structure selective depth superresolution for rgb d cameras this paper describes a method for high quality depth superresolution the standard formulations of image guided depth upsampling using simple joint filtering or quadratic optimization lead to texture copying and depth bleeding artifacts these artifacts are caused by inherent discrepancy of structures in data from different sensors although there exists some correlation between depth and intensity discontinuities they are different in distribution and formation to tackle this problem we formulate an optimization model using a nonconvex regularizer a nonlocal affinity established in a high dimensional feature space is used to offer precisely localized depth boundaries we show that the proposed method iteratively handles differences in structure between depth and intensity images this property enables reducing texture copying and depth bleeding artifacts significantly on a variety of range data sets we also propose a fast alternating direction method of multipliers algorithm to solve our optimization problem our solver shows a noticeable speed up compared with the conventional majorize minimize algorithm extensive experiments with synthetic and real world data sets demonstrate that the proposed method is superior to the existing methods

eigenvalue location for chain graphs abstract chain graphs also called double nested graphs play an important role in the spectral graph theory since every connected bipartite graph of fixed order and size with maximal largest eigenvalue is a chain graph in this paper for a given chain graph g we present an algorithmic procedure for obtaining a diagonal matrix congruent to a x i where a is the adjacency matrix of g and x any real number using this procedure we show that any chain graph has its least positive eigenvalue greater than 1 2 and also prove that this bound is best possible a similar procedure for threshold graphs also called nested split graphs is outlined

a comparison of the bias in four versions of the product limit estimator summary the bias of the product limit estimator depends entirely on the method used to complete the estimator beyond the last observation when it is censored the bias has been investigated for the upper gill 1980 and lower efron 1967 bounds on these methods rather than using a completion method investigators in practice commonly truncate the estimator using data driven rules the bias under two common truncation rules are considered i truncating at the last observation if it is censored and ii truncating at the n l th order statistic a number of inequalities between these biases are derived and properties of the bias functions are proved this investigation shows

stereo matching using tree filtering matching cost aggregation is one of the oldest and still popular methods for stereo correspondence while effective and efficient cost aggregation methods typically aggregate the matching cost by summing averaging over a user specified local support region this is obviously only locally optimal and the computational complexity of the full kernel implementation usually depends on the region size in this paper the cost aggregation problem is re examined and a non local solution is proposed the matching cost values are aggregated adaptively based on pixel similarity on a tree structure derived from the stereo image pair to preserve depth edges the nodes of this tree are all the image pixels and the edges are all the edges between the nearest neighboring pixels the similarity between any two pixels is decided by their shortest distance on the tree the proposed method is non local as every node receives supports from all other nodes on the tree the proposed method can be naturally extended to the time domain for enforcing temporal coherence unlike previous methods the non local property guarantees that the depth edges will be preserved when the temporal coherency between all the video frames are considered a non local weighted median filter is also proposed based on the non local cost aggregation algorithm it has been demonstrated to outperform all local weighted median filters on disparity depth upsampling and refinement

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

a heavy censoring limit theorem for the product limit estimator a key identity for the product limit estimator due to aalen and johansen 1978 and gill 1980 is shown to be a consequence of the exponential formula of doleans dade 1970 the basic counting processes in the censored data problem are shown to converge jointly to poisson processes under heavy censoring g n rightarrow d delta 0 but n 1 g n rightarrow alpha where g n is the censoring distribution the poisson limit theorem for counting processes implies poisson type limit theorems under heavy censoring for the cumulative hazard function estimator and product limit estimator the latter in combination with the key identity of aalen johansen and gill and martingale properties of the limit processes yields a new approximate variance formula for the product limit estimator which is compared numerically with recent finite sample calculations for the case of proportional hazard censoring due to chen hollander and langberg 1982

small sample results for the kaplan meier estimator abstract whereas much is known about the asymptotic properties of the kaplan meier 1958 estimator kme of a survival function exact results for small samples have been difficult to obtain in this article we obtain an exact expression for the th moment 0 of the kme under a model of proportional hazards this enables us under proportional hazards to a study the bias of the kme and b compare the exact variance of the kme to its asymptotic variance

on the eigenvalues of some tridiagonal matrices a solution is given for a problem on eigenvalues of some symmetric tridiagonal matrices suggested by william trench the method presented can be generalizable to other problems

depth superresolution by transduction this paper presents a depth superresolution sr method that uses both of a low resolution lr depth image and a high resolution hr intensity image we formulate depth sr as a graph based transduction problem in particular the hr intensity image is represented as an undirected graph in which pixels are characterized as vertices and their relations are encoded as an affinity function when the vertices initially labeled with certain depth hypotheses from the lr depth image are regarded as input queries all the vertices are scored with respect to the relevances to these queries by a classifying function each vertex is then labeled with the depth hypothesis that receives the highest relevance score we design the classifying function by considering the local and global structures of the hr intensity image this approach enables us to address a depth bleeding problem that typically appears in current depth sr methods furthermore input queries are assigned in a probabilistic manner making depth sr robust to noisy depth measurements we also analyze existing depth sr methods in the context of transduction and discuss their theoretic relations intensive experiments demonstrate the superiority of the proposed method over state of the art methods both qualitatively and quantitatively

the equivalence of half quadratic minimization and the gradient linearization iteration a popular way to restore images comprising edges is to minimize a cost function combining a quadratic data fidelity term and an edge preserving possibly nonconvex regularization term mainly because of the latter term the calculation of the solution is slow and cumbersome half quadratic hq minimization multiplicative form was pioneered by geman and reynolds 1992 in order to alleviate the computational task in the context of image reconstruction with nonconvex regularization by promoting the idea of locally homogeneous image models with a continuous valued line process they reformulated the optimization problem in terms of an augmented cost function which is quadratic with respect to the image and separable with respect to the line process hence the name half quadratic since then a large amount of papers were dedicated to hq minimization and important results including edge preservation along with convex regularization and convergence have been obtained in this paper we show that hq minimization multiplicative form is equivalent to the most simple and basic method where the gradient of the cost function is linearized at each iteration step in fact both methods give exactly the same iterations furthermore connections of hq minimization with other methods such as the quasi newton method and the generalized weiszfeld s method are straightforward

on the adjacency matrix of a threshold graph abstract a threshold graph on n vertices is coded by a binary string of length n 1 we obtain a formula for the inertia of the adjacency matrix of a threshold graph in terms of the code of the graph it is shown that the number of negative eigenvalues of the adjacency matrix of a threshold graph is the number of ones in the code whereas the nullity is given by the number of zeros in the code that are preceded by either a zero or a blank a formula for the determinant of the adjacency matrix of a generalized threshold graph and the inverse when it exists of the adjacency matrix of a threshold graph are obtained results for antiregular graphs follow as special cases

a sparsity promoting image decomposition model for depth recovery abstract this paper proposes a novel image decomposition model for scene depth recovery from low quality depth measurements and its corresponding high resolution color image through our observation the depth map mainly contains smooth regions separated by additive step discontinuities and can be simultaneously decomposed into a local smooth surface and an approximately piecewise constant component therefore the proposed unified model combines the least square polynomial approximation for smooth surface and a sparsity promoting prior for piecewise constant to better portray the 2d depth signal intrinsically as we know the representation of the piecewise constant signal in gradient domain is extremely sparse previous researches using total variation filter based on l1 norm or lp norm 0

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

some new considerations about double nested graphs abstract in the set of all connected graphs with fixed order and size the graphs with maximal index are nested split graphs also called threshold graphs it was recently and independently observed in bell et al 2008 3 and bhattacharya et al 2008 4 that double nested graphs also called bipartite chain graphs play the same role within class of bipartite graphs in this paper we study some structural and spectral features of double nested graphs in studying the spectrum of double nested graphs we rather consider some weighted nonnegative matrices of significantly less order which preserve all positive eigenvalues of former ones moreover their inverse matrices appear to be tridiagonal using this fact we provide several new bounds on the index largest eigenvalue of double nested graphs and also deduce some bounds on eigenvector components for the index we conclude the paper by examining the questions related to main versus non main eigenvalues

fusion of median and bilateral filtering for range image upsampling we present a new upsampling method to enhance the spatial resolution of depth images given a low resolution depth image from an active depth sensor and a potentially high resolution color image from a passive rgb camera we formulate it as an adaptive cost aggregation problem and solve it using the bilateral filter the formulation synergistically combines the median and bilateral filters thus it better preserves the depth edges and is more robust to noise numerical and visual evaluations on a total of 37 middlebury data sets demonstrate the effectiveness of our method a real time high resolution depth capturing system is also developed using commercial active depth sensor based on the proposed upsampling method

graphs for which the least eigenvalue is minimal ii let g be a connected graph whose least eigenvalue g is minimal among the connected graphs of prescribed order and size we show first that either g is complete or g is a simple eigenvalue in the latter case the sign pattern of a corresponding eigenvector determines a partition of the vertex set and we study the structure of g in terms of this partition we find that g is either bipartite or the join of two graphs of a simple form

eigenvalue location in threshold graphs abstract let g be a threshold graph of order n with adjacency matrix a we present an o n algorithm for constructing a diagonal matrix congruent to b x a x i for any x an application using sylvester s law of inertia can determine how many eigenvalues lie in an interval allowing efficient approximation we prove that eigenvalues of threshold graphs other than 0 or 1 are simple we give the spectrum for threshold graphs g k j represented by 0 k 1 j when n 3 g n n 3 n 3 has the minimum eigenvalue min n among threshold graphs of order n and a formula for min n is given there is one more graph if n 2 mod 3

eigenvalue location in graphs of small clique width abstract finding a diagonal matrix congruent to a c i for constants c where a is the adjacency matrix of a graph g allows us to quickly tell the number of eigenvalues in a given interval if g has clique width k and a corresponding k expression is known then diagonalization can be done in time o poly k n where n is the order of g

no threshold graphs are cospectral abstract a threshold graph g on n vertices is defined by binary sequence of length n in this paper we present an explicit formula for computing the characteristic polynomial of a threshold graph from its binary sequence applications include obtaining a formula for the determinant of adjacency matrix of a threshold graph and showing that no two nonisomorphic threshold graphs are cospectral

eigenvalues and energy in threshold graphs abstract assuming a uniform random model of selecting creation sequences we show that almost every connected threshold graph has more negative than positive eigenvalues we show that no threshold graphs have eigenvalues in 1 0 sequences of equienergetic graphs are given including the striking result that for all n 3 there exist n 1 threshold graphs of order n 2 pairwise noncospectral each equienergetic to k n 2 for all n 8 we find an n vertex hyperenergetic threshold graph