on critical point detection of digital shapes in this paper we present a nonlinear algorithm for critical point detection cpd of 2d digital shapes the algorithm eliminates the problems arising from curvature approximation and gaussian filtering in the existing algorithms based on the definition of critical level we establish a set of criteria for the design of an effective cpd algorithm for the first time by quantifying the critical level to the modified area confined by three consecutive pseudocritical points a simple but very effective algorithm is developed the comparison of our experimental results with those of many other cpd algorithms shows that the proposed algorithm is superior in that it provides a sequence of figures at every detail level and each has a smaller integral error than the others with the same number of critical points the experimental results on shapes with various complexities also show the algorithm is reliable and robust with regard to noise

a curve bend function based method to characterize contour shapes in this paper a new curve bend function cbf based method is presented to extract main features of a contour it utilizes two quantities one called a curve bend angle cba and the other known as a type coefficient of curve segment defined on a contour the cba measures the bending degree at each point on the contour while the type coefficient characterizes the properties convexity and concavity of simple curve segments the cbf combines the advantages of the two quantities and provides an overall description of a contour a local maximum or minimum of the cbf corresponds to a critical point of the contour and the peak value is the cosine of the cba hence the problem of locating critical points of a contour is reduced to the problem of finding peak points of the cbf the sign of a peak value indicates the related cba being an inner or outer angle our experimental results and comparisons between the cbf method and rosenfeld johnston s method show that our method is effective and accurate in generating the description of a contour

active reranking for web image search image search reranking methods usually fail to capture the user s intention when the query term is ambiguous therefore reranking with user interactions or active reranking is highly demanded to effectively improve the search performance the essential problem in active reranking is how to target the user s intention to complete this goal this paper presents a structural information based sample selection strategy to reduce the user s labeling efforts furthermore to localize the user s intention in the visual feature space a novel local global discriminative dimension reduction algorithm is proposed in this algorithm a submanifold is learned by transferring the local geometry and the discriminative information from the labelled images to the whole global image database experiments on both synthetic datasets and a real web image search dataset demonstrate the effectiveness of the proposed active reranking scheme including both the structural information based active sample selection strategy and the local global discriminative dimension reduction algorithm

principal component analysis based on l1 norm maximization a method of principal component analysis pca based on a new l1 norm optimization technique is proposed unlike conventional pca which is based on l2 norm the proposed method is robust to outliers because it utilizes l1 norm which is less sensitive to outliers it is invariant to rotations as well the proposed l1 norm optimization technique is intuitive simple and easy to implement it is also proven to find a locally maximal solution the proposed method is applied to several datasets and the performances are compared with those of other conventional methods

ensemble manifold rank preserving for acceleration based human activity recognition with the rapid development of mobile devices and pervasive computing technologies acceleration based human activity recognition a difficult yet essential problem in mobile apps has received intensive attention recently different acceleration signals for representing different activities or even a same activity have different attributes which causes troubles in normalizing the signals we thus cannot directly compare these signals with each other because they are embedded in a nonmetric space therefore we present a nonmetric scheme that retains discriminative and robust frequency domain information by developing a novel ensemble manifold rank preserving emrp algorithm emrp simultaneously considers three aspects 1 it encodes the local geometry using the ranking order information of intraclass samples distributed on local patches 2 it keeps the discriminative information by maximizing the margin between samples of different classes and 3 it finds the optimal linear combination of the alignment matrices to approximate the intrinsic manifold lied in the data experiments are conducted on the south china university of technology naturalistic 3 d acceleration based activity dataset and the naturalistic mobile devices based human activity dataset to demonstrate the robustness and effectiveness of the new nonmetric scheme for acceleration based human activity recognition

wavelet based corner detection abstract a non parametric algorithm for detecting and locating corners of planar curves is proposed the algorithm is based on the multiscale wavelet transform of the orientation of the curve which can effectively utilize both the information of local extrema positions and magnitudes of the transform results the corner candidates can then be selected easily based on this information according to the angle preserving concept intrinsic ratios of several corner models have been derived and used to evaluate the corner candidates the corner angles can also be obtained during these processes to make the evaluation process robust a masking algorithm is proposed experiments depict that our detector is more effective than the single scale corner detectors while is more efficient than the multiscale corner detector by rattarangsi and chin proc int conf pattern recognition pp 923 930 1990

online nonnegative matrix factorization with robust stochastic approximation nonnegative matrix factorization nmf has become a popular dimension reduction method and has been widely applied to image processing and pattern recognition problems however conventional nmf learning methods require the entire dataset to reside in the memory and thus cannot be applied to large scale or streaming datasets in this paper we propose an efficient online rsa nmf algorithm or nmf that learns nmf in an incremental fashion and thus solves this problem in particular or nmf receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation benefitting from the smartly chosen learning rate and averaging technique or nmf converges at the rate of in each update of the bases furthermore we prove that or nmf almost surely converges to a local optimal solution by using the quasi martingale by using a buffering strategy we keep both the time and space complexities of one step of the or nmf constant and make or nmf suitable for large scale or streaming datasets preliminary experimental results on real world datasets show that or nmf outperforms the existing online nmf onmf algorithms in terms of efficiency experimental results of face recognition and image annotation on public datasets confirm the effectiveness of or nmf compared with the existing onmf algorithms

breakpoint detection using covariance propagation presents a statistical approach for detecting breakpoints from chain encoded digital arcs an arc point is declared as a breakpoint if the estimated orientations of the two fitted lines of the two arc segments immediately to the right and left of the arc point are significantly statistically different the major contributions of this research include developing a method for analytically estimating the covariance matrix of the fitted line parameters and proposing a perturbation model to characterize the perturbation associated with each arc point

semi supervised dimension reduction using trace ratio criterion in this brief we address the trace ratio tr problem for semi supervised dimension reduction we first reformulate the objective function of the recent work semi supervised discriminant analysis sda in a tr form we also observe that in sda the low dimensional data representation f is constrained to be in the linear subspace spanned by the training data matrix x i e f xt w in order to relax this hard constraint we introduce a flexible regularizer f xt w 2 which models the regression residual into the reformulated objective function with such relaxation our method referred to as tr based flexible sda tr fsda can better cope with data sampled from a certain type of nonlinear manifold that is somewhat close to a linear subspace in order to address the non trivial optimization problem in tr fsda we further develop an iterative algorithm to simultaneously solve for the low dimensional data representation f and the projection matrix w moreover we theoretically prove that our iterative algorithm converges to the optimum based on the newton raphson method the experiments on two face databases one shape image database and one webpage database demonstrate that tr fsda outperforms the existing semi supervised dimension reduction methods

asymptotics of greedy energy points for a symmetric kernel k x x x u on a locally compact metric space x we investigate the asymptotic behavior of greedy k energy points a i 1 for a compact subset a c x that are defined inductively by selecting a 1 a arbitrarily and a n 1 so that n i 1 k a n l1 a i inf x a n i 1 k x a i we give sufficient conditions under which these points also known as leja points are asymptotically energy minimizing i e have energy n i j k a i aj as n that is asymptotically the same as e a n min i j k x i x j x 1 x n a and have asymptotic distribution equal to the equilibrium measure for a for the case of riesz kernels k s x y x y s s 0 we show that if a is a rectifiable jordan arc or closed curve in rp and s 1 then greedy k s energy points are not asymptotically energy minimizing in contrast to the case s 1 additional results are obtained for greedy k s energy points on a sphere for greedy best packing points the case s and for weighted riesz kernels for greedy best packing points we provide a simple counterexample to a conjecture attributed to l bos

segmentation of two dimensional curve contours abstract segmentation of digitized planar curves is one of the most important elements in early image processing because a segmented image can describe the object profile in a compact form to facilitate higher level vision processing in many applications it is necessary to decompose an object boundary contour into several primitives such as segments and curves in this paper a two stage hybrid technique for the segmentation of two dimensional 2d curves is presented in which the number of segments is assumed to be known first the boundary is iteratively approximated using a split and merge method next an end point adjustment procedure is applied to reach the best fitting polygonal approximation a computational comparison with two existing methods shows that the proposed technique is fast and accurate an application of the new segmentation technique to industrial part inspection is also provided

learning a probabilistic topology discovering model for scene categorization a recent advance in scene categorization prefers a topological based modeling to capture the existence and relationships among different scene components to that effect local features are typically used to handle photographing variances such as occlusions and clutters however in many cases the local features alone cannot well capture the scene semantics since they are extracted from tiny regions e g 4 times 4 patches within an image in this paper we mine a discriminative topology and a low redundant topology from the local descriptors under a probabilistic perspective which are further integrated into a boosting framework for scene categorization in particular by decomposing a scene image into basic components a graphlet model is used to describe their spatial interactions accordingly scene categorization is formulated as an intergraphlet matching problem the above procedure is further accelerated by introducing a probabilistic based representative topology selection scheme that makes the pairwise graphlet comparison trackable despite their exponentially increasing volumes the selected graphlets are highly discriminative and independent characterizing the topological characteristics of scene images a weak learner is subsequently trained for each topology which are boosted together to jointly describe the scene image in our experiment the visualized graphlets demonstrate that the mined topological patterns are representative to scene categories and our proposed method beats state of the art models on five popular scene data sets

asymptotics for minimal discrete energy on the sphere we investigate the energy of arrangements of n points on the surface of the unit sphere sd in rd 1 that interact through a power law potential v 1 rs where s 0 and r is euclidean distance with ed s n denoting the minimal energy for such n point arrangements we obtain bounds valid for all n for ed s n in the cases when 0 s d and 2 d s for s d we determine the precise asymptotic behavior of ed d n as n as a corollary lower bounds are given for the separation of any pair of points in an n point minimal energy configuration when s d 2 for the unit sphere in r3 d 2 we present two conjectures concerning the asymptotic expansion of e2 s n that relate to the zeta function l s for a hexagonal lattice in the plane we prove an asymptotic upper bound that supports the first of these conjectures of related interest we derive an asymptotic formula for the partial sums of l s when 0 s 2 the divergent case

non parametric dominant point detection abstract a new method for detecting dominant points is presented it does not require any input parameter and the dominant points obtained by this method remain relatively the same even when the object curve is scaled or rotated in this method for each boundary point a support region is assigned to the point based on its local properties each point is then smoothed by a gaussian filter with a width proportional to its determined support region a significance measure for each point is then computed dominant points are finally obtained through nonmaximum suppression unlike other dominant point detection algorithms which are sensitive to scaling and rotation of the object curve the new method will overcome this difficulty furthermore it is robust in the presence of noise the proposed new method is compared to the teh chin algorithm see c teh and r t chin ieee trans pattern anal mach intell 11 859 872 1989 in terms of the computational complexity the approximation errors and the number of detected dominant points of an object curve

ranking graph embedding for learning to rerank dimensionality reduction is a key step to improving the generalization ability of reranking in image search however existing dimensionality reduction methods are typically designed for classification clustering and visualization rather than for the task of learning to rank without using of ranking information such as relevance degree labels direct utilization of conventional dimensionality reduction methods in ranking tasks generally cannot achieve the best performance in this paper we show that introducing ranking information into dimensionality reduction significantly increases the performance of image search reranking the proposed method transforms graph embedding a general framework of dimensionality reduction into ranking graph embedding range by modeling the global structure and the local relationships in and between different relevance degree sets respectively the proposed method also defines three types of edge weight assignment between two nodes binary reconstruction and global in addition a novel principal components analysis based similarity calculation method is presented in the stage of global graph construction extensive experimental results on the msra mm database demonstrate the effectiveness and superiority of the proposed range method and the image search reranking framework

reduced resolution and scale space for dominant feature detection in contours abstract analysis of contours or curves at various scales or levels of smoothing scale space is an important tool in curve segmentation and feature detection in this paper we propose the application of the hierarchical discrete correlation algorithm for efficiently calculating and creating a scale space of curves in conjunction with this procedure we also investigate the use of the reduced resolution or gaussian pyramid representation of the set of smoothed curves as the basis for initially localizing and detecting features we also create an approximation to the above algorithms that is computationally less expensive finally we propose a new inter scale method for curve segmentation and feature detection based on the motion of a curve through scale space

asymptotics for discrete weighted minimal riesz energy problems on rectifiable sets given a closed d rectifiable set a embedded in euclidean space we investigate minimal weighted riesz energy points on a that is n points constrained to a and interacting via the weighted power law potential v w x y x y s where s 0 is a fixed parameter and w is an admissible weight in the unweighted case w 1 such points for n fixed tend to the solution of the best packing problem on a as the parameter s our main results concern the asymptotic behavior as n of the minimal energies as well as the corresponding equilibrium configurations given a distribution x with respect to d dimensional hausdorff measure on a our results provide a method for generating n point configurations on a that are well separated and have asymptotic distribution p x as n

boundary simplification using a multiscale dominant point detection algorithm abstract in this paper we intend to characterize boundaries using the scale space theory the aim we try to achieve is the description of a boundary in relation to a subset of points dominant points that are obtained from a new multiscale representation of the boundary dominant points are characterized by a high curvature value in the original or smoothed boundary as a result the boundary is represented using those points as well as an appropriate interpolation method the linear one in the simplest case among them as the basic tool of our work we will introduce a new multiscale dominant point detection algorithm that detects the points at their natural scales through a reliability condition with respect to the original curve because we want to apply the algorithms on complex enough boundaries we use cartographic boundaries in which several structures can be obtained at different scales to evaluate the results

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

a sequence of discrete minimal energy configurations that does not converge in the weak star topology abstract we demonstrate a set a and a value of s for which any sequence of n point discrete minimal riesz s energy configurations on a does not have an asymptotic distribution in the weak star sense as n tends to infinity

scale based detection of corners of planar curves a technique for detecting and localizing corners of planar curves is proposed the technique is based on gaussian scale space which consists of the maxima of absolute curvature of the boundary function presented at all scales the scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners the analysis shows that the resulting scale space contains line patterns that either persist terminate or merge with a neighboring line next the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales finally a multiple scale corner detection scheme is developed using a coarse to fine tree parsing technique the parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales experiments were performed to show that the scale space corner detector is reliable for objects with multiple size features and noisy boundaries and compares favorably with other corner detectors tested

performance comparisons of contour based corner detectors corner detectors have many applications in computer vision and image identification and retrieval contour based corner detectors directly or indirectly estimate a significance measure e g curvature on the points of a planar curve and select the curvature extrema points as corners while an extensive number of contour based corner detectors have been proposed over the last four decades there is no comparative study of recently proposed detectors this paper is an attempt to fill this gap the general framework of contour based corner detection is presented and two major issues curve smoothing and curvature estimation which have major impacts on the corner detection performance are discussed a number of promising detectors are compared using both automatic and manual evaluation systems on two large datasets it is observed that while the detectors using indirect curvature estimation techniques are more robust the detectors using direct curvature estimation techniques are faster

minimal riesz energy point configurations for rectifiable d dimensional manifolds we investigate the energy of arrangements of n points on a rectifiable d dimensional manifold a r d 0 that interact through the power law riesz potential v 1 r s where s 0 and r is euclidean distance in r d 0 with es a n denoting the minimal energy for such n point configurations we determine the asymptotic behavior as n 1 of es a n for each fixed s d moreover if a has positive d dimensional hausdor measure we show that n point configurations on a that minimize the s energy are asymptotically uniformly distributed with respect to d dimensional hausdor measure on a when s d even for the unit sphere s d r d 1 these results are new

nenmf an optimal gradient method for nonnegative matrix factorization nonnegative matrix factorization nmf is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low rank nonnegative matrix factors it has been widely applied to signal processing computer vision and data mining traditional nmf solvers include the multiplicative update rule mur the projected gradient method pg the projected nonnegative least squares pnls and the active set method as however they suffer from one or some of the following three problems slow convergence rate numerical instability and nonconvergence in this paper we present a new efficient nenmf solver to simultaneously overcome the aforementioned problems it applies nesterov s optimal gradient method to alternatively optimize one factor with another fixed in particular at each iteration round the matrix factor is updated by using the pg method performed on a smartly chosen search point where the step size is determined by the lipschitz constant since nenmf does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor it is superior to mur and pg in terms of efficiency as well as approximation accuracy compared to pnls and as that suffer from numerical instability problem in the worst case nenmf overcomes this deficiency in addition nenmf can be used to solve norm norm and manifold regularized nmf with the optimal convergence rate numerical experiments on both synthetic and real world datasets show the efficiency of nenmf for nmf and its variants comparing to representative nmf solvers extensive experiments on document clustering suggest the effectiveness of nenmf

periodic discrete energy for long range potentials we consider periodic energy problems in euclidean space with a special emphasis on long range potentials that cannot be defined through the usual infinite sum one of our main results builds on more recent developments of ewald summation to define the periodic energy corresponding to a large class of long range potentials two particularly interesting examples are the logarithmic potential and the riesz potential when the riesz parameter is smaller than the dimension of the space for these examples we use analytic continuation methods to provide concise formulas for the periodic kernel in terms of the epstein hurwitz zeta function we apply our energy definition to deduce several properties of the minimal energy including the asymptotic order of growth and the distribution of points in energy minimizing configurations as the number of points becomes large we conclude with some detailed calculations in the case of one dimension which shows the utility of this approach

curve segmentation under partial occlusion 2 d shape boundary segmentation is required as a fundamental and important stage in the recognition of partially occluded objects we introduce here a new segmentation method capable of extracting a controlled number of segments along a smooth boundary curve this new approach is invariant to similarity transformation and partial occlusion has only marginal influence on the segmentation of the visible part the basic concept is to transform the curve into another one which intersects itself points of intersection of the new curve are re transformed to the original curve and serve as endpoints of segments properties of the transform are discussed and conditions for existence of intersection points are given simulation results of gray level images are presented and advantages of our method over conventional approaches relying on singular points of the curvature are discussed

maximal linear embedding for dimensionality reduction over the past few decades dimensionality reduction has been widely exploited in computer vision and pattern analysis this paper proposes a simple but effective nonlinear dimensionality reduction algorithm named maximal linear embedding mle mle learns a parametric mapping to recover a single global low dimensional coordinate space and yields an isometric embedding for the manifold inspired by geometric intuition we introduce a reasonable definition of locally linear patch maximal linear patch mlp which seeks to maximize the local neighborhood in which linearity holds the input data are first decomposed into a collection of local linear models each depicting an mlp these local models are then aligned into a global coordinate space which is achieved by applying mds to some randomly selected landmarks the proposed alignment method called landmarks based global alignment lga can efficiently produce a closed form solution with no risk of local optima it just involves some small scale eigenvalue problems while most previous aligning techniques employ time consuming iterative optimization compared with traditional methods such as isomap and lle our mle yields an explicit modeling of the intrinsic variation modes of the observation data extensive experiments on both synthetic and real data indicate the effectivity and efficiency of the proposed algorithm

representing curves at their natural scales abstract the shapes of curves generally contain several structures at different scales an expressive curve representation should explicitly describe each structure at its appropriate scale this greatly simplifies any reasoning processes e g matching applied to the curve rather than exhaustively represent the curve over a full range of scales just the most significant ones should be retained for a compact and useful representation a technique is presented that identifies the significant or natural scales in a curve

corner point detection using nest moving average abstract corners are rich in high frequency components a low pass filter suppresses corners and results in a smooth curve therefore corner points have a larger amount of shift than other points and can easily be detected by a low pass filter experiments suggest that a moving average can do this job suitably with a low computational load and good locality in spatial domain a moving average with a smaller size window is used to perprocess the digital boundary with quantization error or noise

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

relevance preserving projection and ranking for web image search reranking an image search reranking isr technique aims at refining text based search results by mining images visual content feature extraction and ranking function design are two key steps in isr inspired by the idea of hypersphere in one class classification this paper proposes a feature extraction algorithm named hypersphere based relevance preserving projection hrpp and a ranking function called hypersphere based rank h rank specifically an hrpp is a spectral embedding algorithm to transform an original high dimensional feature space into an intrinsically low dimensional hypersphere space by preserving the manifold structure and a relevance relationship among the images an h rank is a simple but effective ranking algorithm to sort the images by their distances to the hypersphere center moreover to capture the user s intent with minimum human interaction a reversed k nearest neighbor knn algorithm is proposed which harvests enough pseudorelevant images by requiring that the user gives only one click on the initially searched images the hrpp method with reversed knn is named one click based hrpp oc hrpp finally an oc hrpp algorithm and the h rank algorithm form a new isr method h reranking extensive experimental results on three large real world data sets show that the proposed algorithms are effective moreover the fact that only one relevant image is required to be labeled makes it has a strong practical significance

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

manifold regularized cross modal embedding for zero shot learning zero shot learning zsl aims at classifying previously unseen class samples and has gained its popularity in applications where samples of some categories are scarce for training the basic idea to address this issue is transferring knowledge from the seen classes to the unseen classes through mapping the visual feature to an embedding space spanned by class semantic information the class semantic information can be obtained from human labeled attributes or text corpus in an unsupervised fashion therefore the embedding function from visual space to the embedding space is extremely important however the existing embedding approaches to zsl mainly focus on aligning pairwise semantic consistency from heterogeneous spaces but ignore the intrinsic structure of the locally homogeneous isomorph in order to preserve the locally visual structure in the embedding process this paper proposes a manifold regularized cross modal embedding mcme approach for zsl by formulating the manifold constraint for intrinsic structure of the visual features as well as aligning pairwise consistency the linear closed form solution makes mcme efficient to compute furthermore rather than applying the embedding function learned from the seen classes directly we also propose a new domain adaptation strategy to overcome the domain shift problem during the knowledge transfer process the mcme with the domain adaptation method is called mcme da extensive experiments on the benchmark datasets of awa and cub validate the superiority and promise of mcme and mcme da

on the convergence of planar curves under smoothing curve smoothing has two important applications in computer vision and image processing 1 the curvature scale space css technique for shape analysis and 2 the gaussian filter for noise suppression in this paper we study how planar curves converge as they are smoothed with increasing scales first two types of convergence behavior are clarified the coined term shrinkage refers to the reduction of arc length of a smoothed planar curve which describes the convergence of the curve latitudinally and another coined term collapse refers to the movement of each point to its limiting position which describes the convergence of the curve longitudinally a systematic study on the shrinkage and collapse of three categories of curve models is then presented the corner models helps to reveal how the local structures of planar curves collapse and what the smoothed curves may converge to the sawtooth models allows us to gain insights regarding how noise is suppressed from noisy planar curves by the gaussian filter our investigation on the closed curves shows that each curve collapses to a point at its center of mass however different curves may yield different limiting shapes at the infinity scale finally based upon the derived results the performance of the css technique in corner detection and shape representation is analyzed and a fast implementation method of the gaussian filter for noise suppression is proposed

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

reliable polygonal approximations of imaged real objects through dominant point detection abstract the problem of dominant point detection is posed taking into account what usually happens in practice the algorithms found in the literature often prove their performance with laboratory contours but the shapes in real images present noise quantization and high inter and intra shape variability these effects are analyzed and solutions to them are proposed we will also focus on the conditions for an efficient few points and precise low error dominant point extraction that preserves the original shape a measurement of the committed error optimization error e 0 that takes into account both aspects is defined for studying this feature

polygonal representation of digital planar curves through dominant point detection a nonparametric algorithm we describe a new algorithm that detects a set of feature points on the boundary of an 8 connected shape that constitute the vertices of a polygonal approximation of the shape itself the set of feature points nodes is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape nodes are ranked based on their strength in terms of their importance to other boundary points length of support region and distance from the centroid the polygon obtained by linking the detected nodes approximates the contour in an intuitive way the proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes

curvature and tangential deflection of discrete arcs a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data this paper introduces a new theory for the tangential deflection and curvature of plane discrete curves our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats its rationale is drawn from the statistical and geometric properties associated with the eigenvalue eigenvector structure of sample covariance matrices specifically we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces and further we show that this entry is in certain limiting cases also proportional to the analytical curvature of the plane curve from which the discrete data are drawn these results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection and moreover they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts as a concrete example we develop the commutator vertex detection cvd algorithm which identifies the location of vertices in shape data based on excessive cummulative tangential deflection and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding approximate curvature extrema

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

learning visual models from shape contours using multiscale convex concave structure matching a novel approach is proposed for learning a visual model from real shape samples of the same class the approach can directly acquire a visual model by generalizing the multiscale convex concave structure of a class of shapes that is the approach is based on the concept that shape generalization is shape simplification wherein perceptually relevant features are retained the simplification does not mean the approximation of shapes but rather the extraction of the optimum scale convex concave structure common to shape samples of the class the common structure is obtained by applying the multiscale convex concave structure matching method to all shape pairs among given shape samples of the class and by integrating the matching results the matching method is applicable to heavily deformed shapes and is effectively implemented with dynamic programming techniques the approach can acquire a visual model from a few samples without any a priori knowledge of the class the obtained model is very useful for shape recognition results of applying the proposed method are presented

web image search re ranking with click based similarity and typicality in image search re ranking besides the well known semantic gap intent gap which is the gap between the representation of users query demand and the real intent of the users is becoming a major problem restricting the development of image retrieval to reduce human effects in this paper we use image click through data which can be viewed as the implicit feedback from users to help overcome the intention gap and further improve the image search performance generally the hypothesis visually similar images should be close in a ranking list and the strategy images with higher relevance should be ranked higher than others are widely accepted to obtain satisfying search results thus image similarity and the level of relevance typicality are determinate factors correspondingly however when measuring image similarity and typicality conventional re ranking approaches only consider visual information and initial ranks of images while overlooking the influence of click through data this paper presents a novel re ranking approach named spectral clustering re ranking with click based similarity and typicality first to learn an appropriate similarity measurement we propose click based multi feature similarity learning algorithm which conducts metric learning based on click based triplets selection and integrates multiple features into a unified similarity space via multiple kernel learning then based on the learnt click based image similarity measure we conduct spectral clustering to group visually and semantically similar images into same clusters and get the final re rank list by calculating click based clusters typicality and within clusters click based image typicality in descending order our experiments conducted on two real world query image data sets with diverse representative queries show that our proposed re ranking approach can significantly improve initial search results and outperform several existing re ranking approaches

estimating the number of stable configurations for the generalized thomson problem given a natural number n one may ask what configuration of n points on the two sphere minimizes the discrete generalized coulomb energy if one applies a gradient based numerical optimization to this problem one encounters many configurations that are stable but not globally minimal this led the authors of this manuscript to the question how many stable configurations are there in this manuscript we report methods for identifying and counting observed stable configurations and estimating the actual number of stable configurations these estimates indicate that for n approaching two hundred there are at least tens of thousands of stable configurations

multimodal graph based reranking for web image search this paper introduces a web image search reranking approach that explores multiple modalities in a graph based learning scheme different from the conventional methods that usually adopt a single modality or integrate multiple modalities into a long feature vector our approach can effectively integrate the learning of relevance scores weights of modalities and the distance metric and its scaling for each modality into a unified scheme in this way the effects of different modalities can be adaptively modulated and better reranking performance can be achieved we conduct experiments on a large dataset that contains more than 1000 queries and 1 million images to evaluate our approach experimental results demonstrate that the proposed reranking approach is more robust than using each individual modality and it also performs better than many existing methods

cascaded subpatch networks for effective cnns conventional convolutional neural networks use either a linear or a nonlinear filter to extract features from an image patch region of spatial size h times w typically h is small and is equal to w e g h is 5 or 7 generally the size of the filter is equal to the size h times w of the input patch we argue that the representational ability of equal size strategy is not strong enough to overcome the drawback we propose to use subpatch filter whose spatial size h times w is smaller than h times w the proposed subpatch filter consists of two subsequent filters the first one is a linear filter of spatial size h times w and is aimed at extracting features from spatial domain the second one is of spatial size 1 times 1 and is used for strengthening the connection between different input feature channels and for reducing the number of parameters the subpatch filter convolves with the input patch and the resulting network is called a subpatch network taking the output of one subpatch network as input we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain these subpatch networks form a new network called the cascaded subpatch network csnet the feature layer generated by csnet is called the csconv layer for the whole input image we construct a deep neural network by stacking a sequence of csconv layers experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed csnet for example our csnet reaches a test error of 5 68 on the cifar10 data set without model averaging to the best of our knowledge this is the best result ever obtained on the cifar10 data set

the detection of dominant points on digital curves by scale space filtering the detection of dominant points is an important preprocessing step for shape recognition an effective method of scale space filtering with a gaussian kernel is introduced to detect dominant points on digital curves the conventional polygonal approximation algorithms are time consuming and need input parameter tuning for gaussian smoothing the noise and quantization error also they are sensitive to scaling and rotation of the object curve the above dit culty can be overcome by finding out the dominant points at each scale by scale space filtering by tracing back the dominant point contours in the scale space image the stable cardinal curvature points can be detected very accurately this new method requires no input parameters and the resultant dominant points do not change under translation rotation and scaling meanwhile a fast convolution algorithm is proposed to detect the dominant points at each scale dominant points scale space gaussian smoothing curvature

corner detection and curve segmentation by multiresolution chain code linking in this paper we propose a new method to characterise a curve by means of the hierarchical computation of a multiresolution structure this structure consisting of successive lower resolution versions of the same object is processed using the linked pyramid approach we adapt the multiresolution pixel linking algorithm to the processing of curve contours which are described by their chain code we also introduce a selective class selection process which allows application of the algorithm to segmentation and detection of contour features the resulting framework presents good performance for a wide range of object sizes without the need of any parameter tweaking and allows detection of shape detail at different scales

non negative patch alignment framework in this paper we present a non negative patch alignment framework npaf to unify popular non negative matrix factorization nmf related dimension reduction algorithms it offers a new viewpoint to better understand the common property of different nmf algorithms although multiplicative update rule mur can solve npaf and is easy to implement it converges slowly thus we propose a fast gradient descent fgd to overcome the aforementioned problem fgd uses the newton method to search the optimal step size and thus converges faster than mur experiments on synthetic and real world datasets confirm the efficiency of fgd compared with mur for optimizing npaf based on npaf we develop non negative discriminative locality alignment ndla experiments on face image and handwritten datasets suggest the effectiveness of ndla in classification tasks and its robustness to image occlusions compared with representative nmf related dimension reduction algorithms

contour shape description based on an arch height function abstract a new method to extract contour features is proposed for any contour c a function which we call arch height function ahf is defined for each point and its value on c is computed the set of ahf values is then used as a description of the shape of c in particular its local maxima if they exist correspond precisely to the cornerpoints of c besides the method is computationally efficient as compared with the existing techniques of the contour feature extraction the new method provides an effective and reliable tool for contour description especially for angle detection some experimental results that demonstrate the adaptability and reliability of the ahf method are presented

toward the optimization of normalized graph laplacian normalized graph laplacian has been widely used in many practical machine learning algorithms e g spectral clustering and semisupervised learning however all of them use the euclidean distance to construct the graph laplacian which does not necessarily reflect the inherent distribution of the data in this brief we propose a method to directly optimize the normalized graph laplacian by using pairwise constraints the learned graph is consistent with equivalence and nonequivalence pairwise relationships and thus it can better represent similarity between samples meanwhile our approach unlike metric learning automatically determines the scale factor during the optimization the learned normalized laplacian matrix can be directly applied in spectral clustering and semisupervised learning algorithms comprehensive experiments demonstrate the effectiveness of the proposed approach

a new algorithm for dominant points detection and polygonization of digital curves a new algorithm for detecting dominant points and polygonal approximation of digitized closed curves is presented it uses an optimal criterion for determining the region of support of each boundary point and a new mechanism for selecting the dominant points the algorithm does not require an input parameter and can handle shapes that contain features of multiple sizes efficiently in addition the approximating polygon preserves the symmetry of the shape

fast high dimensional node generation with variable density abstract we present an algorithm for producing discrete distributions with a prescribed nearest neighbor distance function our approach is a combination of quasi monte carlo q mc methods and weighted riesz energy minimization the initial distribution is a stratified q mc sequence with some modifications a suitable energy functional on the configuration space is then minimized to ensure local regularity the resulting node sets are good candidates for building meshless solvers and interpolants as well as for other purposes where a point cloud with a controlled separation covering ratio is required applications of a three dimensional implementation of the algorithm in particular to atmospheric modeling are also given

quasi monte carlo rules for numerical integration over the unit sphere mathbb s 2 we study numerical integration on the unit sphere mathbb s 2 subseteq mathbb r 3 using equal weight quadrature rules where the weights are such that constant functions are integrated exactly the quadrature points are constructed by lifting a 0 m 2 net given in the unit square 0 1 2 to the sphere mathbb s 2 by means of an area preserving map a similar approach has previously been suggested by cui and freeden siam j sci comput 18 2 595 609 1997 we prove three results the first one is that the construction is almost optimal with respect to discrepancies based on spherical rectangles further we prove that the point set is asymptotically uniformly distributed on mathbb s 2 and finally we prove an upper bound on the spherical cap l 2 discrepancy of order n 1 2 log n 1 2 where n denotes the number of points this improves upon the bound on the spherical cap l 2 discrepancy of the construction by lubotzky phillips and sarnak commun pure appl math 39 s suppl s149 s186 1986 by a factor of sqrt log n numerical results suggest that the 0 m 2 nets lifted to the sphere mathbb s 2 have spherical cap l 2 discrepancy converging with the optimal order of n 3 4