the quermassintegral inequalities for k convex starshaped domains abstract we give a proof of the isoperimetric inequality for quermassintegrals of non convex starshaped domains using a result of gerhardt c gerhardt flow of nonconvex hypersurfaces into spheres j differential geometry 32 1990 299 314 and urbas j urbas on the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures math z 205 1990 355 372 on an expanding geometric curvature flow

a theory of automatic parameter selection for feature extraction with application to feature based multisensor image registration this paper generalizes the previously developed automated edge detection parameter selection algorithm of yitzhaky and peli we generalize the approach to arbitrary multidimensional continuous or discrete parameter spaces and feature spaces this generalization enables use of the parameter selection approach with more general image features for use in feature based multisensor image registration applications we investigate the problem of selecting a suitable parameter space sampling density in the automated parameter selection algorithm a real valued sensitivity measure is developed which characterizes the effect of parameter space sampling on feature set variability closed form solutions of the sensitivity measure for special feature set relationships are derived we conduct an analysis of the convergence properties of the sensitivity measure as a function of increasing parameter space sampling density for certain parameter space sampling sequence types closed form expressions for the sensitivity measure limit values are presented we discuss an approach to parameter space sampling density selection which uses the sensitivity measure convergence behavior we provide numerical results indicating the utility of the sensitivity measure for selecting suitable parameter values

a model based approach to junction detection using radial energy a novel junction detector is presented that fits the neighborhood around a point to a junction model the junction model segments the neighborhood into wedges by determining a set of radial edges the radial edges are invariant to affine transforms creating an affine invariant junction detector the radial edges are evaluated based upon the pixels along the edge the angle between the pixel gradient and the vector to the potential junction point forms the initial basis for the measurement an initial set of radial edges is selected based upon identifying local maximums within a given arc distance an energy function is applied to the resulting radial segmentation and a greedy optimization routine is used to construct the minimal set of radial edges to identify the final junctions a second energy function is used that combines the components of the first energy function with the resulting change in standard deviation by separation into radial segments the junctions with the most energy in their local neighborhoods are selected as potential junctions the neighborhoods about the potential junctions are analyzed to determine if they represent a single line or multiple non parallel lines if the neighborhood represents multiple non parallel lines the point is classified as a junction point the junction detector is tested on several images including both synthetic and real images highlights of radially segmented junction points are displayed for the real images

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

singular value decomposition via gradient and self equivalent flows the task of finding the singular value decomposition svd of a finite dimensional complex linear operator is here addressed via gradient flows evolving on groups of complex unitary matrices and associated self equivalent flows the work constitutes a generalization of that of brockett on the diagonalization of real symmetric matrices via gradient flows on orthogonal matrices and associated isospectral flows it complements results of symes chu and other authors on continuous analogs of the classical qr algorithm as well as earlier work by the authors on svd via gradient flows on positive definite matrices

a new scheme for robust gradient vector estimation in color images gradient estimators are mostly designed to yield accurate and robust estimates of the gradient magnitude not the gradient direction this paper proposes a method for the accurate and robust estimation of both the gradient magnitude and direction it robustly estimates the gradient in the x and y directions the robustness against noise is achieved by prefiltering and postfiltering of the gradient in each direction to reduce edge blurring effects introduced by these filters the gradient in a certain direction is obtained by applying the prefilter and postfilter in the perpendicular direction the basic elements employed in each window are highpass lowpass and aggregation operators the highpass operator is used as a gradient estimator the lowpass operator is for prefiltering and postfiltering and the aggregation operator is for aggregating the prefiltered and postfiltered gradients four different combinations of highpass lowpass and aggregation operators are proposed mvd median mean mvd median max rcmg median mean and rcmg median max experimental results show that the rcmg median mean has the best performance in estimating the gradient and detecting the edges in noisy color images it is computationally more efficient than the state of the art gradient estimators and is able to accurately estimate the gradient direction as well as the gradient magnitude computer simulation results show that the proposed method outperforms other recently proposed color gradient estimators and edge detectors

model based edge detector for spectral imagery using sparse spatiospectral masks two model based algorithms for edge detection in spectral imagery are developed that specifically target capturing intrinsic features such as isoluminant edges that are characterized by a jump in color but not in intensity given prior knowledge of the classes of reflectance or emittance spectra associated with candidate objects in a scene a small set of spectral band ratios which most profoundly identify the edge between each pair of materials are selected to define a edge signature the bands that form the edge signature are fed into a spatial mask producing a sparse joint spatiospectral nonlinear operator the first algorithm achieves edge detection for every material pair by matching the response of the operator at every pixel with the edge signature for the pair of materials the second algorithm is a classifier enhanced extension of the first algorithm that adaptively accentuates distinctive features before applying the spatiospectral operator both algorithms are extensively verified using spectral imagery from the airborne hyperspectral imager and from a dots in a well midinfrared imager in both cases the multicolor gradient mcg and the hyperspectral spatial detection of edges hyspade edge detectors are used as a benchmark for comparison the results demonstrate that the proposed algorithms outperform the mcg and hyspade edge detectors in accuracy especially when isoluminant edges are present by requiring only a few bands as input to the spatiospectral operator the algorithms enable significant levels of data compression in band selection in the presented examples the required operations per pixel are reduced by a factor of 71 with respect to those required by the mcg edge detector

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

inverse curvature flows in riemannian warped products abstract the long time existence and umbilicity estimates for compact graphical solutions to expanding curvature flows are deduced in riemannian warped products of a real interval with a compact fibre notably we do not assume the ambient manifold to be rotationally symmetric nor the radial curvature to converge nor a lower bound on the ambient sectional curvature the inverse speeds are given by powers 0 p 1 of a curvature function satisfying few common properties

standardization of edge magnitude in color images edge detection is a useful task in low level image processing the efficiency of many image processing and computer vision tasks depends on the perfection of detecting meaningful edges to get a meaningful edge thresholding is almost inevitable in any edge detection algorithm many algorithms reported in the literature adopt ad hoc schemes for this purpose these algorithms require the threshold values to be supplied and tuned by the user there are many high level tasks in computer vision which are to be performed without human intervention thus there is a need to develop a scheme where a single set of threshold values would give acceptable results for many color images in this paper an attempt has been made to devise such an algorithm statistical variability of partial derivatives at each pixel is used to obtain standardized edge magnitude and is thresholded using two threshold values the advantage of standardization is evident from the results obtained

accurate junction detection and characterization in natural images accurate junction detection and characterization are of primary importance for several aspects of scene analysis including depth recovery and motion analysis in this work we introduce a generic junction analysis scheme the first asset of the proposed procedure is an automatic criterion for the detection of junctions permitting to deal with textured parts in which no detection is expected second the method yields a characterization of l y and x junctions including a precise computation of their type localization and scale contrary to classical approaches scale characterization does not rely on the linear scale space first an a contrario approach is used to compute the meaningfulness of a junction this approach relies on a statistical modeling of suitably normalized gray level gradients then exclusion principles between junctions permit their precise characterization we give implementation details for this procedure and evaluate its efficiency through various experiments

judoca junction detection operator based on circumferential anchors in this paper we propose an edge based junction detector in addition to detecting the locations of junctions this operator specifies their orientations as well in this respect a junction is defined as a meeting point of two or more ridges in the gradient domain into which an image can be transformed through gaussian derivative filters to accelerate the detection process two binary edge maps are produced a thick edge map is obtained by imposing a threshold on the gradient magnitude image and another thin edge map is obtained by calculating the local maxima circular masks are centered at putative junctions in the thick edge map and the so called circumferential anchors or ca points are detected in the thin map radial lines are scanned to determine the presence of junctions comparisons are made with other well known detectors this paper proposes a new formula for measuring the detection accuracy in addition the so called junction coordinate systems are introduced our operator has been successfully used to solve many problems such as wide baseline matching 3 d reconstruction camera parameter enhancing and indoor and obstacle localization

an efficient color quantization based on generic roughness measure color quantization is a process to compress image color space while minimizing visual distortion the quantization based on preclustering has low computational complexity but cannot guarantee quantization precision the quantization based on postclustering can produce high quality quantization results however it has to traverse image pixels iteratively and suffers heavy computational burden its computational complexity was not reduced although the revised versions have improved the precision in the work of color quantization balancing quantization quality and quantization complexity is always a challenging point in this paper a two stage quantization framework is proposed to achieve this balance in the first stage high resolution color space is initially compressed to a condensed color space by thresholding roughness indices instead of linear compression we propose generic roughness measure to generate the delicate segmentation of image color in this way it causes less distortion to the image in the second stage the initially compressed colors are further clustered to a palette using weighted rough k means to obtain final quantization results our objective is to design a postclustering quantization strategy at the color space level rather than the pixel level applying the quantization in the precisely compressed color space the computational cost is greatly reduced meanwhile the quantization quality is maintained the substantial experimental results validate the high efficiency of the proposed quantization method which produces high quality color quantization while possessing low computational complexity

multiscale roughness measure for color image segmentation color image segmentation is always an important technique in image processing system highly precise segmentation with low computation complexity can be achieved through roughness measurement which approximate the color histogram based on rough set theory however due to the imprecise description of neighborhood similarity the existing roughness measure tends to over focus on the trivial homogeneous regions but is not accurate enough to measure the color homogeneity this paper aims to construct a multiscale roughness measure through simulating the human vision we apply the theories of linear scale space and rough sets to generate the hierarchical roughness of color distribution under multiple scales this multiscale roughness can tolerate the disturbance of trivial regions and also can provide the multilevel homogeneity representation in vision which therefore produces precise and intuitive segmentation results furthermore we propose roughness entropy for scale selection the optimal scale for segmentation is decided by the entropy variation the proposed method shows the encouraging performance in the experiments based on berkeley segmentation database

on the detection of edges in vector images a novel method for edge detection in vector images is proposed that does not require any prior knowledge of the imaged scenes in the derivation it is assumed that the observed vector images are realizations of spatially quasistationary processes and that the vector observations are generated by parametric probability distribution functions of known form whose parameters are in general unknown the method detects and estimates the edge locations using a criterion derived by bayesian theory it chooses the number of edges and their locations according to the maximum a posteriori probability map principle we provide results that demonstrate its performance on synthesized and real images

a computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

a morphological gradient approach to color edge detection a new color edge detector based on vector differences is proposed the basic technique gives as its output the maximum distance between the vectors within a mask when applied to scalar valued images the method reduces to the classic morphological gradient the technique is relatively computationally efficient and can also be readily applied to other vector valued images to improve the performance in the presence of noise a novel pairwise outlier rejection scheme is employed a quantitative evaluation using pratt s figure of merit shows the new technique to outperform other recently proposed color edge detectors in addition application to real images demonstrates the approach to be highly effective despite its low complexity

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

corner detection and classification using anisotropic directional derivative representations this paper proposes a corner detector and classifier using anisotropic directional derivative andd representations the andd representation at a pixel is a function of the oriented angle and characterizes the local directional grayscale variation around the pixel the proposed corner detector fuses the ideas of the contour and intensity based detection it consists of three cascaded blocks first the edge map of an image is obtained by the canny detector and from which contours are extracted and patched next the andd representation at each pixel on contours is calculated and normalized by its maximal magnitude the area surrounded by the normalized andd representation forms a new corner measure finally the nonmaximum suppression and thresholding are operated on each contour to find corners in terms of the corner measure moreover a corner classifier based on the peak number of the andd representation is given experiments are made to evaluate the proposed detector and classifier the proposed detector is competitive with the two recent state of the art corner detectors the he yung detector and cpda detector in detection capability and attains higher repeatability under affine transforms the proposed classifier can discriminate effectively simple corners y type corners and higher order corners

isoperimetric type problems and alexandrov fenchel type inequalities in the hyperbolic space abstract in this paper we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space h n by using quermassintegral preserving curvature flows as a byproduct we obtain hyperbolic alexandrov fenchel inequalities

color image segmentation advances and prospects abstract image segmentation is very essential and critical to image processing and pattern recognition this survey provides a summary of color image segmentation techniques available now basically color segmentation approaches are based on monochrome segmentation approaches operating in different color spaces therefore we first discuss the major segmentation approaches for segmenting monochrome images histogram thresholding characteristic feature clustering edge detection region based methods fuzzy techniques neural networks etc then review some major color representation methods and their advantages disadvantages finally summarize the color image segmentation techniques using different color representations the usage of color models for image segmentation is also discussed some novel approaches such as fuzzy method and physics based method are investigated as well

separability criteria for the evaluation of boundary detection benchmarks there exist a significant number of benchmarks for evaluating the performance of boundary detection algorithms most of them relying on some sort of comparison of the automatically generated boundaries with human labeled ones such benchmarks are composed of a representative image data set as well as a comparison measure on the universe of boundary images despite many such data sets and measures have been proposed there is no clear way of knowing which combinations of them are the most suitable for the task in this paper we introduce four criteria that allow for a sensible evaluation of the performance of a comparison measure on a given data set the criteria mimic the way in which humans understand boundary images as well as their ability to recognize the underlying scenes these criteria can as a final goal quantify the ability of the boundary detection benchmarks to evaluate the performance of boundary detection methods either edge based or segmentation based

rapid and brief communication color edge detection using the minimal spanning tree in this study the edge detection task in vector valued images is examined as a clustering problem using samples within a data window the minimal spanning tree mst provides the ordering of multivariate observations and facilitates the identification of similar classes the edge detector parameters like edge strength type and orientation are subsequently determined from the clustered data experiments and comparisons are performed revealing the enhanced performance of the proposed approach

an application of lie groups in distributed control networks abstract here we introduce a class of linear operators called recursive orthogonal transforms rots that allow a natural implementation on a distributed control network we derive conditions under which rots can be used to represent so n for n 4 we propose a paradigm for distributed feedback control based on plant matrix diagonalization to find an rot suitable for this task we derive a gradient flow on the appropriate underlying lie group a numerical example is presented

a minkowski inequality for hypersurfaces in the anti de sitter schwarzschild manifold we prove a sharp inequality for hypersurfaces in the n dimensional anti de sitter schwarzschild manifold for general n 3 this inequality generalizes the classical minkowski inequality for surfaces in the three dimensional euclidean space and has a natural interpretation in terms of the penrose inequality for collapsing null shells of dust the proof relies on a new monotonicity formula for inverse mean curvature flow and uses a geometric inequality established by the first author in 3 c 2015 wiley periodicals inc

color edge extraction using orthogonal polynomials based zero crossings scheme abstract a new color edge extraction scheme based on identifying the zero crossings in the second directional derivatives in terms of orthogonal polynomials has been proposed in this paper the proposed scheme supports a complete set of finite difference operators which are easily configured from orthogonal polynomials a color image region in presence of gaussian noise is represented as a linear combination of these operators towards color edges and noise statistical hypothesis testing procedures are employed to separate out the responses towards noise from those towards color edges the usage of the proposed framework is highlighted in devising a color edge detector based on identifying the zero crossings in the second directional derivatives of the color image region the proposed color edge extraction scheme is also compared with two existing color edge extraction schemes

difference based image noise modeling using skellam distribution by the laws of quantum physics pixel intensity does not have a true value but should be a random variable contrary to the conventional assumptions the distribution of intensity may not be an additive gaussian we propose to directly model the intensity difference and show its validity by an experimental comparison to the conventional additive model as a model of the intensity difference we present a skellam distribution derived from the poisson photon noise model this modeling induces a linear relationship between intensity and skellam parameters while conventional variance computation methods do not yield any significant relationship between these parameters under natural illumination the intensity skellam line is invariant to scene illumination and even most of camera parameters we also propose practical methods to obtain the line using a color pattern and an arbitrary image under natural illumination because the skellam parameters that can be obtained from this linearity determine a noise distribution for each intensity value we can statistically determine whether any intensity difference is caused by an underlying signal difference or by noise we demonstrate the effectiveness of this new noise model by applying it to practical applications of background subtraction and edge detection

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

a geometric inequality on hypersurface in hyperbolic space in this paper we use the inverse curvature flow to prove a sharp geometric inequality on star shaped and two convex hypersurface in hyperbolic space

color edge detection using vector order statistics a method is proposed whereby a color image is treated as a vector field and the edge information carried directly by the vectors is exploited a class of color edge detectors is defined as the minimum over the magnitudes of linear combinations of the sorted vector samples from this class a specific edge detector is obtained and its performance characteristics studied results of a quantitative evaluation and comparison to other color edge detectors using pratt s 1991 figure of merit and an artificially generated test image are presented edge detection results obtained for real color images demonstrate the efficiency of the detector

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

harmonic mean curvature flow and geometric inequalities abstract we employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in hyperbolic space to prove alexandrov fenchel type inequalities relating quermassintegrals to the total curvature which is the integral of gaussian curvature on the hypersurface the resulting inequality allows us to use the inverse mean curvature flow to prove alexandrov fenchel inequalities between the total curvature and the area for strictly convex hypersurfaces finally we apply the harmonic mean curvature flow to prove a new class of geometric inequalities for h convex hypersurfaces in hyperbolic space

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

boundary detection using double opponency and spatial sparseness constraint brightness and color are two basic visual features integrated by the human visual system hvs to gain a better understanding of color natural scenes aiming to combine these two cues to maximize the reliability of boundary detection in natural scenes we propose a new framework based on the color opponent mechanisms of a certain type of color sensitive double opponent do cells in the primary visual cortex v1 of hvs this type of do cells has oriented receptive field with both chromatically and spatially opponent structure the proposed framework is a feedforward hierarchical model which has direct counterpart to the color opponent mechanisms involved in from the retina to v1 in addition we employ the spatial sparseness constraint ssc of neural responses to further suppress the unwanted edges of texture elements experimental results show that the do cells we modeled can flexibly capture both the structured chromatic and achromatic boundaries of salient objects in complex scenes when the cone inputs to do cells are unbalanced meanwhile the ssc operator further improves the performance by suppressing redundant texture edges with competitive contour detection accuracy the proposed model has the additional advantage of quite simple implementation with low computational cost

the local structure of image discontinuities in one dimension the detailed structure of intensities in the local neighborhood of an edge can often indicate the nature of the physical event givinig rise to that edge we argue that the limit as we approach arbitrarily close to either side of an edge of such image parameters as type of texture texture gradient color appropriate directional derivatives of intensity etc is a key aspect of this structure however the general problem of capturing this local structure is surprisingly complex thus we restrict ourselves in this paper to a relatively simple domain one dimensional cuts through idealized images modeled by piecewise smooth c1 functions corrupted by gaussian noise within this domain we define local structure to be the limit of the uncorrupted intensity and of its derivatives as we approach arbitrarily close to either side of a discontinuity we develop a technique that captures this local structure while simultaneously locating the discontinuities and demonstrate that these tasks are in fact inseparable the technique is an extension using estimation theory of the classical definition of discontinuity it handles in a consistent fashion both jump discontinuities in the function and jump discontinuities in its first derivative so called step edges are a special case of the former and roof edges of the latter it also integrates again in a consistent fashion information derived from a number of different neighborhood sizes

determining hysteresis thresholds for edge detection by combining the advantages and disadvantages of thresholding methods hysteresis is an important technique for edge detection but the unsupervised determination of its parameters is not an easy problem in this paper we propose a method for unsupervised determination of hysteresis thresholds using the advantages and disadvantages of two thresholding methods the basic idea of our method is to look for the best hysteresis thresholds in a set of candidates first the method finds a subset and a overset of the unknown edge points set then it determines the best edge map with the measure 2 compared with a general method to determine the parameters of an edge detector our method performs well and is less computationally complex the basic idea of our method can be generalized to other pattern recognition problems

a penrose type inequality for graphs over reissner nordstrom anti desitter manifold in this paper we use the inverse mean curvature flow to establish an optimal minkowski type inequality a weighted alexandrov fenchel inequality for the mean convex star shaped hypersurfaces in the reissner nordstrom anti desitter manifold and a penrose type inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over the reissner nordstrom anti desitter manifold

locally constrained curvature flows and geometric inequalities in hyperbolic space in this paper we first study the locally constrained curvature flow of hypersurfaces in hyperbolic space which was introduced by brendle guan and li an inverse curvature type hypersurface flow in mathbb h n 1 preprint this flow preserves the mth quermassintegral and decreases m 1 th quermassintegral so the convergence of the flow yields sharp alexandrov fenchel type inequalities in hyperbolic space some special cases have been studied in brendle et al in the first part of this paper we show that h convexity of the hypersurface is preserved along the flow and then the smooth convergence of the flow for h convex hypersurfaces follows we then apply this result to establish some new sharp geometric inequalities comparing the integral of kth gauss bonnet curvature of a smooth h convex hypersurface to its mth quermassintegral for 0 le m le 2k 1 le n and comparing the weighted integral of kth mean curvature to its mth quermassintegral for 0 le m le k le n in particular we give an affirmative answer to a conjecture proposed by ge wang and wu math z 281 257 297 2015 in the second part of this paper we introduce a new locally constrained curvature flow using the shifted principal curvatures this is natural in the context of h convexity we prove the smooth convergence to a geodesic sphere of the flow for h convex hypersurfaces and provide a new proof of the geometric inequalities proved by andrews chen and the third author of this paper in 2018 we also prove a family of new sharp inequalities involving the weighted integral of kth shifted mean curvature for h convex hypersurfaces which as application implies a higher order analogue of brendle hung and wang s commun pure appl math 69 1 124 144 2016 inequality

stabilization and estimation for perturbed discrete time delay large scale systems based on a derived algebraic inequality a criterion to guarantee the robust stabilization and the state estimation for perturbed discrete time delay large scale systems is proposed this criterion is independent of time delay and does not need the solution of a lyapunov equation or riccati equation furthermore the same problem for the continuous time systems is also solved by a much simpler derivation

applications of vector fields to image processing we use rotational and curvature properties of vector fields to identify critical features of an image using vector analysis and dif ferential geometry we establish the properties needed and then use these properties in three ways first our results make it theoretically possible to identify extremal edges of an intensity function f x y of two variables by considering the gradient vector field v f there is also enough information in f to find regions of high curvature i e high curvature of the level paths of f for color images we use the vector field v i q in application the image is partitioned into a grid of squares on the boundary of each square v v is sampled and these unit vectors are used as the tangents of a curve the rotation number or topological degree and the average curvature f are computed for each square analysis of these numbers yields infor mation on edges and curvature experimental results from both simu lated and real data are described

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

demosaicing of color filter array captured images using gradient edge detection masks and adaptive heterogeneity projection without demosaicing processing this paper first proposes a new approach to extract more accurate gradient edge information on mosaic images directly next based on spectral spatial correlation a novel adaptive heterogeneity projection with proper mask size for each pixel is presented combining the extracted gradient edge information and the adaptive heterogeneity projection values a new edge sensing demosaicing algorithm is presented based on 24 popular testing images experimental results demonstrated that our proposed high quality demosaicing algorithm has the best image quality performance when compared with several recently published algorithms

anti impulse noise edge detection via anisotropic morphological directional derivatives traditional differential based edge detection suffers from abrupt degradation in performance when images are corrupted by impulse noises the morphological operators such as the median filters and weighted median filters possess the intrinsic ability to counteract impulse noise in this paper by combining the biwindow configuration with weighted median filters anisotropic morphological directional derivatives amdds robust to impulse noise are proposed to measure the local grayscale variation around a pixel for ideal step edges the amdd spatial response and directional representation are derived the characteristics and edge resolution of two kinds of typical biwindows are analyzed thoroughly in terms of the amdd spatial response and directional representation of ideal step edges the spatial matched filter is used to extract the edge strength map esm from the amdds of an image the spatial and directional matched filters are used to extract the edge direction map edm embedding the extracted esm and edm into the standard route of the differential based edge detection an anti impulse noise amdd based edge detector is constructed it is compared with the existing state of the art detectors on a recognized image dataset for edge detection evaluation the results show that it attains competitive performance in noise free and gaussian noise cases and the best performance in impulse noise cases

unified detection of skewed rotation reflection and translation symmetries from affine invariant contour features symmetry detection is significant for object detection and recognition since symmetries are salient cues for distinguishing geometrical structures from cluttered backgrounds this paper proposes a unified framework to detect rotation reflection and translation symmetries simultaneously on unsegmented real world images the detection is performed based on affine invariant contour features and is applicable under skewed imaging with distortions contours on a natural image are first matched to each other to find affine invariant matching pairs which are then classified into three groups using a sign change criterion corresponding to the three types of symmetries the three groups are used to vote for the corresponding symmetries the voting for rotation utilizes a scheme of short line segments the voting for reflection is based on a parameterization of axis equation and the voting for translation uses a cascade like approach experimental results of real world images are provided with quantitative evaluations validating that the proposed framework achieves desired performance

the contracting curve density algorithm fitting parametric curve models to images using local self adapting separation criteria the task of fitting parametric curve models to the boundaries of perceptually meaningful image regions is a key problem in computer vision with numerous applications such as image segmentation pose estimation object tracking and 3 d reconstruction in this article we propose the contracting curve density ccd algorithm as a solution to the curve fitting problem the ccd algorithm extends the state of the art in two important ways first it applies a novel likelihood function for the assessment of a fit between the curve model and the image data this likelihood function can cope with highly inhomogeneous image regions because it is formulated in terms of local image statistics the local image statistics are learned on the fly from the vicinity of the expected curve they provide therefore locally adapted criteria for separating the adjacent image regions these local criteria replace often used predefined fixed criteria that rely on homogeneous image regions or specific edge properties the second contribution is the use of blurred curve models as efficient means for iteratively optimizing the posterior density over possible model parameters these blurred curve models enable the algorithm to trade off two conflicting objectives namely heaving a large area of convergence and achieving high accuracy we apply the ccd algorithm to several challenging image segmentation and 3 d pose estimation problems our experiments with rgb images show that the ccd algorithm achieves a high level of robustness and sub pixel accuracy even in the presence of severe texture shading clutter partial occlusion and strong changes of illumination

directional processing of color images theory and experimental results the processing of color image data using directional information is studied the class of vector directional filters vdf which was introduced by the authors in a previous work is further considered the analogy of vdf to the spherical median is shown and their relation to the spatial median is examined moreover their statistical and deterministic properties are studied which demonstrate their appropriateness in image processing vdf result in optimal estimates of the image vectors in the directional sense this is very important in the case of color images where the vectors direction signifies the chromaticity of a given color issues regarding the practical implementation of vdf are also considered in addition efficient filtering schemes based on vdf are proposed which include adaptive and or double window structures experimental and comparative results in image filtering show very good performance measures when the error is measured in the l a b space l a b is known as a space where equal color differences result in equal distances and therefore it is very close to the human perception of colors moreover an indication of the chromaticity error is obtained by measuring the error on the maxwell triangle the results demonstrate that vdf are very accurate chromaticity estimators

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

improved direction estimation for di zenzo s multichannel image gradient operator gradient estimation is one of the most important tasks in image video processing for multichannel images a classical and widely used gradient method is di zenzo s gradient operator which is based on the measure of squared local contrast variation of multichannel images however up to now the indetermination of di zenzo s gradient direction has not been well solved which results in errors occurring in most of the subsequent studies in which di zenzo s vector gradient is used in this paper this problem is solved thoroughly furthermore the ranges of the values that the gradient angle should take in various cases are also analyzed as an application in color image processing a color version of canny edge detector is implemented by introducing the new gradient estimator to the traditional grayscale image canny operator the experimental results indicate that the improved di zenzo s gradient operator is currently one of the best color gradient estimators and outperforms other state of the art color image gradient methods the improved multichannel gradient operator not only provides accurate gradient estimation but also is efficient and easy to implement

noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative matrix in this paper a noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative andd matrix is proposed in order to alleviate the conflict between high edge resolution and noise robustness in the color canny detector where the isotropic gaussian kernels and gradient matrix of the r g b components are used the andds of the three components of a color image are arranged into the andd matrix from its singular value decomposition svd the andd based color edge strength map cesm is constructed and is relevant to the pixelwise optimal fusion of the andds of the three components in the sense of color edge enhancement the merits and defects of the andd based cesm and gradient based cesm are contrasted to show their complementarity in color edge detection the two cesms are fused to develop a new color edge detector it is compared with the color canny detector and two recent color edge detectors the results show that the proposed detector attains better detection performance for noiseless and noisy color images corrupted by white gaussian noise or impulsive noise of small percentage a color edge detector using gradient matrix and andd matrix is proposed the svd of the andd matrix is used to determine cesm and cesd of a color image the new detector has both high edge resolution and noise robustness it attains better performance than the two existing color edge detectors

monocular depth ordering using t junctions and convexity occlusion cues this paper proposes a system that relates objects in an image using occlusion cues and arranges them according to depth the system does not rely on a priori knowledge of the scene structure and focuses on detecting special points such as t junctions and highly convex contours to infer the depth relationships between objects in the scene the system makes extensive use of the binary partition tree as hierarchical region based image representation jointly with a new approach for candidate t junction estimation since some regions may not involve t junctions occlusion is also detected by examining convex shapes on region boundaries combining t junctions and convexity leads to a system which only relies on low level depth cues and does not rely on semantic information however it shows a similar or better performance with the state of the art while not assuming any type of scene as an extension of the automatic depth ordering system a semi automatic approach is also proposed if the user provides the depth order for a subset of regions in the image the system is able to easily integrate this user information to the final depth order for the complete image for some applications user interaction can naturally be integrated improving the quality of the automatically generated depth map

edge junction and corner detection using color distributions for over 30 years 1970 2000 researchers in computer vision have been proposing new methods for performing low level vision tasks such as detecting edges and corners one key element shared by most methods is that they represent local image neighborhoods as constant in color or intensity with deviations modeled as noise due to computational considerations that encourage the use of small neighborhoods where this assumption holds these methods remain popular the research presented models a neighborhood as a distribution of colors the goal is to show that the increase in accuracy of this representation translates into higher quality results for low level vision tasks on difficult natural images especially as neighborhood size increases we emphasize large neighborhoods because small ones often do not contain enough information we emphasize color because it subsumes gray scale as an image range and because it is the dominant form of human perception we discuss distributions in the context of detecting edges corners and junctions and we show results for each