a triparametric family of cardinality based fuzzy similarity measures previously we introduced a biparametric family of cardinality based fuzzy similarity measures in this paper we generalize this family by adding a third parameter we also study the generalized family for specific values of the third parameter more precisely we show that for particular values of this parameter certain properties can be ensured by imposing constraints on the two remaining parameters to conclude we examine some members of the presented family of fuzzy similarity measures

fuzzy implication operators for difference operations for fuzzy sets and cardinality based measures of comparison in this paper we determine by means of fuzzy implication operators two classes of difference operations for fuzzy sets and two classes of symmetric difference operations for fuzzy sets which preserve properties of the classical difference operation for crisp sets and the classical symmetric difference operation for crisp sets respectively the obtained operations allow us to construct as in b de baets h de meyer transitivity preserving fuzzification schemes for cardinality based similarity measures european journal of operational research 160 2005 726 740 cardinality based similarity measures which are reflexive symmetric and transitive fuzzy relations and to propose two classes of distances metrics which are fuzzy versions of the well known distance of cardinality of the symmetric difference of crisp sets

symmetric difference operators on fuzzy sets abstract based on the properties of symmetric difference of sets a symmetric difference operator for fuzzy sets is defined to be a continuous and associative binary operator on the closed unit interval with some boundary condition structures and properties of these operators are investigated in this paper the main results are 1 it is proved that a symmetric difference operator is determined by a continuous t conorm and a strong negation operator on the unit interval 2 two models of these operators are discussed these models are related to the solutions of certain functional equations on the unit interval in particular the results presented here provide a partial answer to a problem raised by alsina frank and schweizer in 2003 about functional equations on the unit interval

feature augmentation for learning confidence measure in stereo matching confidence estimation is essential for refining stereo matching results through a post processing step this problem has recently been studied using a learning based approach which demonstrates a substantial improvement on conventional simple non learning based methods however the formulation of learning based methods that individually estimates the confidence of each pixel disregards spatial coherency that might exist in the confidence map thus providing a limited performance under challenging conditions our key observation is that the confidence features and resulting confidence maps are smoothly varying in the spatial domain and highly correlated within the local regions of an image we present a new approach that imposes spatial consistency on the confidence estimation specifically a set of robust confidence features is extracted from each superpixel decomposed using the gaussian mixture model and then these features are concatenated with pixel level confidence features the features are then enhanced through adaptive filtering in the feature domain in addition the resulting confidence map estimated using the confidence features with a random regression forest is further improved through k nearest neighbor based aggregation scheme on both pixel and superpixel level to validate the proposed confidence estimation scheme we employ cost modulation or ground control points based optimization in stereo matching experimental results demonstrate that the proposed method outperforms state of the art approaches on various benchmarks including challenging outdoor scenes

meta theorems on inequalities for scalar fuzzy set cardinalities we present meta theorems stating general conditions ensuring that certain inequalities for cardinalities of ordinary sets are preserved under fuzzification when adopting a scalar approach to fuzzy set cardinality the conditions pertain to the commutative conjunctor used for modelling fuzzy set intersection in particular this conjunctor should fulfil a number of bell type inequalities the advantage of these meta theorems is that repetitious calculations can be avoided this is illustrated in the demonstration of the lukasiewicz transitivity of fuzzified versions of the simple matching coefficient and the jaccard coefficient or equivalently the triangle inequality of the corresponding dissimilarity measures

patchmatch filter edge aware filtering meets randomized search for visual correspondence though many tasks in computer vision can be formulated elegantly as pixel labeling problems a typical challenge discouraging such a discrete formulation is often due to computational efficiency recent studies on fast cost volume filtering based on efficient edge aware filters provide a fast alternative to solve discrete labeling problems with the complexity independent of the support window size however these methods still have to step through the entire cost volume exhaustively which makes the solution speed scale linearly with the label space size when the label space is huge or even infinite which is often the case for subpixel accurate stereo and optical flow estimation their computational complexity becomes quickly unacceptable developed to search approximate nearest neighbors rapidly the patchmatch method can significantly reduce the complexity dependency on the search space size but its pixel wise randomized search and fragmented data access within the 3d cost volume seriously hinder the application of efficient cost slice filtering this paper presents a generic and fast computational framework for general multi labeling problems called patchmatch filter pmf we explore effective and efficient strategies to weave together these two fundamental techniques developed in isolation i e patchmatch based randomized search and efficient edge aware image filtering by decompositing an image into compact superpixels we also propose superpixel based novel search strategies that generalize and improve the original patchmatch method further motivated to improve the regularization strength we propose a simple yet effective cross scale consistency constraint which handles labeling estimation for large low textured regions more reliably than a single scale pmf algorithm focusing on dense correspondence field estimation in this paper we demonstrate pmf s applications in stereo and optical flow our pmf methods achieve top tier correspondence accuracy but run much faster than other related competing methods often giving over 10 100 times speedup

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

bayesian clustering of fuzzy feature vectors using a quasi likelihood approach bayesian model based classifiers both unsupervised and supervised have been studied extensively and their value and versatility have been demonstrated on a wide spectrum of applications within science and engineering a majority of the classifiers are built on the assumption of intrinsic discreteness of the considered data features or on their discretization prior to the modeling on the other hand gaussian mixture classifiers have also been utilized to a large extent for continuous features in the bayesian framework often the primary reason for discretization in the classification context is the simplification of the analytical and numerical properties of the bayesian models however the discretization can be problematic due to its ad hoc nature and the decreased statistical power to detect the correct classes or clusters in the resulting procedure here we introduce an unsupervised classification approach for fuzzy feature vectors that utilizes a discrete model structure while preserving the continuous characteristics of data this goal is achieved by replacing the ordinary likelihood by a binomial quasi likelihood to yield an analytical expression for the posterior probability of a given clustering solution the resulting model can also be justified from an information theoretic perspective our method is shown to yield highly accurate clusterings for challenging synthetic and empirical data sets and to perform favorably compared to some alternative approaches

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

a multisize superpixel approach for salient object detection based on multivariate normal distribution estimation this paper presents a new method for salient object detection based on a sophisticated appearance comparison of multisize superpixels those superpixels are modeled by multivariate normal distributions in cie lab color space which are estimated from the pixels they comprise this fitting facilitates an efficient application of the wasserstein distance on the euclidean norm formula see text to measure perceptual similarity between elements saliency is computed in two ways on the one hand we compute global saliency by probabilistically grouping visually similar superpixels into clusters and rate their compactness on the other hand we use the same distance measure to determine local center surround contrasts between superpixels then an innovative locally constrained random walk technique that considers local similarity between elements balances the saliency ratings inside probable objects and background the results of our experiments show the robustness and efficiency of our approach against 11 recently published state of the art saliency detection methods on five widely used benchmark data sets

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

salient region detection using diffusion process on a two layer sparse graph diffusion based salient region detection has recently received intense research attention in this paper we present some effective improvements concerning two important aspects of diffusion based methods the construction of the diffusion matrix and the seed vector first we construct a two layer sparse graph which is generated by connecting each node to its neighboring nodes and the most similar node that shares common boundaries with its neighboring nodes compared with the most frequently used two layer neighborhood graph our graph not only effectively uses local spatial relationships but also removes dissimilar redundant nodes second we use the spatial variance of superpixel clusters to obtain the seed vector and compared with the previously most used boundary prior our approach can better distinguish saliency seeds from the background seeds especially when salient objects appear near the image boundaries finally we calculate two preliminary saliency maps using the saliency and background seed vectors and more accurate results are obtained using the manifold ranking diffusion method integrating these two diffusion based saliency maps we obtain the final saliency map extensive experiments in which we compare our method with 20 existing state of the art methods on five benchmark data sets asd dut omron ecssd msra5k and msra10k show that the proposed method performs better in terms of various evaluation metrics

recursive nearest agglomeration rena fast clustering for approximation of structured signals in this work we revisit fast dimension reduction approaches as with random projections and random sampling our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis such dimension reduction can be very efficient when the signals of interest have a strong structure such as with images we focus on this setting and investigate feature clustering schemes for data reductions that capture this structure an impediment to fast dimension reduction is then that good clustering comes with large algorithmic costs we address it by contributing a linear time agglomerative clustering scheme recursive nearest agglomeration rena unlike existing fast agglomerative schemes it avoids the creation of giant clusters we empirically validate that it approximates the data as well as traditional variance minimizing clustering schemes that have a quadratic complexity in addition we analyze signal approximation with feature clustering and show that it can remove noise improving subsequent analysis steps as a consequence data reduction by clustering features with rena yields very fast and accurate models enabling to process large datasets on budget our theoretical analysis is backed by extensive experiments on publicly available data that illustrate the computation efficiency and the denoising properties of the resulting dimension reduction scheme

a stochastic polygons model for glandular structures in colon histology images in this paper we present a stochastic model for glandular structures in histology images of tissue slides stained with hematoxylin and eosin choosing colon tissue as an example the proposed random polygons model rpm treats each glandular structure in an image as a polygon made of a random number of vertices where the vertices represent approximate locations of epithelial nuclei we formulate the rpm as a bayesian inference problem by defining a prior for spatial connectivity and arrangement of neighboring epithelial nuclei and a likelihood for the presence of a glandular structure the inference is made via a reversible jump markov chain monte carlo simulation to the best of our knowledge all existing published algorithms for gland segmentation are designed to mainly work on healthy samples adenomas and low grade adenocarcinomas one of them has been demonstrated to work on intermediate grade adenocarcinomas at its best our experimental results show that the rpm yields favorable results both quantitatively and qualitatively for extraction of glandular structures in histology images of normal human colon tissues as well as benign and cancerous tissues excluding undifferentiated carcinomas

branching rules and even dimensional rotation groups so2k unambiguous methods are developed for calculating branching rules for the classical subgroups of the even dimensional rotation group so2k complete results are given for the subgroups suk u1 so2k 2 u1 so2p so2q and so2p 1 so2q 1 a number of examples relevant to problems in supergravity and unification theories are given a complete resolution of the antisymmetric powers of the basic spinor irrep of so10 is given and the results extended to so11

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

transitivity preserving fuzzification schemes for cardinality based similarity measures abstract a family of fuzzification schemes is proposed that can be used to transform cardinality based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe the family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets in particular the fuzzy set intersections are pointwisely generated by frank t norms the fuzzification schemes are applied to a variety of previously studied rational cardinality based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process

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

estimation of signal dependent noise level function in transform domain via a sparse recovery model this paper proposes a novel algorithm to estimate the noise level function nlf of signal dependent noise sdn from a single image based on the sparse representation of nlfs noise level samples are estimated from the high frequency discrete cosine transform dct coefficients of nonlocal grouped low variation image patches then an nlf recovery model based on the sparse representation of nlfs under a trained basis is constructed to recover nlf from the incomplete noise level samples confidence levels of the nlf samples are incorporated into the proposed model to promote reliable samples and weaken unreliable ones we investigate the behavior of the estimation performance with respect to the block size sampling rate and confidence weighting simulation results on synthetic noisy images show that our method outperforms existing state of the art schemes the proposed method is evaluated on real noisy images captured by three types of commodity imaging devices and shows consistently excellent sdn estimation performance the estimated nlfs are incorporated into two well known denoising schemes nonlocal means and bm3d and show significant improvements in denoising sdn polluted images

similarity and dissimilarity measures between fuzzy sets a formal relational study the paper deals with the well known notion of dis similarity measures between fuzzy sets we provide three separate lists of axioms that fit with the respective notions of general comparison measure similarity measure and dissimilarity measure then we review some of the most important axiomatic definitions of dis similarity measures in the literature by referring to the axioms in those lists satisfied by each specific definition this common framework will make our study about the formal relationships among different axiomatic definitions much easier some of them which are apparently different do in fact share many commonalities we provide a self contained picture of these relationships by providing formal results and counterexamples that reflect which of the dis similarity definitions in the literature are connected by implication relations and which of them are not we finalize the paper with an in depth study about the notion of duality between similarity and dissimilarity measures as well as with some concluding remarks

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

structure regularized compressive tracking with online data driven sampling being a powerful appearance model compressive random projection derives effective haar like features from non rotated 4 d parameterized rectangles thus supporting fast and reliable object tracking in this paper we show that such successful fast compressive tracking scheme can be further significantly improved by structural regularization and online data driven sampling our major contribution is threefold first we find that superpixel guided compressive projection can generate more discriminative features by sufficiently capturing rich local structural information of images second we propose fast directional integration that enables low cost extraction of feasible haar like features from arbitrarily rotated 5 d parameterized rectangles to realize more accurate object localization third beyond naive dense uniform sampling we present two practical online data driven sampling strategies to produce less yet more effective candidate and training samples for object detection and classifier updating respectively extensive experiments on real world benchmark data sets validate the superior performance i e much better object localization ability and robustness of the proposed approach over state of the art trackers

bell type inequalities for quasi copulas we present all bell type inequalities regarding at most four random events of which not more than two are intersected at the same time reformulating these inequalities in the context of fuzzy probability calculus leads to related inequalities on commutative conjunctors we prove that some of these inequalities hold for quasi copulas or copulas additionally for the important parametric family of frank t norms which are also copulas we identify for each of the inequalities the parameter values for which it is fulfilled thereby completing the results of pykacz and d hooghe

a distance metric for a space of linguistic summaries producing linguistic summaries of large databases or temporal sequences of measurements is an endeavor that is receiving increasing attention these summaries can be used in a continuous monitoring situation like eldercare where it is important to ascertain if the current summaries represent an abnormal condition it is therefore necessary to compute the distance between summaries as a basis for such a determination in this paper we propose a dissimilarity measure between summaries based on fuzzy protoforms and prove that this measure is a metric we take into account not only the linguistic meaning of the summaries but also two quality evaluations namely the truth values and the degrees of focus we present examples of how the distance metric behaves and show that it corresponds with intuition

learning dictionary of discriminative part detectors for image categorization and cosegmentation this paper proposes a novel approach to learning mid level image models for image categorization and cosegmentation we represent each image class by a dictionary of part detectors that best discriminate that class from the background we learn category specific part detectors in a weakly supervised setting in which the training images are only annotated with category labels without part object location information we use a latent svm model regularized using the ell 2 1 l2 1 group sparsity norm to learn the part detectors starting from a large set of initial parts the group sparsity regularizer forces the model to jointly select and optimize a set of discriminative part detectors in a max margin framework we propose a stochastic version of a proximal algorithm to solve the corresponding optimization problem we apply the learned part detectors to image classification and cosegmentation and present extensive comparative experiments with standard benchmarks

salient object detection with spatiotemporal background priors for video saliency detection for images has been studied for many years for which a lot of methods have been designed in saliency detection background priors which are often regarded as pseudo background are effective clues to find salient objects in images although image boundary is commonly used as background priors it does not work well for images of complex scenes and videos in this paper we explore how to identify the background priors for a video and propose a saliency based method to detect the visual objects by using the background priors for a video we integrate multiple pairs of scale invariant feature transform flows from long range frames and a bidirectional consistency propagation is conducted to obtain the accurate and sufficient temporal background priors which are combined with spatial background priors to generate spatiotemporal background priors next a novel dual graph based structure using spatiotemporal background priors is put forward in the computation of saliency maps fully taking advantage of appearance and motion information in videos experimental results on different challenging data sets show that the proposed method robustly and accurately detects the video objects in both simple and complex scenes and achieves better performance compared with other the state of the art video saliency models

the fiedler vector of a laplacian tensor for hypergraph partitioning based on recent advances in spectral hypergraph theory l qi and z luo tensor anaysis spectral theory and special tensors siam philadelphia 2017 we explore the fiedler vector of an even uniform hypergraph which is the z eigenvector associated with the second smallest z eigenvalue of a normalized laplacian tensor arising from the hypergraph then we develop a novel tensor based spectral method for partitioning vertices of the hypergraph for this purpose we extend the normalized laplacian matrix of a simple graph to the normalized laplacian tensor of an even uniform hypergraph the corresponding fiedler vector is related to the cheeger constant of the hypergraph then we establish a feasible optimization algorithm to compute the fiedler vector according to the normalized laplacian tensor the convergence of the proposed algorithm and the probability of obtaining the fiedler vector of the hypergraph are analyzed theoretically finally preliminary numerical experiments illustrate that the new a

robust deformable and occluded object tracking with dynamic graph while some efforts have been paid to handle deformation and occlusion in visual tracking they are still great challenges in this paper a dynamic graph based tracker dgt is proposed to address these two challenges in a unified framework in the dynamic target graph nodes are the target local parts encoding appearance information and edges are the interactions between nodes encoding inner geometric structure information this graph representation provides much more information for tracking in the presence of deformation and occlusion the target tracking is then formulated as tracking this dynamic undirected graph which is also a matching problem between the target graph and the candidate graph the local parts within the candidate graph are separated from the background with markov random field and spectral clustering is used to solve the graph matching the final target state is determined through a weighted voting procedure according to the reliability of part correspondence and refined with recourse to a foreground background segmentation an effective online updating mechanism is proposed to update the model allowing dgt to robustly adapt to variations of target structure experimental results show improved performance over several state of the art trackers in various challenging scenarios

weakly supervised part proposal segmentation from multiple images weakly supervised local part segmentation is challenging due to the difficulty of modeling multiple local parts from image level prior in this paper we propose a new weakly supervised local part proposal segmentation method based on the observation that local parts will keep fixed along the object pose variations hence the local part can be segmented by capturing object pose variations based on such observation a new local part proposal segmentation model is proposed three aspects such as shape similarity based cosegmentation shape matching based part detection and segmentation and graph matching based part assignment are considered a part segmentation energy function is first proposed four terms such as mrf based single image segmentation term shape feature based foreground consistency term ncuts based part segmentation term and two order graphs matching based part consistency term are contained then a three sub minimization based energy minimization method is proposed to accomplish approximation solution finally we verify our method based on three image data sets pascal voc 2008 part data set ucb bird data set and cat dog data set and one video data set ucf sports data set the experimental results demonstrate a better segmentation performance compared with the existing object cosegmentation and part proposal generation methods

foreground segmentation with tree structured sparse rpca background subtraction is a fundamental video analysis technique that consists of creation of a background model that allows distinguishing foreground pixels we present a new method in which the image sequence is assumed to be made up of the sum of a low rank background matrix and a dynamic tree structured sparse matrix the decomposition task is then solved using our approximated robust principal component analysis arpca method which is an extension to the rpca that can handle camera motion and noise our model dynamically estimates the support of the foreground regions via a superpixel generation step so that spatial coherence can be imposed on these regions unlike conventional smoothness constraints such as mrf our method is able to obtain crisp and meaningful foreground regions and in general handles large dynamic background motion better to reduce the dimensionality and the curse of scale that is persistent in the rpca based methods we model the background via column subset selection problem that reduces the order of complexity and hence decreases computation time comprehensive evaluation on four benchmark datasets demonstrate the effectiveness of our method in outperforming state of the art alternatives

a bottom up approach for pancreas segmentation using cascaded superpixels and deep image patch labeling robust organ segmentation is a prerequisite for computer aided diagnosis quantitative imaging analysis pathology detection and surgical assistance for organs with high anatomical variability e g the pancreas previous segmentation approaches report low accuracies compared with well studied organs such as the liver or heart we present an automated bottom up approach for pancreas segmentation in abdominal computed tomography ct scans the method generates a hierarchical cascade of information propagation by classifying image patches at different resolutions and cascading segments superpixels the system contains four steps 1 decomposition of ct slice images into a set of disjoint boundary preserving superpixels 2 computation of pancreas class probability maps via dense patch labeling 3 superpixel classification by pooling both intensity and probability features to form empirical statistics in cascaded random forest frameworks and 4 simple connectivity based post processing dense image patch labeling is conducted using two methods efficient random forest classification on image histogram location and texture features and more expensive but more accurate deep convolutional neural network classification on larger image windows i e with more spatial contexts over segmented 2 d ct slices by the simple linear iterative clustering approach are adopted through model parameter calibration and labeled at the superpixel level for positive pancreas or negative non pancreas or background classes the proposed method is evaluated on a data set of 80 manually segmented ct volumes using six fold cross validation its performance equals or surpasses other state of the art methods evaluated by leave one patient out with a dice coefficient of 70 7 and jaccard index of 57 9 in addition the computational efficiency has improved significantly requiring a mere 6 8 min per testing case versus 10 h for other methods the segmentation framework using deep patch labeling confidences is also more numerically stable as reflected in the smaller performance metric standard deviations finally we implement a multi atlas label fusion malf approach for pancreas segmentation using the same data set under six fold cross validation our bottom up segmentation method significantly outperforms its malf counterpart 70 7 13 0 versus 52 51 20 84 in dice coefficients

random forest construction with robust semisupervised node splitting random forest rf is a very important classifier with applications in various machine learning tasks but its promising performance heavily relies on the size of labeled training data in this paper we investigate constructing of rfs with a small size of labeled data and find that the performance bottleneck is located in the node splitting procedures hence existing solutions fail to properly partition the feature space if there are insufficient training data to achieve robust node splitting with insufficient data we present semisupervised splitting to overcome this limitation by splitting nodes with the guidance of both labeled and abundant unlabeled data in particular an accurate quality measure of node splitting is obtained by carrying out the kernel based density estimation whereby a multiclass version of asymptotic mean integrated squared error criterion is proposed to adaptively select the optimal bandwidth of the kernel to avoid the curse of dimensionality we project the data points from the original high dimensional feature space onto a low dimensional subspace before estimation a unified optimization framework is proposed to select a coupled pair of subspace and separating hyperplane such that the smoothness of the subspace and the quality of the splitting are guaranteed simultaneously our algorithm efficiently avoids overfitting caused by bad initialization and local maxima when compared with conventional margin maximization based semisupervised methods we demonstrate the effectiveness of the proposed algorithm by comparing it with state of the art supervised and semisupervised algorithms for typical computer vision applications such as object categorization face recognition and image segmentation on publicly available data sets