposed by encoding contour fragments in shape the proposed shape representation is compact yet informative the proposed shape representation is robust to shape deformation and conclusion we obtain the state of the art shape classification performance on several bench mark datasets

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

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

w1 p quasiconvexity and variational problems for multiple integrals abstract variational problems for the multiple integral i u g u x dx where r m and u r n are studied a new condition on g called w1 p quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of c b morrey it being shown in particular to be necessary for sequential weak lower semicontinuity of i in w 1 p r n and for the existence of minimizers for certain related integrals counterexamples are given concerning the weak continuity properties of jacobians in w 1 p r n p n m an existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses

landmarks inside the shape in the last few decades significant advances in image matching are provided by rich local descriptors that are defined through physical measurements such as reflectance as such measurements are not naturally available for silhouettes existing arsenal of image matching tools cannot be utilized in shape matching we propose that the recently presented spem representation can be used analogous to image intensities to detect local keypoints using invariant image salient point detectors we devise a shape similarity measure based on the number of matching internal regions the performance of the similarity measure in planar shape retrieval indicates that the landmarks inside the shape silhouettes provide a strong representation of the regional characteristics of 2d planar shapes graphical abstractdisplay omitted highlightsan internal landmark based planar shape matching scheme is proposed the shape landmarks are obtained using the recently proposed spem representation properties of spem that allow the use of image descriptors inside shapes are discussed statistical evidence indicates that the number of matches can be used as a similarity measure

characterising shape patterns using features derived from best fitting ellipsoids abstract a method is developed to characterise highly irregular shape patterns especially those appearing in biomedical settings a collection of best fitting ellipsoids is found using principal component analysis and features are defined based on these ellipsoids in four different ways the method is defined in a general setting but is illustrated using two dimensional images of dimorphic yeast exhibiting pseudohyphal growth three dimensional images of cancellous bone and three dimensional images of marbling in beef classifiers successfully distinguish between the yeast colonies with a mean classification accuracy of 0 843 sd 0 021 and between cancellous bone from rats in different experimental groups with a mean classification accuracy of 0 745 sd 0 024 a strong correlation r 2 0 797 is found between marbling ratio and a shape feature key aspects of the method are that local shape patterns including orientation are learned automatically from the data and the method applies to objects that are irregular in shape to the point where landmark points cannot be identified between samples

lower semicontinuity of certain quasiconvex functionals in orlicz sobolev spaces abstract let u r n r n be any vector valued function we prove a semicontinuity result in the weak topology of orlicz sobolev spaces of the functional f u f d u x d x where f is a quasiconvex function satisfying non standard growth conditions

lower semi continuity for non coercive polyconvex integrals in the limit case lower semi continuity results for polyconvex functionals of the calculus of variations along sequences of maps u n m in w 1 m 2 m n weakly converging in w 1 m 1 are established in addition for m n 1 we also consider the autonomous case for weakly converging maps in w 1 n 1

on the relaxation in bv ω rm of quasi convex integrals abstract given a quasi convex function f with linear growth we find the integral representation in bv r m of the functional f arising from the relaxation of f u f u dx u c 1 r m in the l loc 1 r m topology

unsupervised shape discovery using synchronized spectral networks a new unsupervised shape discovery method using a novel joint foreground background segmentation and a dense part part correspondence between all image pairs a new multiscale spectral synchronization method which jointly align the spectral representations of all input images a novel unsupervised superpixel based groupwise co registration which converts the implicit eigenvector eigenvector synchronization to superpixel superpixel dense correspondences unsupervised discovery and extraction of common shapes from unlabeled images is a fundamental problem in object recognition and has broad applications in practice however shape discovery suffers from the lack of consistent matching methods for finding the correspondences between objects with different colors textures among the input images in this paper we propose a novel unsupervised shape discovery method using synchronized spectral network ssn which provides automatic part part correspondences across images the ssn is spectral graph based model that encodes the pixel self similarities of different images in spectral bases and synchronizes the bases between images to achieve the part part correspondences unlike explicit feature matching correspondences obtained by spectral synchronization are independent of colors textures and image modalities an image network can then be built by spectral correspondences where the common shapes among them can be easily identified and segmented our results in multiple shape discovery datasets demonstrate that we outperform the state of the art object shape discovery methods providing better segmentations for common shapes

rank one convexity does not imply quasiconvexity we consider variational integrals defined for sufficiently regular functions u r m here is a bounded open subset of r n du x denotes the gradient matrix of u at x and f is a continuous function on the space of all real m n matrices m m n one of the important problems in the calculus of variations is to characterise the functions f for which the integral i is lower semicontinuous in this connection the following notions were introduced see 3 9 10

an iterative polynomial chaos approach for solution of structural mechanics problem with gaussian material property abstract a new approach for solution of stochastic structural mechanics problem with random coefficient in the framework of polynomial chaos pc expansion is proposed the basic strategy of the proposed method is to iteratively construct a pc expansion with reduced numbers of unknown coefficients the method is based on orthogonal expansion of stochastic responses and generation of an iterative pc based on the responses of the previous iteration the polynomials are evaluated using gram schmidt orthogonalization process the number of random variables in pc expansion is reduced by considering only the dominant components of the response characteristics which is evaluated using karhunen loeve kl expansion in case of random material field problem kl expansion is used to discretize the random field the usefulness of the proposed method in terms of accuracy and computational efficiency is examined the results of linear static structural mechanics problems are compared with mcs and pc method the proposed method is observed to be computationally more efficient and accurate than pc method

parameter free modelling of 2d shapes with ellipses our goal is to represent a given 2d shape with an automatically determined number of ellipses so that the total area covered by the ellipses is equal to the area of the original shape without any assumption or prior knowledge about the object structure to solve this interesting theoretical problem first we employ the skeleton of the 2d shape which provides important information on the parameters of the ellipses that could approximate the original shape for a given number of such ellipses the hard expectation maximisation em algorithm is employed to maximise the shape coverage under the equal area constraint different models i e solutions involving different numbers of ellipses are evaluated based on the akaike information criterion aic this considers a novel entropy based shape complexity measure that balances the model complexity and the model approximation error in order to minimise the aic criterion two variants are proposed and evaluated a the augmentative method that gradually increases the number of considered ellipses starting from a single one and b the decremental method that decreases the number of ellipses starting from a large automatically defined set the obtained quantitative results on more than 4000 2d shapes included in standard as well as in custom datasets quantify the performance of the proposed methods and illustrate that their solutions agree with human intuition highlights2d shape representation with an automatically determined number of ellipses we propose a novel definition of shape complexity that exploits the shape skeleton good balance between model complexity and shape coverage experiments on more than 4000 2d shapes show the effectiveness of the proposed methods the solutions proposed by aefa and defa seem to agree with human intuition

perceptually motivated shape context which uses shape interiors in this paper we identify some of the limitations of current day shape matching techniques we provide examples of how contour based shape matching techniques cannot provide a good match for certain visually similar shapes to overcome this limitation we propose a perceptually motivated variant of the well known shape context descriptor we identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties we show that our method can easily be augmented with any other shape matching algorithm we also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

relaxation of quasiconvex functional in bv ω ℝp for integrands f x u u in this paper it is shown that if p x u is a quasiconvex function with linear growth then the relaxed functional in bv p of u to int limits omega f x u x nabla u x dx with respect to the l1 topology has an integral representation of the form begin gathered mathfrak f u int limits omega f x u x nabla u x dx int limits sigma u k x u x u x v x dh n 1 x hfill int limits omega f infty x u x dc u hfill end gathered where du u dx u u v dhn 1l u c u the proof relies on a blow up argument introduced by fonseca muller in the case where u w1 1 and on a recent result by alberti showing that the cantor part c u is rank one valued