generalized quasilinearization method and rapid convergence for first order initial value problems abstract we apply the generalized quasilinearization method of 7 and the extended method of 12 to the first order initial value problem ivp for short x t f t x x 0 x 0 t j with wider class functions f and obtain rapid convergence of monotone sequences which converge uniformly to the unique solution of the ivp

random covering of the circle the configuration space of the free deposition process consider a circle of circumference 1 throw at random n points sequentially on this circle and append clockwise an arc or rod of length s to each such point the resulting random set the free gas of rods is a collection of a random number of clusters with random sizes it models a free deposition process on a 1d substrate for such processes we shall consider the occurrence times number of rods and probabilities as n grows of the following configurations those avoiding rod overlap the hard rod gas those for which the largest gap is smaller than rod length s the packing gas those parking configurations for which hard rod and packing constraints are both fulfilled and covering configurations special attention is paid to the statistical properties of each such rare configuration in the asymptotic density domain when ns for some finite density of points using results from spacings in the random division of the circle explicit large deviation rate functions can be computed in each case from state equations lastly a process consisting in selecting at random one of these specific equilibrium configurations called the observable can be modelled when particularized to the parking model this system produces parking configurations differently from renyi s random sequential adsorption model

real time superpixel segmentation by dbscan clustering algorithm in this paper we propose a real time image superpixel segmentation method with 50 frames s by using the density based spatial clustering of applications with noise dbscan algorithm in order to decrease the computational costs of superpixel algorithms we adopt a fast two step framework in the first clustering stage the dbscan algorithm with color similarity and geometric restrictions is used to rapidly cluster the pixels and then small clusters are merged into superpixels by their neighborhood through a distance measurement defined by color and spatial features in the second merging stage a robust and simple distance function is defined for obtaining better superpixels in these two steps the experimental results demonstrate that our real time superpixel algorithm 50 frames s by the dbscan clustering outperforms the state of the art superpixel segmentation methods in terms of both accuracy and efficiency

including the size of regions in image segmentation by region based graph applying a fast over segmentation algorithm to image and working on a region based graph instead of the pixel based graph is an efficient approach to reduce the computational complexity of graph based image segmentation methods nevertheless some undesirable effects may arise if the conventional cost functions such as ncut averagecut and mincut are employed for partitioning the region based graph this is because these cost functions are generally tailored to pixel based graphs in order to resolve this problem we first introduce a new class of cost functions containing ncut and averagecut for graph partitioning whose corresponding suboptimal solution can be efficiently computed by solving a generalized eigenvalue problem then among these cost functions we propose one that considers the size of regions in the partitioning procedure by simulation the performance of the proposed cost function is quantitatively compared with that of the ncut and averagecut

pose estimation with segmentation consistency in this paper we propose a novel method that treats pose estimation as a problem with the constraints of human segmentation consistency from single images different from the previous paper we integrate pose estimation and object segmentation into a joint optimization with the support of segmentation consistency we can obtain more reliable pose results through analyzing the energy function of pose estimation and human segmentation we convert the pose estimation into a binary optimization problem that has the same formation as segmentation the top down pose shape cues bottom up visual cues and the consistency constraints that penalize the mismatching of pose and human foreground are incorporated into our final objective function qualitative and quantitative experimental results demonstrate the merits of our method in pose estimation on ramanan benchmark and buffy data sets

covering by random intervals and one dimensional continuum percolation a brief historical introduction is given to the problem of covering a line by random overlapping intervals the problem for equal intervals was first solved by whitworth in the 1890s a brief resume is given of his solution the advantages of the present author s approach which uses a poisson process are outlined and a solution is derived by laplace transforms the method of hammersley for dealing with a stochastic distribution of intervals is described and a solution can still be derived by laplace transforms the asymptotic behavior as the line becomes long is calculated and is related to the one dimensional continuum percolation problem it is shown that as long as the mean interval size is finite the probability of complete coverage decays exponentially so that the critical percolation probabilityp c 1 however as soon as the mean interval size becomes infinite the critical percolation probabilityp c switches to 0 this is in accord with previous results for a lattice model by chinese workers but differs from those of schulman a possible reason for the discrepancy is a difference in boundary conditions

random subspace based ensemble sparse representation a new random subspace based joint sparse representation model is proposed the sparse representations in multiple subspaces are integrated into an ensemble sparse representation the spectral clustering algorithm with random subspace based ensemble sparse representation is shown the semi supervised classification method with random subspace based ensemble sparse representation is described in this paper a new random subspace based ensemble sparse representation rs esr algorithm is proposed where the random subspace is introduced into sparse representation model for high dimensional data the random subspace method can not only reduce dimension of data but also make full use of effective information of data it is not like traditional dimensionality reduction methods that may lose some information of original data additionally a joint sparse representation model is emloyed to obtain the sparse representation of a sample set in the low dimensional random subspace then the sparse representations in multiple random subspaces are integrated as an ensemble sparse representation moreover the obtained rs esr is applied in classical clustering and semi supervised classification the experimental results on different real world data sets show the superiority of rs esr over traditional methods

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

a probabilistic graph based framework for plug and play multi cue visual tracking in this paper we propose a novel approach for integrating multiple tracking cues within a unified probabilistic graph based markov random fields mrfs representation we show how to integrate temporal and spatial cues encoded by unary and pairwise probabilistic potentials as the inference of such high order mrf models is known to be np hard we propose an efficient spectral relaxation based inference scheme the proposed scheme is exemplified by applying it to a mixture of five tracking cues and is shown to be applicable to wider sets of cues this paves the way for a modular plug and play tracking framework that can be easily adapted to diverse tracking scenarios the proposed scheme is experimentally shown to compare favorably with contemporary state of the art schemes and provides accurate tracking results

image segmentation via probabilistic graph matching this paper presents an unsupervised and semi automatic image segmentation approach where we formulate the segmentation as an inference problem based on unary and pairwise assignment probabilities computed using low level image cues the inference is solved via a probabilistic graph matching scheme which allows rigorous incorporation of low level image cues and automatic tuning of parameters the proposed scheme is experimentally shown to compare favorably with contemporary semi supervised and unsupervised image segmentation schemes when applied to contemporary state of the art image sets

exploiting superpixel and hybrid hash for kernel based visual tracking superpixel analysis approach is employed to reconstruct target appearance in visual tracking representative superpixel blocks combined with kernel based filter are exploited for roughly target location superpixel block modification method based on hybrid hash is proposed to accurately locate target conventional kernel based filter is improved with peak response scale estimation and color features comprehensive experiments on publicly available datasets demonstrate our tracker superior to state of the art trackers in recent years significant advances in visual tracking have been made and numerous outstanding algorithms have been proposed however the constraint between tracking accuracy and speed has not yet been comprehensively addressed in this paper to address the challenging aspects of visual tracking and in particular to achieve accurate real time tracking we propose a novel real time kernel based visual tracking algorithm based on superpixel clustering and hybrid hash analysis by adopting superpixel clustering and segmentation we reconstruct the appearance model of the target and its surrounding context in the initialization step via introducing the approach of overlap and intensity analysis we divide the reconstructed model into several superpixel blocks based on the theory of circulant matrices and fourier analysis we build a gaussian kernel correlation filter to roughly locate the position of each candidate block to further improve the kernel correlation filter method we compute each block s maximal response value in the confidence map and estimate each block s scale variation based on a peak value comparison additionally we also propose a hybrid hash analysis strategy and integrate it with superpixel analysis for target blocks modification by calculating a hybrid hash sequence based on l a b color and the discrete cosine transform we conduct superpixel block modification to accurately locate the target and estimate the target s scale variation extensive experiments on visual tracking benchmark datasets show that our tracking algorithm outperforms the state of the art algorithms and demonstrate its effectiveness and efficiency

turbopixel segmentation using eigen images turbopixel tp is a powerful tool for image over segmentation it is fast and can yield a lattice like structure of superpixel regions with uniform size this paper presents a method to learn eigen images from the image to be segmented such eigen images are used to generate the evolution speed in the tp framework the task is formulated as a problem of pixel clustering specifically for the pixels in each local window a linear transformation is introduced to map their color vectors to be the cluster indicator vectors the errors under all such linear transformations are estimated and summed together to obtain an objective function from which a global optimum is finally obtained in this process the eigen images are constructed based upon these eigen images multidimensional image gradient operator is defined to evaluate the gradient which is supplied to the tp algorithm to obtain the final superpixel segmentations the computational issues are discussed and an image pyramid is introduced to speed up the computation comparative experiments illustrate the effectiveness of our method

generalized quasilinearization method for mixed boundary value problems a generalized quasilinearization method for a nonlinear mixed bvp is developed and a sequence of approximate solutions converging monotonically and quadratically to a solution of the given problem is presented

entropy rate clustering cluster analysis via maximizing a submodular function subject to a matroid constraint we propose a new objective function for clustering this objective function consists of two components the entropy rate of a random walk on a graph and a balancing term the entropy rate favors formation of compact and homogeneous clusters while the balancing function encourages clusters with similar sizes and penalizes larger clusters that aggressively group samples we present a novel graph construction for the graph associated with the data and show that this construction induces a matroid a combinatorial structure that generalizes the concept of linear independence in vector spaces the clustering result is given by the graph topology that maximizes the objective function under the matroid constraint by exploiting the submodular and monotonic properties of the objective function we develop an efficient greedy algorithm furthermore we prove an approximation bound of 1 2 for the optimality of the greedy solution we validate the proposed algorithm on various benchmarks and show its competitive performances with respect to popular clustering algorithms we further apply it for the task of superpixel segmentation experiments on the berkeley segmentation data set reveal its superior performances over the state of the art superpixel segmentation algorithms in all the standard evaluation metrics

local variation as a statistical hypothesis test the goal of image oversegmentation is to divide an image into several pieces each of which should ideally be part of an object one of the simplest and yet most effective oversegmentation algorithms is known as local variation lv felzenszwalb and huttenlocher in efficient graph based image segmentation ijcv 59 2 167 181 2004 in this work we study this algorithm and show that algorithms similar to lv can be devised by applying different statistical models and decisions thus providing further theoretical justification and a well founded explanation for the unexpected high performance of the lv approach some of these algorithms are based on statistics of natural images and on a hypothesis testing decision we denote these algorithms probabilistic local variation plv the best plv algorithm which relies on censored estimation presents state of the art results while keeping the same computational complexity of the lv algorithm

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

discontinuity of the percolation density in one dimensional 1 x y 2 percolation models we consider one dimensional percolation models for which the occupation probability of a bond kx y has a slow power decay as a function of the bond s length for independent models and with suitable reformulations also for more general classes of models it is shown that i no percolation is possible if for short bondskx y p 1 this dichotomy resembles one for the magnetization in 1 x y 2 ising models which was first proposed by thouless and further supported by the renormalization group flow equations of anderson yuval and hamann the proofs of the above percolation phenomena involve rigorous renormalization type arguments of a different sort

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

a morphological approach to curvature based evolution of curves and surfaces we introduce new results connecting differential and morphological operators that provide a formal and theoretically grounded approach for stable and fast contour evolution contour evolution algorithms have been extensively used for boundary detection and tracking in computer vision the standard solution based on partial differential equations and level sets requires the use of numerical methods of integration that are costly computationally and may have stability issues we present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension we approximate the numerical solution of the curve evolution pde by the successive application of a set of morphological operators defined on a binary level set and with equivalent infinitesimal behavior these operators are very fast do not suffer numerical stability issues and do not degrade the level set function so there is no need to reinitialize it moreover their implementation is much easier since they do not require the use of sophisticated numerical algorithms we validate the approach providing a morphological implementation of the geodesic active contours the active contours without borders and turbopixels in the experiments conducted the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions but with significant gains in simplicity speed and stability

one dimensional 1 j i s percolation models the existence of a transition for s 2 consider a one dimensional independent bond percolation model withpj denoting the probability of an occupied bond between integer sitesi andi j j 1 ifpj is fixed forj 2 and mathop lim limits j to infty j2pj 1 then unoriented percolation occurs forp1 sufficiently close to 1 this result analogous to the existence of spontaneous magnetization in long range one dimensional ising models is proved by an inductive series of bounds based on a renormalization group approach using blocks of variable size oriented percolation is shown to occur forp1 close to 1 if mathop lim limits j to infty jspj 0 for somes 2 analogous results are valid for one dimensional site bond percolation models

cross trees edge and superpixel priors based cost aggregation for stereo matching in this paper we propose a novel cross trees structure to perform the non local cost aggregation strategy and the cross trees structure consists of a horizontal tree and a vertical tree compared to other spanning trees the significant superiorities of the cross trees are that the trees constructions are efficient and the trees are exactly unique since the constructions are independent on any local or global property of the image itself additionally two different priors edge prior and superpixel prior are proposed to tackle the false cost aggregations which cross the depth boundaries hence our method contains two different algorithms in terms of cross trees prior by traversing the two crossed trees successively a fast non local cost aggregation algorithm is performed twice to compute the aggregated cost volume performance evaluation on the 27 middlebury data sets shows that both our algorithms outperform the other two tree based non local methods namely minimum spanning tree mst and segment tree st graphical abstractdisplay omitted highlightswe propose a novel cross trees structure to perform the non local cost aggregation the trees constructions are unique and independent on the image itself we propose and incorporate two priors into the non local framework new edge weights function is designed according to the trees and the priors optimal support regions can be chose by cutting the cost aggregation flow on paths

multiscale superpixels and supervoxels based on hierarchical edge weighted centroidal voronoi tessellation superpixels and supervoxels play an important role in many computer vision applications such as image segmentation object recognition and video analysis in this paper we propose a new hierarchical edge weighted centroidal voronoi tessellation hewcvt method for generating superpixels supervoxels in multiple scales in this method we model the problem as a multilevel clustering process superpixels supervoxels in one level are clustered to obtain larger size superpixels supervoxels in the next level in the finest scale the initial clustering is directly conducted on pixels voxels the clustering energy involves both color similarities and boundary smoothness of superpixels supervoxels the resulting superpixels supervoxels can be easily represented by a hierarchical tree which describes the nesting relation of superpixels supervoxels across different scales we first investigate the performance of obtained superpixels supervoxels under different parameter settings then we evaluate and compare the proposed method with several state of the art superpixel supervoxel methods on standard image and video data sets both quantitative and qualitative results show that the proposed hewcvt method achieves superior or comparable performances with other methods

a numerical approach to nonlinear two point boundary value problems for odes in this paper we propose a numerical approach to solve some problems connected with the implementation of the newton type methods for the resolution of the nonlinear system of equations related to the discretization of a nonlinear two point bvps for odes with mixed linear boundary conditions by using the finite difference method

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

orientation guided geodesic weighting for patchmatch based stereo matching we propose an orientation guided geodesic weighting oggw strategy for local stereo matching we propose a method of cost volume filtering combining a multipoint lpa method with our oggw strategy we propose a patchmatch filter with curved surface fitting pmf cs to obtain a disparity map with sub pixel accuracy recently patchmatch based methods for local stereo matching are experiencing great progress with the use of compact and over segmented regions that have similar intensities or colors using patches as support regions this paper proposes an orientation guided geodesic weighting oggw strategy to search for an approximate shortest path from a support pixel in the patch to a pixel of interest along a guided orientation the oggw is computed by accumulating intensity differences or color dissimilarities between connected pixels along the path after obtaining matching cost updates by model fitting the oggw is used for weighted averaging on the updated costs to obtain a filtered cost volume in addition a new filtering method that combines the patchmatch filter with curved surface fitting pmf cs is presented in this paper curved surface fitting along with outliers removal is carried out to seek for a reliable regression model for estimating the disparities on a patch and to achieve a disparity map with sub pixel accuracy we conduct a number of experiments to evaluate the performances of oggw and pmf cs on cost volume filtering and disparity estimation experimental results show that our algorithm produces accurate stereo matching results and outperforms the current state of the art patchmatch based methods

the bellman kalaba lakshmikantham quasilinearization method for neumann problems in this paper we develop a generalized quasilinearization method for a nonlinear neumann problem and obtain a sequence of approximate solutions converging monotonically and quadratically to a solution of the problem

turbopixels fast superpixels using geometric flows we describe a geometric flow based algorithm for computing a dense oversegmentation of an image often referred to as superpixels it produces segments that on one hand respect local image boundaries while on the other hand limiting undersegmentation through a compactness constraint it is very fast with complexity that is approximately linear in image size and can be applied to megapixel sized images with high superpixel densities in a matter of minutes we show qualitative demonstrations of high quality results on several complex images the berkeley database is used to quantitatively compare its performance to a number of oversegmentation algorithms showing that it yields less undersegmentation than algorithms that lack a compactness constraint while offering a significant speedup over n cuts which does enforce compactness

long range percolation in one dimension the problem of long range percolation in one dimension is proposed the authors consider a one dimensional bond percolation system with bonds connecting an infinite number of neighbours where the occupation probability for the nth nearest neighbour bond pn varies as p1 ns using the transfer matrix method they find that when s 2 only the short range percolation exists namely the system percolates only when p1 1 a transition to long range percolation is found at s 2 where the percolation threshold drops suddenly from the short range value p1c 1 to the long range value p1c 0

continuous percolation in one dimension the continuous percolation problem for equal disc size in a one dimensional space is treated exact expressions are given for the relevant functions and the critical exponents it is shown that with an appropriate selection of scaling fields this problem as well as the further neighbour discrete problem belongs to the same universality class as the more common nearest neighbour one dimensional discrete problem

linear spectral clustering superpixel in this paper we present a superpixel segmentation algorithm called linear spectral clustering lsc which is capable of producing superpixels with both high boundary adherence and visual compactness for natural images with low computational costs in lsc a normalized cuts based formulation of image segmentation is adopted using a distance metric that measures both the color similarity and the space proximity between image pixels however rather than directly using the traditional eigen based algorithm we approximate the similarity metric through a deliberately designed kernel function such that pixel values can be explicitly mapped to a high dimensional feature space we then apply the conclusion that by appropriately weighting each point in this feature space the objective functions of the weighted k means and the normalized cuts share the same optimum points consequently it is possible to optimize the cost function of the normalized cuts by iteratively applying simple k means clustering in the proposed feature space lsc possesses linear computational complexity and high memory efficiency since it avoids both the decomposition of the affinity matrix and the generation of the large kernel matrix by utilizing the underlying mathematical equivalence between the two types of seemingly different methods lsc successfully preserves global image structures through efficient local operations experimental results show that lsc performs as well as or even better than the state of the art superpixel segmentation algorithms in terms of several commonly used evaluation metrics in image segmentation the applicability of lsc is further demonstrated in two related computer vision tasks

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

intrinsic manifold slic a simple and efficient method for computing content sensitive superpixels superpixels are perceptually meaningful atomic regions that can effectively capture image features among various methods for computing uniform superpixels simple linear iterative clustering slic is popular due to its simplicity and high performance in this paper we extend slic to compute content sensitive superpixels i e small superpixels in content dense regions with high intensity or colour variation and large superpixels in content sparse regions rather than using the conventional slic method that clusters pixels in mathbb r 5 we map the input image i to a 2 dimensional manifold mathcal m subset mathbb r 5 whose area elements are a good measure of the content density in i we propose a simple method called intrinsic manifold slic imslic for computing a geodesic centroidal voronoi tessellation gcvt a uniform tessellation on mathcal m which induces the content sensitive superpixels in i in contrast to the existing algorithms imslic characterizes the content sensitivity by measuring areas of voronoi cells on mathcal m using a simple and fast approximation to a closed form solution the method can compute the gcvt at a very low cost and guarantees that all voronoi cells are simply connected we thoroughly evaluate imslic and compare it with eleven representative methods on the bsds500 dataset and seven representative methods on the nyuv2 dataset computational results show that imslic outperforms existing methods in terms of commonly used quality measures pertaining to superpixels such as compactness adherence to boundaries and achievable segmentation accuracy we also evaluate imslic and seven representative methods in an image contour closure application and the results on two datasets whd and wsd show that imslic achieves the best foreground segmentation performance

replacing the finite difference methods for nonlinear two point boundary value problems by successive application of the linear shooting method abstract this paper studies numerical solution of nonlinear two point boundary value problems for second order ordinary differential equations first it establishes a connection between the finite difference method and the quasi linearization method we prove that using finite differences to discretize the sequence of linear differential equations arising from quasi linearization newton method on operator level leads to the usual iteration formula of the newton finite difference method from the provided derivation it can easily be inferred that such a relation holds also for the picard and the constant slope methods based on this result we propose a way of replacing the newton picard and constant slope finite difference methods by respective successive application of the linear shooting method this approach has a number of advantages it removes the necessity of solving systems of algebraic equations hence working with matrices altogether compared to the usual finite difference method with general solver it reduces the number of computational operations from o n 3 where n is the number of mesh points to only o n

image segmentation with ratio cut this paper proposes a new cost function cut ratio for segmenting images using graph based methods the cut ratio is defined as the ratio of the corresponding sums of two different weights of edges along the cut boundary and models the mean affinity between the segments separated by the boundary per unit boundary length this new cost function allows the image perimeter to be segmented guarantees that the segments produced by bipartitioning are connected and does not introduce a size shape smoothness or boundary length bias the latter allows it to produce segmentations where boundaries are aligned with image edges furthermore the cut ratio cost function allows efficient iterated region based segmentation as well as pixel based segmentation these properties may be useful for some image segmentation applications while the problem of finding a minimum ratio cut in an arbitrary graph is np hard one can find a minimum ratio cut in the connected planar graphs that arise during image segmentation in polynomial time while the cut ratio alone is not sufficient as a baseline method for image segmentation it forms a good basis for an extended method of image segmentation when combined with a small number of standard techniques we present an implemented algorithm for finding a minimum ratio cut prove its correctness discuss its application to image segmentation and present the results of segmenting a number of medical and natural images using our techniques

shortest path constraints for 3d multiobject semiautomatic segmentation via clustering and graph cut we derive shortest path constraints from graph models of structure adjacency relations and introduce them in a joint centroidal voronoi image clustering and graph cut multiobject semiautomatic segmentation framework the vicinity prior model thus defined is a piecewise constant model incurring multiple levels of penalization capturing the spatial configuration of structures in multiobject segmentation qualitative and quantitative analyses and comparison with a potts prior based approach and our previous contribution on synthetic simulated and real medical images show that the vicinity prior allows for the correct segmentation of distinct structures having identical intensity profiles and improves the precision of segmentation boundary placement while being fairly robust to clustering resolution the clustering approach we take to simplify images prior to segmentation strikes a good balance between boundary adaptivity and cluster compactness criteria furthermore allowing to control the trade off compared with a direct application of segmentation on voxels the clustering step improves the overall runtime and memory footprint of the segmentation process up to an order of magnitude without compromising the quality of the result

automatic segmentation of mitochondria in em data using pairwise affinity factorization and graph based contour searching in this paper we investigate the segmentation of closed contours in subcellular data using a framework that primarily combines the pairwise affinity grouping principles with a graph partitioning contour searching approach one salient problem that precluded the application of these methods to large scale segmentation problems is the onerous computational complexity required to generate comprehensive representations that include all pairwise relationships between all pixels in the input data to compensate for this problem a practical solution is to reduce the complexity of the input data by applying an over segmentation technique prior to the application of the computationally demanding strands of the segmentation process this approach opens the opportunity to build specific shape and intensity models that can be successfully employed to extract the salient structures in the input image which are further processed to identify the cycles in an undirected graph the proposed framework has been applied to the segmentation of mitochondria membranes in electron microscopy data which are characterized by low contrast and low signal to noise ratio the algorithm has been quantitatively evaluated using two datasets where the segmentation results have been compared with the corresponding manual annotations the performance of the proposed algorithm has been measured using standard metrics such as precision and recall and the experimental results indicate a high level of segmentation accuracy

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

the generalized quasilinearization method for partial differential equations of first order this paper applies the method of generalized quasilinearization to investigating the monotone iterative technique for partial differential equations of first order the rate of convergence is also discussed

stochastic species abundance models involving special copulas abstract copulas offer a very general tool to describe the dependence structure of random variables supported by the hypercube inspired by problems of species abundances in biology we study three distinct toy models where copulas play a key role in a first one a marshall olkin copula arises in a species extinction model with catastrophe in a second one a quasi copula problem arises in a flagged species abundance model in a third model we study completely random species abundance models in the hypercube as those not of product type with uniform margins and singular these can be understood from a singular copula supported by an inflated simplex an exchangeable singular dirichlet copula is also introduced together with its induced completely random species abundance vector

winding number constrained contour detection salient contour detection can benefit from the integration of both contour cues and region cues however this task is difficult due to different nature of region representations and contour representations to solve this problem this paper proposes an energy minimization framework based on winding number constraints in this framework both region cues such as color texture homogeneity and contour cues such as local contrast and continuity are represented in a joint objective function which has both region and contour labels the key problem is how to design constraints that ensure the topological consistency of the two kinds of labels our technique is based on the topological concept of winding number using a fast method for winding number computation a small number of linear constraints are derived to ensure label consistency our method is instantiated by ratio based energy functions by successfully integrating both region and contour cues our method shows advantages over competitive methods our method is extended to incorporate user interaction which leads to further improvements

area and length minimizing flows for shape segmentation a number of active contour models have been proposed that unify the curve evolution framework with classical energy minimization techniques for segmentation such as snakes the essential idea is to evolve a curve in two dimensions or a surface in three dimensions under constraints from image forces so that it clings to features of interest in an intensity image the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional tailored to features such as edges however because the flow may be slow to converge in practice a constant hyperbolic term is added to keep the curve surface moving in the desired direction we derive a modification of this term based on the gradient flow derived from a weighted area functional with image dependent weighting factor when combined with the earlier modified length gradient flow we obtain a partial differential equation pde that offers a number of advantages as illustrated by several examples of shape segmentation on medical images in many cases the weighted area flow may be used on its own with significant computational savings

the segmentation of 3d images using the random walking technique on a randomly created image adjacency graph this paper considers the problem of image segmentation using the random walker algorithm in the case of 3d images the method uses an extreme amount of memory and time resources these are required in order to represent the corresponding enormous image graph and to solve the resulting sparse linear system having in mind these limitations this paper proposes techniques for the optimization of the random walker approach the optimization is obtained by processing supervoxels representing homogeneous image regions rather than single voxels a fast and efficient method for supervoxel determination is introduced a method for the creation of an image adjacency graph from an irregular grid of supervoxels is also proposed the results of applying the introduced approach to segmentation of 3d ct data sets are presented and compared with the results of the original random walker approach and other state of the art methods the accuracy and the computational overhead is regarded in the comparison the analysis of results shows that the modified method can be successfully applied for the segmentation of volumetric images and provides results in a reasonable time without a significant loss in the image segmentation accuracy it also outperforms the state of the art methods considered in the comparison

an improved quasilinearization method for second order nonlinear boundary value problems abstract solutions to the general second order nonlinear boundary value problems arising in many physical phenomena such as dynamic programming fluid flow over a solid object and heat transfer in a solid and or adjacent to a solid body in a liquid are obtained also existence uniqueness and convergence results are established by using quasilinearization and monotone iterative methods furthermore examples are presented to demonstrate the application of the solution techniques

optimal image and video closure by superpixel grouping detecting independent objects in images and videos is an important perceptual grouping problem one common perceptual grouping cue that can facilitate this objective is the cue of contour closure reflecting the spatial coherence of objects in the world and their projections as closed boundaries separating figure from background detecting contour closure in images consists of finding a cycle of disconnected contour fragments that separates an object from its background searching the entire space of possible groupings is intractable and previous approaches have adopted powerful perceptual grouping heuristics such as proximity and co curvilinearity to constrain the search we introduce a new formulation of the problem by transforming the problem of finding cycles of contour fragments to finding subsets of superpixels whose collective boundary has strong edge support few gaps in the image our cost function a ratio of a boundary gap measure to area promotes spatially coherent sets of superpixels moreover its properties support a global optimization procedure based on parametric maxflow extending closure detection to videos we introduce the concept of spatiotemporal closure analogous to image closure we formulate our spatiotemporal closure cost over a graph of spatiotemporal superpixels our cost function is a ratio of motion and appearance discontinuity measures on the boundary of the selection to an internal homogeneity measure of the selected spatiotemporal volume the resulting approach automatically recovers coherent components in images and videos corresponding to objects object parts and objects with surrounding context providing a good set of multiscale hypotheses for high level scene analysis we evaluate both our image and video closure frameworks by comparing them to other closure detection approaches and find that they yield improved performance

quadratic approximation of solutions for boundary value problems with nonlocal boundary conditions in this paper using the quasilinearization method coupled with the method of upper and lower solutions we study a class of second order nonlinear boundary value problems with nonlocal boundary conditions we establish some sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem an example is also included to illustrate the main result

example based image colorization using locality consistent sparse representation image colorization aims to produce a natural looking color image from a given gray scale image which remains a challenging problem in this paper we propose a novel example based image colorization method exploiting a new locality consistent sparse representation given a single reference color image our method automatically colorizes the target gray scale image by sparse pursuit for efficiency and robustness our method operates at the superpixel level we extract low level intensity features mid level texture features and high level semantic features for each superpixel which are then concatenated to form its descriptor the collection of feature vectors for all the superpixels from the reference image composes the dictionary we formulate colorization of target superpixels as a dictionary based sparse reconstruction problem inspired by the observation that superpixels with similar spatial location and or feature representation are likely to match spatially close regions from the reference image we further introduce a locality promoting regularization term into the energy formulation which substantially improves the matching consistency and subsequent colorization results target superpixels are colorized based on the chrominance information from the dominant reference superpixels finally to further improve coherence while preserving sharpness we develop a new edge preserving filter for chrominance channels with the guidance from the target gray scale image to the best of our knowledge this is the first work on sparse pursuit image colorization from single reference images experimental results demonstrate that our colorization method outperforms the state of the art methods both visually and quantitatively using a user study

vcells simple and efficient superpixels using edge weighted centroidal voronoi tessellations vcells the proposed edge weighted centroidal voronoi tessellations ewcvts based algorithm is used to generate superpixels i e an oversegmentation of an image for a wide range of images the new algorithm is capable of generating roughly uniform subregions and nicely preserving local image boundaries the undersegmentation error is effectively limited in a controllable manner moreover vcells is very efficient with core computational cost at o k nc n in which k nc and n are the number of iterations superpixels and pixels respectively extensive qualitative discussions are provided together with the high quality segmentation results of vcells on a wide range of complex images the simplicity and efficiency of our model are demonstrated by complexity analysis time and accuracy evaluations