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

segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

unsupervised learning of human action categories using spatial temporal words we present a novel unsupervised learning method for human action categories a video sequence is represented as a collection of spatial temporal words by extracting space time interest points the algorithm automatically learns the probability distributions of the spatial temporal words and the intermediate topics corresponding to human action categories this is achieved by using latent topic models such as the probabilistic latent semantic analysis plsa model and latent dirichlet allocation lda our approach can handle noisy feature points arisen from dynamic background and moving cameras due to the application of the probabilistic models given a novel video sequence the algorithm can categorize and localize the human action s contained in the video we test our algorithm on three challenging datasets the kth human motion dataset the weizmann human action dataset and a recent dataset of figure skating actions our results reflect the promise of such a simple approach in addition our algorithm can recognize and localize multiple actions in long and complex video sequences containing multiple motions

comparison of symbolic and ordinary powers of ideals all given rings in this paper are commutative associative with identity and noetherian recently l ein r lazarsfeld and k smith els discovered a remarkable and surprising fact about the behavior of symbolic powers of ideals in affine regular rings of equal characteristic 0 if h is the largest height of an associated prime of i then i hn i n for all n 0 here if w is the complement of the union of the associated primes of i i t denotes the contraction of i t rw to r where rw is the localization of r at the multiplicative system w their proof depends on the theory of multiplier ideals including an asymptotic version and in particular requires resolution of singularities as well as vanishing theorems we want to acknowledge that without their generosity and quickness in sharing their research this manuscript would not exist our objective here is to give stronger results that can be proved by methods that are in some ways more elementary our results are valid in both equal characteristic 0 and in positive prime characteristic p but depend on reduction to characteristic p we use tight closure methods and in consequence we need neither resolution of singularities nor vanishing theorems that may fail in positive characteristic for the most basic form of the result all that we need from tight closure theory is the definition of tight closure and the fact that in a regular ring every ideal is tightly closed we note that the main argument here is closely related to a proof given in hu 5 14 16 p 45 that regular local rings in characteristic p are ufds

robust object detection with interleaved categorization and segmentation this paper presents a novel method for detecting and localizing objects of a visual category in cluttered real world scenes our approach considers object categorization and figure ground segmentation as two interleaved processes that closely collaborate towards a common goal as shown in our work the tight coupling between those two processes allows them to benefit from each other and improve the combined performance the core part of our approach is a highly flexible learned representation for object shape that can combine the information observed on different training examples in a probabilistic extension of the generalized hough transform the resulting approach can detect categorical objects in novel images and automatically infer a probabilistic segmentation from the recognition result this segmentation is then in turn used to again improve recognition by allowing the system to focus its efforts on object pixels and to discard misleading influences from the background moreover the information from where in the image a hypothesis draws its support is employed in an mdl based hypothesis verification stage to resolve ambiguities between overlapping hypotheses and factor out the effects of partial occlusion an extensive evaluation on several large data sets shows that the proposed system is applicable to a range of different object categories including both rigid and articulated objects in addition its flexible representation allows it to achieve competitive object detection performance already from training sets that are between one and two orders of magnitude smaller than those used in comparable systems

frobenius splitting and cohomology vanishing for schubert varieties let k be an algebraically closed field of characteristic p 0 and x be a projective variety over k we then have the absolute frobenius f x x and an injection ox f 6x given by f fp f e o9x if this makes ox a direct summand in f ox as an x module we call x a frobenius split variety for such a variety the vanishing theorem for ample line bundles follows trivially from serre s vanishing theorem for tensoring ox f ox by an ample line bundle l and noting that l f x f f l f lp projection formula we get that the map in cohomology h x l h x f lp h x lp is an injection iterating this we see that h x l injects into h x lp for every p but for large v the latter is zero thus frobenius split varieties have quite pleasant properties it also turns out that using duality for the frobenius morphism or equivalently the cartier operator one can give a manageable criterion for frobenius splitting the point here is the local nature of duality the relevance of the compatibility of local and global duality was suggested to us by grothendieck s proof of h x y 0 for a noncomplete variety x of dimension n 4 theorem 6 9 and by kempf s paper 10 by this criterion and the bott samelson demazure desingularisation of schubert varieties it follows very easily that schubert varieties in characteristic p are frobenius split the following vanishing theorem is then an immediate consequence let g be a reductive group over the field k of arbitrary characteristic zero or positive let q be a parabolic subgroup and x c g q a schubert variety let l be an ample line bundle on g q then hi x l 0 for i 0 and the restriction map h0 g q l h0 x l is surjective if char k 0 this is a consequence of the compatible frobenius splitting of x in g q and the char k 0 case is handled by semicontinuity the above result for special schubert varieties has been proved by seshadrimusili lakshmibai 12 13 and by kempf 9 by using characteristic free methods for x g q andersen 1 and haboush 5 have given simple proofs using characteristic p methods

the uniform symbolic topology property for diagonally f regular algebras abstract let k be a field of positive characteristic building on the work of the second named author we define a new class of k algebras called diagonally f regular algebras for which the so called uniform symbolic topology property ustp holds effectively we show that this class contains all essentially smooth k algebras we also show that this class contains certain singular algebras such as the affine cone over p k r p k s when k is perfect by reduction to positive characteristic it follows that ustp holds effectively for the affine cone over p c r p c s and more generally for complex varieties of diagonal f regular type

multidimensional morphable models a framework for representing and matching object classes we describe a flexible model for representing images of objects of a certain class known a priori such as faces and introduce a new algorithm for matching it to a novel image and thereby perform image analysis the flexible model known as a multidimensional morphable model is learned from example images of objects of a class in this paper we introduce an effective stochastic gradient descent algorithm that automatically matches a model to a novel image several experiments demonstrate the robustness and the broad range of applicability of morphable models our approach can provide novel solutions to several vision tasks including the computation of image correspondence object verification and image compression

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

uniform bounds and symbolic powers on smooth varieties the purpose of this note is to show how one can use multiplier ideals toestablish effective uniform bounds on the multiplicative behavior of certainfamilies of ideal sheaves on a smooth algebraic variety in particular weprove a quick but rather surprising result concerning the symbolic powersof radical ideals on such a variety let

best constants and minimizers for embeddings of second order sobolev spaces by considering the kernels of the first two traces four different second order sobolev spaces may be constructed for these spaces embeddings into lebesgue spaces the best embedding constant and the possible existence of minimizers are studied the euler equation corresponding to some of these minimization problems is a semilinear biharmonic equation with boundary conditions involving third order derivatives it is shown that the complementing condition is satisfied

f signature of pairs and the asymptotic behavior of frobenius splittings abstract we generalize f signature to pairs r d where d is a cartier subalgebra on r as defined by the first two authors in particular we show the existence and positivity of the f signature for any strongly f regular pair in one application we answer an open question of aberbach and enescu by showing that the f splitting ratio of an arbitrary f pure local ring is strictly positive furthermore we derive effective methods for computing the f signature and the f splitting ratio in the spirit of the work of r fedder

uniform symbolic topologies in normal toric rings abstract given a normal toric algebra r we compute a uniform integer d d r 0 such that the symbolic power p d n p n for all n 0 and all monomial primes p we compute the multiplier d explicitly in terms of the polyhedral cone data defining r illustrating the output for segre veronese algebras

mining layered grammar rules for action recognition we propose a layered grammar model to represent actions using this model an action is represented by a set of grammar rules the bottom layer of an action instance s parse tree contains action primitives such as spatiotemporal st interest points at each layer above we iteratively mine grammar rules and super rules that account for the high order compositional feature structures the grammar rules are categorized into three classes according to three different st relations of their action components namely the strong relation weak relation and stochastic relation these st relations characterize different action styles degree of stiffness and they are pursued in terms of grammar rules for the purpose of action recognition by adopting the emerging pattern ep mining algorithm for relation pursuit the learned production rules are statistically significant and discriminative using the learned rules the parse tree of an action video is constructed by combining a bottom up rule detection step and a top down ambiguous rule pruning step an action instance is recognized based on the discriminative configurations generated by the production rules of its parse tree experiments confirm that by incorporating the high order feature statistics the proposed method largely improves the recognition performance over the bag of words models

globalizing f invariants abstract in this paper we define and study the global hilbert kunz multiplicity and the global f signature of prime characteristic rings which are not necessarily local our techniques are made meaningful by extending many known theorems about hilbert kunz multiplicity and f signature to the non local case

perfectoid multiplier test ideals in regular rings and bounds on symbolic powers using perfectoid algebras we introduce a mixed characteristic analog of the multiplier ideal respectively test ideal from characteristic zero respectively p 0 in the case of a regular ambient ring we prove several properties about this ideal such as subadditivity we then use these techniques to derive a uniform bound on the growth of symbolic powers of radical ideals in all excellent regular rings the analogous result was shown in equal characteristic by ein lazarsfeld smith and hochster huneke

explaining activities as consistent groups of events we propose a method for disambiguating uncertain detections of events by seeking global explanations for activities given a noisy visual input and exploiting our knowledge of the activity and its constraints one can provide a consistent set of events explaining all the detections the paper presents a complete framework that starts with a general way to formalise the set of global explanations for a given activity using attribute multiset grammars amg an amg combines the event hierarchy with the necessary features for recognition and algebraic constraints defining allowable combinations of events and features parsing a set of detections by such a grammar finds a consistent set of events that satisfies the activity s constraints each parse tree has a posterior probability in a bayesian sense to find the best parse tree the grammar and a finite set of detections are mapped into a bayesian network the set of possible labellings of the bayesian network corresponds to the set of all parse trees for a given set of detections we compare greedy multiple hypotheses trees reversible jump mcmc and integer programming for finding the maximum a posteriori map solution over the space of explanations the framework is tested for two applications the activity in a bicycle rack and around a building entrance

linear equivalence of ideal topologies it is proved that whenever p is a prime ideal in a commutative noetherian ring such that the p adic and thep symbolic topologies are equivalent then the two topologies are equivalent linearly several explicit examples are calculated in particular for all prime ideals corresponding to non torsion points on nonsingular elliptic cubic curves

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

on a conjecture of lin ni for a semilinear neumann problem let q be a bounded domain in rn n 3 and a 0 we consider au au u n 2 n 2 in q2 u 0 in q au av 0 on i2 and show that for a sufficiently small the minimal energy solutions are only constants