networked slepian wolf theory algorithms and scaling laws consider a set of correlated sources located at the nodes of a network and a set of sinks that are the destinations for some of the sources the minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered for both the data gathering scenario which is relevant in sensor networks and general traffic matrices relevant for general networks the minimization is achieved by jointly optimizing a the transmission structure which is shown to consist in general of a superposition of trees and b the rate allocation across the source nodes which is done by slepian wolf coding the overall minimization can be achieved in two concatenated steps first the optimal transmission structure is found which in general amounts to finding a steiner tree and second the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure and with linear constraints given by the slepian wolf rate region for the case of data gathering the optimal transmission structure is fully characterized and a closed form solution for the optimal rate allocation is provided for the general case of an arbitrary traffic matrix the problem of finding the optimal transmission structure is np complete for large networks in some simplified scenarios the total costs associated with slepian wolf coding and explicit communication conditional encoding based on explicitly communicated side information are compared finally the design of decentralized algorithms for the optimal rate allocation is analyzed

range image registration using a photometric metric under unknown lighting based on the spherical harmonics representation of image formation we derive a new photometric metric for evaluating the correctness of a given rigid transformation aligning two overlapping range images captured under unknown distant and general illumination we estimate the surrounding illumination and albedo values of points of the two range images from the point correspondences induced by the input transformation we then synthesize the color of both range images using albedo values transferred using the point correspondences to compute the photometric reprojection error this way allows us to accurately register two range images by finding the transformation that minimizes the photometric reprojection error we also propose a practical method using the proposed photometric metric to register pairs of range images devoid of salient geometric features captured under unknown lighting our method uses a hypothesize and test strategy to search for the transformation that minimizes our photometric metric transformation candidates are efficiently generated by employing the spherical representation of each range image experimental results using both synthetic and real data demonstrate the usefulness of the proposed metric

continuous procrustes distance between two surfaces the procrustes distance is used to quantify the similarity or dissimilarity of three dimensional shapes and extensively used in biological morphometrics typically each normalized shape is represented by n landmark points chosen to be homologous as far as possible and the procrustes distance is then computed as where the minimization is over all euclidean transformations and the correspondences are picked in an optimal way the discrete procrustes distance has the drawback that each shape is represented by only a finite number of points which may not capture all the geometric aspects of interest a need has been expressed for alternatives that are still easy to compute we propose in this paper the concept of continuous procrustes distance and prove that it provides a true metric for two dimensional surfaces embedded in three dimensions we also propose an efficient algorithm to calculate approximations to this new distance 2012 wiley periodicals inc

automatic model construction and pose estimation from photographs using triangular splines this paper addresses the automatic construction of complex spline object models from a few photographs our approach combines silhouettes from registered images to construct a g sup 1 continuous triangular spline approximation of an object with unknown topology we apply a similar optimization procedure to estimate the pose of a modeled object from a single image experimental examples of model construction and pose estimation are presented for several complex objects

a continuous linear optimal transport approach for pattern analysis in image datasets we present a new approach to facilitate the application of the optimal transport metric to pattern recognition on image databases the method is based on a linearized version of the optimal transport metric which provides a linear embedding for the images hence it enables shape and appearance modeling using linear geometric analysis techniques in the embedded space in contrast to previous work we use monge s formulation of the optimal transport problem which allows for reasonably fast computation of the linearized optimal transport embedding for large images we demonstrate the application of the method to recover and visualize meaningful variations in a supervised learning setting on several image datasets including chromatin distribution in the nuclei of cells galaxy morphologies facial expressions and bird species identification we show that the new approach allows for high resolution construction of modes of variations and discrimination and can enhance classification accuracy in a variety of image discrimination problems highlightsa continuous version of the lot framework is described that bypasses many of the difficulties associated with the discrete formulation using continuous transport maps a forward and inverse transform operation is defined for images an improved reference average image estimation algorithm is proposed the range within which points in lot space are invertible according to the continuous formulation is calculated we show that our method significantly speeds up the computation of the lot embedding

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

minimum cost distributed source coding over a network this paper considers the problem of transmitting multiple compressible sources over a network at minimum cost the aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be transmitted so that the cost of the transmission is minimal we consider networks with capacity constraints and linear cost functions the problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources this renders general purpose solvers inefficient we present a framework in which these problems can be solved efficiently by exploiting the structure of the feasible rate regions coupled with dual decomposition and optimization techniques such as the subgradient method and the proximal bundle method

feature guided gaussian mixture model with semi supervised em and local geometric constraint for retinal image registration abstract retinal image registration which can be formulated by matching two sets of sparse features extracted from two observed retinal images is a crucial step in the diagnosis and treatment of various eye diseases existing methods suffer from missing true correspondences or do not fully consider local appearance information which causes difficulty in matching low quality retinal images due to insufficient reliable features in addition the relationships between retinal image pairs are usually modeled by linear transformation such as affine transformation which cannot generate accurate alignments in large viewpoint changes due to the nonplanar eyeball surface to address these issues a feature guided gaussian mixture model gmm is proposed for the non rigid registration of retinal images we formulate the problem as an estimation of a feature guided mixture of densities a gmm is fitted to one point set in which the centers of the gaussian densities characterized by spatial positions associated with local appearance descriptors are constrained to coincide with the other point set the problem is solved under a maximum likelihood framework and semi supervised expectation maximization is used to iteratively estimate the feature correspondence and spatial transformation which is initialized by a set of confidential feature matches obtained previously non rigid transformation is specified in a reproducing kernel hilbert space and a local geometric constraint is imposed to establish the transformation estimation for obtaining a meaningful solution a fast implementation based on sparse approximation is also provided and reduces the time complexity from cubic to quadratic moreover we use the edge map which can extract more reliable features as a uniform representation of retinal images experimental results on publicly available retinal images show that our approach is robust in different registration tasks and outperforms several competing approaches especially when data is severely degraded

fast and scalable approximate spectral graph matching for correspondence problems establishing consistent correspondences between two sets of features is a fundamental problem in computer vision this problem can be well formulated as graph matching in which nodes and edges represent feature points and pairwise relationships between feature points respectively spectral matching 19 is the state of the art eigenvector based method for graph matching the spectral matching algorithm has been used successfully for small data but its heavy memory requirement limited the maximum data sizes and contexts it can be used in this paper we propose fasm a fast and scalable approximate spectral matching algorithm the main ideas are twofold first we exploit the redundancy in the data generation process to approximate the affinity matrix with the linear combination of kronecker products between bases and index matrices the bases and index matrices are highly compressed representation of the approximated affinity matrix requiring much smaller memory than in previous works which store the whole affinity matrix second we compute the eigenvector of the approximated affinity matrix using the small bases and index matrices without explicitly materializing the approximated matrix experimental results show that our proposed method is up to 33x faster requiring up to 645x smaller memory than the exact algorithm with little or no loss of accuracy

algorithms to automatically quantify the geometric similarity of anatomical surfaces we describe approaches for distances between pairs of two dimensional surfaces embedded in three dimensional space that use local structures and global information contained in interstructure geometric relationships we present algorithms to automatically determine these distances as well as geometric correspondences this approach is motivated by the aspiration of students of natural science to understand the continuity of form that unites the diversity of life at present scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points landmarks identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists this necessity renders these studies inaccessible to nonmorphologists and causes phenomics to lag behind genomics in elucidating evolutionary patterns unlike other algorithms presented for morphological correspondences our approach does not require any preliminary marking of special features or landmarks by the user it also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster making pairwise comparisons feasible for significantly larger numbers of digitized surfaces we illustrate our approach using three datasets representing teeth and different bones of primates and humans and show that it leads to highly accurate results

an achievable rate region for joint compression and dispersive information routing for networks this paper considers the problem of minimum cost communication of correlated sources over a network with multi ple sinks which consists of distributed source coding followed by routing we introduce a new routing paradigm called dispersive information routing dir wherein the intermediate nodes are allowed to split a packet and forward subsets of the received bits on each of the forward paths this paradigm opens up a rich class of research problems which focus on the interplay between encoding and routing in a network unlike conventional routing methods such as in 1 dir ensures that each sink receives just the information needed to reconstruct the sources it is required to reproduce we demonstrate using simple examples that the proposed approach offers better asymptotic performance than conventional routing techniques we show that under certain assumptions on the cost function the problem of finding the minimum cost under dir essentially reduces to characterizing an achievable rate region for a new multiterminal information theoretic setup while it is possible to derive an achievable region for this setup using prior results from general multiterminal source coding 3 these techniques do not exploit the underlying problem structure and thereby lead to suboptimal regions in this paper we propose a new coding scheme using principles from multiple descriptions encoding 2 and show that it strictly improves upon a corresponding variant of coding scheme in 3 we further show that the new coding scheme achieves the complete rate region for certain special cases of the general setup and thereby achieves the minimum communication cost under this routing paradigm

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

on the repeatability and quality of keypoints for local feature based 3d object retrieval from cluttered scenes 3d object recognition from local features is robust to occlusions and clutter however local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features we present an algorithm for the detection of such keypoints on 3d models and partial views of objects the keypoints are highly repeatable between partial views of an object and its complete 3d model we also propose a quality measure to rank the keypoints and select the best ones for extracting local features keypoints are identified at locations where a unique local 3d coordinate basis can be derived from the underlying surface in order to extract invariant features we also propose an automatic scale selection technique for extracting multi scale and scale invariant features to match objects at different unknown scales features are projected to a pca subspace and matched to find correspondences between a database and query object each pair of matching features gives a transformation that aligns the query and database object these transformations are clustered and the biggest cluster is used to identify the query object experiments on a public database revealed that the proposed quality measure relates correctly to the repeatability of keypoints and the multi scale features have a recognition rate of over 95 for up to 80 occluded objects

optimal mass transport for registration and warping image registration is the process of establishing a common geometric reference frame between two or more image data sets possibly taken at different times in this paper we present a method for computing elastic registration and warping maps based on the monge kantorovich theory of optimal mass transport this mass transport method has a number of important characteristics first it is parameter free moreover it utilizes all of the grayscale data in both images places the two images on equal footing and is symmetrical the optimal mapping from image a to image b being the inverse of the optimal mapping from b to a the method does not require that landmarks be specified and the minimizer of the distance functional involved is uniques there are no other local minimizers finally optimal transport naturally takes into account changes in density that result from changes in area or volume although the optimal transport method is certainly not appropriate for all registration and warping problems this mass preservation property makes the monge kantorovich approach quite useful for an interesting class of warping problems as we show in this paper our method for finding the registration mapping is based on a partial differential equation approach to the minimization of the l2 kantorovich wasserstein or earth mover s distance under a mass preservation constraint we show how this approach leads to practical algorithms and demonstrate our method with a number of examples including those from the medical field we also extend this method to take into account changes in intensity and show that it is well suited for applications such as image morphing

distributed rate distortion with common components we describe a scheme for rate distortion with distributed encoding in which the sources to be compressed contain a common component we show that this scheme is optimal in some situations and that it strictly improves upon existing schemes which do not make full use of common components this establishes that independent quantization followed by independent binning is not optimal for the two encoder problem with a distortion constraint on one source we also show that independent quantization and binning is suboptimal for the three encoder problem in which the goal is to reproduce one of the sources losslessly this provides a counterexample that is fundamentally different from one provided earlier by korner and marton the proofs rely on the binary analogue of the entropy power inequality and the existence of a rate loss for the binary symmetric wyner ziv problem

tracking by detection of 3d human shapes from surfaces to volumes 3d human shape tracking consists in fitting a template model to temporal sequences of visual observations it usually comprises an association step that finds correspondences between the model and the input data and a deformation step that fits the model to the observations given correspondences most current approaches follow the iterative closest point icp paradigm where the association step is carried out by searching for the nearest neighbors it fails when large deformations occur and errors in the association tend to propagate over time in this paper we propose a discriminative alternative for the association that leverages random forests to infer correspondences in one shot regardless the choice of shape parameterizations being surface or volumetric meshes we convert 3d shapes to volumetric distance fields and thereby design features to train the forest we investigate two ways to draw volumetric samples voxels of regular grids and cells from centroidal voronoi tessellation cvt while the former consumes considerable memory and in turn limits us to learn only subject specific correspondences the latter yields much less memory footprint by compactly tessellating the interior space of a shape with optimal discretization this facilitates the use of larger cross subject training databases generalizes to different human subjects and hence results in less overfitting and better detection the discriminative correspondences are successfully integrated to both surface and volumetric deformation frameworks that recover human shape poses which we refer to as tracking by detection of 3d human shapes it allows for large deformations and prevents tracking errors from being accumulated when combined with icp for refinement it proves to yield better accuracy in registration and more stability when tracking over time evaluations on existing datasets demonstrate the benefits with respect to the state of the art

information theoretic shape matching in this paper we describe two related algorithms that provide both rigid and non rigid point set registration with different computational complexity and accuracy the first algorithm utilizes a nonlinear similarity measure known as correntropy the measure combines second and high order moments in its decision statistic showing improvements especially in the presence of impulsive noise the algorithm assumes that the correspondence between the point sets is known which is determined with the surprise metric the second algorithm mitigates the need to establish a correspondence by representing the point sets as probability density functions pdf the registration problem is then treated as a distribution alignment the method utilizes the cauchy schwarz divergence to measure the similarity distance between the point sets and recover the spatial transformation function needed to register them both algorithms utilize information theoretic descriptors however correntropy works at the realizations level whereas cauchy schwarz divergence works at the pdf level this allows correntropy to be less computationally expensive and for correct correspondence more accurate the two algorithms are robust against noise and outliers and perform well under varying levels of distortion they outperform several well known and state of the art methods for point set registration

snapshots a novel local surface descriptor and matching algorithm for robust 3d surface alignment in this paper a novel local surface descriptor is proposed and applied to the problem of aligning partial views of a 3d object the descriptor is based on taking snapshots of the surface over each point using a virtual camera oriented perpendicularly to the surface this representation has the advantage of imposing minimal loss of information be robust to self occlusions and also be very efficient to compute then we describe an efficient search technique to deal with the rotation ambiguity of our representation and experimentally demonstrate the benefits of our approaches which are pronounced especially when we align views with small overlap

the combinatorics of local constraints in model based recognition and localization from sparse data the problem of recognizing what objects are where in the workspace of a robot can be cast as one of searching for a consistent matching between sensory data elements and equivalent model elements in principle this search space is enormous and to control the potential combinatorial explosion constraints between the data and model elements are needed a set of constraints for sparse sensory data that are applicable to a wide variety of sensors are derived and their characteristics are examined known bounds on the complexity of constraint satisfaction problems are used together with explicit estimates of the effectiveness of the constraints derived for the case of sparse noisy three dimensional sensory data to obtain general theoretical bounds on the number of interpretations expected to be consistent with the data it is shown that these bounds are consistent with empirical results reported previously the results are used to demonstrate the graceful degradation of the recognition technique with the presence of noise in the data and to predict the number of data points needed in general to uniquely determine the object being sensed

zonal spherical functions on the complex reflection groups and n 1 m 1 hypergeometric functions abstract the pair of groups complex reflection group g r 1 n and symmetric group s n is a gelfand pair its zonal spherical functions are expressed in terms of multivariate hypergeometric functions called n 1 m 1 hypergeometric functions since the zonal spherical functions have orthogonality they form discrete orthogonal polynomials also shown is a relation between monomial symmetric functions and the n 1 m 1 hypergeometric functions

multiple description coding with many channels an achievable region for the l channel multiple description coding problem is presented this region generalizes two channel results of el gamal and cover 1982 and of zhang and berger 1987 it further generalizes three channel results of gray and wyner 1974 and of zhang and berger a source that is successively refinable on chains is shown to be successively refinable on trees a new outer bound on the rate distortion rd region for memoryless gaussian sources with mean squared error distortion is also derived the achievable region meets this outer bound for certain symmetric cases

a frequency domain technique for range data registration this work introduces an original method for registering pairs of 3d views consisting of range data sets which operates in the frequency domain the fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters our algorithm exploits this well known property by suggesting a three step procedure the rotation parameters are estimated by the first two steps through convenient representations and projections of the fourier transforms magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation the performance of the algorithm which is well suited for unsupervised registration is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3d rigid motion are achievable our algorithm can be used as a prealignment tool for more accurate space domain registration techniques like the icp algorithm

graph connection laplacian methods can be made robust to noise recently several data analytic techniques based on graph connection laplacian gcl ideas have appeared in the literature at this point the properties of these methods are starting to be understood in the setting where the data is observed without noise we study the impact of additive noise on these methods and show that they are remarkably robust as a by product of our analysis we propose modifications of the standard algorithms that increase their robustness to noise we illustrate our results in numerical simulations

robust similarity registration technique for volumetric shapes represented by characteristic functions this paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by characteristic functions cfs here the calculation of rotation parameters is considered as a spherical cross correlation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis pca thus fast fourier transform fft is employed to vastly improve efficiency and robustness geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters it is numerically demonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses further validation of our method is performed by registering a lung database highlightswe propose a similarity registration method that registers volumetric shapes the method naturally handles shapes with topological differences the method is validated by registering a lung database the method can be applied to shape based image segmentation

automatic range image registration in the markov chain in this paper a novel entropy that can describe both long and short tailed probability distributions of constituents of a thermodynamic system out of its thermodynamic limit is first derived from the lyapunov function for a markov chain we then maximize this entropy for the estimation of the probabilities of possible correspondences established using the traditional closest point criterion between two overlapping range images when we change our viewpoint to look carefully at the minimum solution to the probability estimate of the correspondences the iterative range image registration process can also be modeled as a markov chain in which lessons from past experience in estimating those probabilities are learned to impose the two way constraint outliers are explicitly modeled due to the almost ubiquitous occurrence of occlusion appearance and disappearance of points in either image the estimated probabilities of the correspondences are finally embedded into the powerful mean field annealing scheme for global optimization leading the camera motion parameters to be estimated in the weighted least squares sense a comparative study using real images shows that the proposed algorithm usually outperforms the state of the art icp variants and the latest genetic algorithm for automatic overlapping range image registration

fast descriptors and correspondence propagation for robust global point cloud registration in this paper we present a robust global approach for point cloud registration from uniformly sampled points based on eigenvalues and normals computed from multiple scales we design fast descriptors to extract local structures of these points the eigenvalue based descriptor is effective at finding seed matches with low precision using nearest neighbor search generally recovering the transformation from matches with low precision is rather challenging therefore we introduce a mechanism named correspondence propagation to aggregate each seed match into a set of numerous matches with these sets of matches multiple transformations between point clouds are computed a quality function formulated from distance errors is used to identify the best transformation and fulfill a coarse alignment of the point clouds finally we refine the alignment result with the trimmed iterative closest point algorithm the proposed approach can be applied to register point clouds with significant or limited overlaps and small or large transformations more encouragingly it is rather efficient and very robust to noise a comparison to traditional descriptor based methods and other global algorithms demonstrates the fine performance of the proposed approach we also show its promising application in large scale reconstruction with the scans of two real scenes in addition the proposed approach can be used to register low resolution point clouds captured by kinect as well

new results in binary multiple descriptions an encoder whose input is a binary equiprobable memoryless source produces one output of rate r 1 and another of rate r 2 let d 1 d 2 and d 0 respectively denote the average error frequencies with which the source data can be reproduced on the basis of the encoder output of rate r l only the encoder output of rate r 2 only and both encoder outputs the two descriptions problem is to determine the region r of all quintuples r 1 r 2 d 1 d 2 d 0 that are achievable in thc usual shannon sense let r d 1 d log 2 d 1 d log 2 1 d denote the error frequency rate distortion function of the source the no excess rate case prevails when r 1 r 2 r d 0 and the excess rate case when r 1 r 2 r d 0 denote the section of r at r 1 r 2 d 0 by d r 1 r 2 d 0 d 1 d 2 r 1 r 2 d 1 d 2 d 0 in r in the no excess rate case we show that a portion of the boundary of d r 1 r 2 d 0 coincides with the curve frac 1 2 d 1 2d 0 frac 1 2 d 2 2d 0 frac 1 2 1 2d 0 2 this curve is an extension of witsenhausen s hyperbola bound to the case d 0 0 it follows that the projection of r onto the d 1 d 2 plane at fixed d 0 consists of all d 1 geq d 0 and d 2 geq d 0 that lie on or above this hyperbola in the excess rate case we show by counterexample that the achievable region of el gamal and cover is not tight

evaluation of marton s inner bound for the general broadcast channel the best known inner bound on the two receiver general broadcast channel is due to marton however this region is not computable except in certain special cases as no bounds on the cardinality of its auxiliary random variables exist nor is it even clear that the inner bound is a closed set the main obstacle in proving cardinality bounds is the fact that the traditional use of the caratheodory theorem the main known tool for proving cardinality bounds does not yield a finite cardinality result one of the main contributions of this paper is the introduction of a new tool based on an identity that relates the second derivative of the shannon entropy of a discrete random variable under a certain perturbation to the corresponding fisher information in order to go beyond the traditional caratheodory type arguments we identify certain properties that the auxiliary random variables corresponding to the extreme points of the inner bound need to satisfy these properties are then used to establish cardinality bounds on the auxiliary random variables of the inner bound thereby proving the computability of the region and its closedness lastly we establish a conjecture of nair and zizhou that marton s inner bound and the recent outer bound of nair and el gamal do not match in general

articulated and generalized gaussian kernel correlation for human pose estimation in this paper we propose an articulated and generalized gaussian kernel correlation gkc based framework for human pose estimation we first derive a unified gkc representation that generalizes the previous sum of gaussians sog based methods for the similarity measure between a template and an observation both of which are represented by various sog variants then we develop an articulated gkc agkc by integrating a kinematic skeleton in a multivariate sog template that supports subject specific shape modeling and articulated pose estimation for both the full body and the hands we further propose a sequential body hand pose tracking algorithm by incorporating three regularization terms in the agkc function including visibility intersection penalty and pose continuity our tracking algorithm is simple yet effective and computationally efficient we evaluate our algorithm on two benchmark depth data sets the experimental results are promising and competitive when compared with the state of the art algorithms

robust matching of 3d contours using iterative closest point algorithm improved by m estimation abstract an extension of the iterative closest point matching by m estimation is proposed for realization of robustness to non overlapping data or outlying data in two sets of contour data or depth images for rigid bodies an objective function which includes independent residual components for each of x y and z coordinates is originally defined and proposed to evaluate the fitness simultaneously dealing with a distribution of outlying gross noise the proposed procedure is based on modified m estimation iterations with bi weighting coefficients for selecting corresponding points for optimization of estimating the transforms for matching the transforms can be represented by quaternions in the procedure to eliminate redundancy in representation of rotational degree of freedom by linear matrices optimization steps are performed by the simplex method because it does not need computation of differentiation some fundamental experiments utilizing real data of 2d and 3d measurement show effectiveness of the proposed method when reasonable initial positions are given the unique solution of position could be provided in spite of surplus point data in the objects and then the outlying data could be filtered out from the normal ones by the proposed method

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

conformal wasserstein distances comparing surfaces in polynomial time abstract we present a constructive approach to surface comparison realizable by a polynomial time algorithm we determine the similarity of two given surfaces by solving a mass transportation problem between their conformal densities this mass transportation problem differs from the standard case in that we require the solution to be invariant under global mobius transformations we present in detail the case where the surfaces to compare are disk like we also sketch how the approach can be generalized to other types of surfaces

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

achievable rates for multiple descriptions consider a sequence of independent identically distributed i i d random variables x l x 2 cdots x n and a distortion measure d x i x i on the estimates x i of x i two descriptions i x in 1 2 cdots 2 nr 1 and j x in 1 2 cdots 2 nr 2 are given of the sequence x x 1 x 2 cdots x n from these two descriptions three estimates i x x2 j x and hat x o i x j x are formed with resulting expected distortions e frac 1 n sum n k 1 d x k hat x mk d m m 0 1 2 we find that the distortion constraints d 0 d 1 d 2 are achievable if there exists a probability mass distribution p x p hat x 1 hat x 2 hat x 0 x with ed x hat x m leq d m such that r 1 i x hat x 1 r 2 i x hat x 2 where i cdot denotes shannon mutual information these rates are shown to be optimal for deterministic distortion measures

optimal mass transport for shape matching and comparison surface based 3d shape analysis plays a fundamental role in computer vision and medical imaging this work proposes to use optimal mass transport map for shape matching and comparison focusing on two important applications including surface registration and shape space the computation of the optimal mass transport map is based on monge brenier theory in comparison to the conventional method based on monge kantorovich theory this method significantly improves the efficiency by reducing computational complexity from o n 2 to o n for surface registration problem one commonly used approach is to use conformal map to convert the shapes into some canonical space although conformal mappings have small angle distortions they may introduce large area distortions which are likely to cause numerical instability thus resulting failures of shape analysis this work proposes to compose the conformal map with the optimal mass transport map to get the unique area preserving map which is intrinsic to the riemannian metric unique and diffeomorphic for shape space study this work introduces a novel riemannian framework conformal wasserstein shape space by combing conformal geometry and optimal mass transport theory in our work all metric surfaces with the disk topology are mapped to the unit planar disk by a conformal mapping which pushes the area element on the surface to a probability measure on the disk the optimal mass transport provides a map from the shape space of all topological disks with metrics to the wasserstein space of the disk and the pullback wasserstein metric equips the shape space with a riemannian metric we validate our work by numerous experiments and comparisons with prior approaches and the experimental results demonstrate the efficiency and efficacy of our proposed approach

generalized characters of the symmetric group normalized irreducible characters of the symmetric group s n can be understood as zonal spherical functions of the gelfand pair s n s n diags n they form an orthogonal basis in the space of the functions on the group s n invariant with respect to conjugations by s n in this paper we consider a different gelfand pair connected with the symmetric group that is an unbalanced gelfand pair s n s n 1 diags n 1 zonal spherical functions of this gelfand pair form an orthogonal basis in a larger space of functions on s n namely in the space of functions invariant with respect to conjugations by s n 1 we refer to these zonal spherical functions as normalized generalized characters of s n the main discovery of the present paper is that these generalized characters can be computed on the same level as the irreducible characters of the symmetric group the paper gives a murnaghan nakayama type rule a frobenius type formula and an analogue of the determinantal formula for the generalized characters of s n

partial similarity of objects or how to compare a centaur to a horse similarity is one of the most important abstract concepts in human perception of the world in computer vision numerous applications deal with comparing objects observed in a scene with some a priori known patterns often it happens that while two objects are not similar they have large similar parts that is they are partially similar here we present a novel approach to quantify partial similarity using the notion of pareto optimality we exemplify our approach on the problems of recognizing non rigid geometric objects images and analyzing text sequences

surface bounded growth modeling applied to human mandibles from a set of longitudinal three dimensional scans of the same anatomical structure the authors have accurately modeled the temporal shape and size changes using a linear shape model on a total of 31 computed tomography scans of the mandible from six patients 14 851 semilandmarks are found automatically using shape features and a new algorithm called geometry constrained diffusion the semilandmarks are mapped into procrustes space principal component analysis extracts a one dimensional subspace which is used to construct a linear growth model the worst case mean modeling error in a cross validation study is 3 7 mm

adaptively merging large scale range data with reflectance properties in this paper we tackle the problem of geometric and photometric modeling of large intricately shaped objects typical target objects we consider are cultural heritage objects when constructing models of such objects we are faced with several important issues that have not been addressed in the past issues that mainly arise due to the large amount of data that has to be handled we propose two novel approaches to efficiently handle such large amounts of data a highly adaptive algorithm for merging range images and an adaptive nearest neighbor search to be used with the algorithm we construct an integrated mesh model of the target object in adaptive resolution taking into account the geometric and or photometric attributes associated with the range images we use surface curvature for the geometric attributes and laser reflectance values for the photometric attributes this adaptive merging framework leads to a significant reduction in the necessary amount of computational resources furthermore the resulting adaptive mesh models can be of great use for applications such as texture mapping as we will briefly demonstrate additionally we propose an additional test for the k d tree nearest neighbor search algorithm our approach successfully omits back tracking which is controlled adaptively depending on the distance to the nearest neighbor since the main consumption of computational cost lies in the nearest neighbor search the proposed algorithm leads to a significant speed up of the whole merging process in this paper we present the theories and algorithms of our approaches with pseudo code and apply them to several real objects including large scale cultural assets

trace a topological graph representation for automatic sulcal curve extraction a proper geometric representation of the cortical regions is a fundamental task for cortical shape analysis and landmark extraction however a significant challenge has arisen due to the highly variable convoluted cortical folding patterns in this paper we propose a novel topological graph representation for automatic sulcal curve extraction trace in practice the reconstructed surface suffers from noise influences introduced during image acquisition surface reconstruction in the presence of noise on the surface trace determines stable sulcal fundic regions by employing the line simplification method that prevents the sulcal folding pattern from being significantly smoothed out the sulcal curves are then traced over the connected graph in the determined regions by the dijkstra s shortest path algorithm for validation we used the state of the art surface reconstruction pipelines on a reproducibility data set the experimental results showed higher reproducibility and robustness to noise in trace than the existing method li et al 2010 with over 20 relative improvement in error for both surface reconstruction pipelines in addition the extracted sulcal curves by trace were well aligned with manually delineated primary sulcal curves we also provided a choice of parameters to control quality of the extracted sulcal curves and showed the influences of the parameter selection on the resulting curves

hyperbolic harmonic mapping for surface registration automatic computation of surface correspondence via harmonic map is an active research field in computer vision computer graphics and computational geometry it may help document and understand physical and biological phenomena and also has broad applications in biometrics medical imaging and motion capture industries although numerous studies have been devoted to harmonic map research limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints this work conquers this problem by changing the riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints the computational algorithms are based on ricci flow and nonlinear heat diffusion methods the approach is general and robust we employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications experimental results demonstrate that by changing the riemannian metric the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards

on the algebraic combinatorics of injections and its applications to injection codes we consider the algebraic combinatorics of the set of injections from a k element set to an n element set in particular we give a new combinatorial formula for the spherical functions of the gelfand pair s k times s n diag s k times s n k we use this combinatorial formula to give new delsarte linear programming bounds on the size of codes over injections

surface fluid registration of conformal representation application to detect disease burden and genetic influence on hippocampus in this paper we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1 forms inverse consistent surface fluid registration and multivariate tensor based morphometry mtbm first we conformally map a surface onto a planar rectangle space with holomorphic 1 forms second we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface third we align the feature image with a chosen template image via the fluid image registration algorithm which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization the inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images this alignment induces a corresponding deformation on the surface we tested the system on alzheimer s disease neuroimaging initiative adni baseline dataset to study ad symptoms on hippocampus in our system by modeling a hippocampus as a 3d parametric surface we nonlinearly registered each surface with a selected template surface then we used mtbm to analyze the morphometry difference between diagnostic groups experimental results show that the new system has better performance than two publicly available subcortical surface registration tools first and spharm we also analyzed the genetic influence of the apolipoprotein e 4 allele apoe4 which is considered as the most prevalent risk factor for ad our work successfully detected statistically significant difference between apoe4 carriers and non carriers in both patients of mild cognitive impairment mci and healthy control subjects the results show evidence that the apoe genotype may be associated with accelerated brain atrophy so that our work provides a new mri analysis tool that may help presymptomatic ad research

automatic alignment of genus zero surfaces a new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero the algorithm takes as input a pair of surfaces that are topological 2 spheres each surface given by a distinct triangulation the algorithm then constructs a map f between the two surfaces first each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm the two mappings are then composed with a mobius transformation to generate the function f the mobius transformation is chosen by minimizing an energy that measures the distance of f from an isometry we illustrate our approach using several real life data sets we show first that the algorithm allows for accurate automatic and landmark free nonrigid registration of brain surfaces we then validate our approach by comparing shapes of proteins we provide numerical experiments to demonstrate that the distances computed with our algorithm between low resolution surface based representations of proteins are highly correlated with the corresponding distances computed between high resolution atomistic models for the same proteins

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

morphometry of anatomical shape complexes with dense deformations and sparse parameters we propose a generic method for the statistical analysis of collections of anatomical shape complexes namely sets of surfaces that were previously segmented and labeled in a group of subjects the method estimates an anatomical model the template complex that is representative of the population under study its shape reflects anatomical invariants within the dataset in addition the method automatically places control points near the most variable parts of the template complex vectors attached to these points are parameters of deformations of the ambient 3d space these deformations warp the template to each subject s complex in a way that preserves the organization of the anatomical structures multivariate statistical analysis is applied to these deformation parameters to test for group differences results of the statistical analysis are then expressed in terms of deformation patterns of the template complex and can be visualized and interpreted the user needs only to specify the topology of the template complex and the number of control points the method then automatically estimates the shape of the template complex the optimal position of control points and deformation parameters the proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes spikes inconsistent orientation or irregular meshing the approach is illustrated with a neuroimaging study of down syndrome ds the results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and ds subjects the deformation based modelingis able to classify subjects with very high specificity and sensitivity thus showing important generalization capability even given a low sample size we show that the results remain significant even if the number of control points and hence the dimension of variables in the statistical model are drastically reduced the analysis may even suggest that parsimonious models have an increased statistical performance the method has been implemented in the software deformetrica which is publicly available at www deformetrica org

geometric graph matching using monte carlo tree search we present an efficient matching method for generalized geometric graphs such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing or vessel networks in medical imaging graph matching can be used for very fast and possibly multimodal registration of images of these structures we formulate the matching problem as a single player game solved using monte carlo tree search which automatically balances exploring new possible matches and extending existing matches our method can handle partial matches topological differences geometrical distortion does not use appearance information and does not require an initial alignment moreover our method is very efficient it can match graphs with thousands of nodes which is an order of magnitude better than the best competing method and the matching only takes a few seconds

point based rigid body registration using an unscented kalman filter we present and validate a novel registration algorithm mapping two data sets generated from a rigid object in the presence of gaussian noise the proposed method is based on the unscented kalman filter ukf algorithm that is generally employed for analyzing nonlinear systems corrupted by additive gaussian noise first we employ our proposed registration algorithm to fit two randomly generated data sets in the presence of isotropic gaussian noise when the corresponding points between the two data sets are assumed to be known then we extend the registration method to the case where the data with known correspondences is stimulated by anisotropic gaussian noise the new registration method not only reliably converges to the correct registration solution but it also estimates the variance as a confidence measure for each of the estimated registration transformation parameters furthermore we employ the proposed registration algorithm for rigid body point based registration where corresponding points between two registering data sets are unknown the algorithm is tested on point data sets which are garnered from a pelvic cadaver and a scaphoid bone phantom by means of computed tomography ct and tracked free hand ultrasound imaging the collected 3 d points in the ultrasound frame are registered to the 3 d meshes in the ct frame by using the proposed and the standard iterative closest points icp registration algorithms experimental results demonstrate that our proposed method significantly outperforms the icp registration algorithm in the presence of additive gaussian noise it is also shown that the proposed registration algorithm is more robust than the icp registration algorithm in terms of outliers in data sets and initial misalignment between the two data sets

murnaghan nakayama rules for characters of iwahori hecke algebras of classical type in this paper we give murnaghan nakayama type formulas for computing the irreducible characters of the iwahori hecke algebras of types an 1 bn and dn our method is a generalization of a derivation of the murnaghan nakayama formula for the irreducible characters of the symmetric group given by curtis greene greene s approach is to sum up the diagonal entries of the matrices of certain cycle permutations in young s seminormal representations the analogues of the young seminormal representations for the iwahori hecke algebras of types an 1 bn and dn were given by hoefsmit

side information scalable source coding we consider the problem of side information scalable si scalable source coding where the encoder constructs a two layer description such that the receiver with high quality side information will be able to use only the first layer to reconstruct the source in a lossy manner while the receiver with low quality side information will have to receive both layers in order to decode we provide inner and outer bounds to the rate distortion r d region for general discrete memoryless sources the achievable region is tight when either one of the decoders requires a lossless reconstruction and when the distortion measures are degraded and deterministic furthermore the gap between the inner and the outer bounds can be bounded by certain constants when the squared error distortion measure is used the notion of perfect scalability is introduced for which necessary and sufficient conditions are given for sources satisfying a mild support condition using si scalable coding and successive refinement wyner ziv coding as basic building blocks we provide a complete characterization of the rate distortion region for the important quadratic gaussian source with multiple jointly gaussian side informations where the side information quality is not necessarily monotonic along the scalable coding order a partial result is provided for the doubly symmetric binary source under the hamming distortion measure when the worse side information is a constant for which one of the outer bounds is strictly tighter than the other

the tps direct transport a new method for transporting deformations in the size and shape space modern shape analysis allows the fine comparison of shape changes occurring between different objects very often the classic machineries of generalized procrustes analysis and principal component analysis are used in order to contrast the shape change occurring among configurations represented by homologous landmarks however if size and shape data are structured in different groups thus constituting different morphological trajectories a data centering is needed if one wants to compare solely the deformation representing the trajectories to do that inter individual variation must be filtered out this maneuver is rarely applied in studies using simulated or real data a geometrical procedure named parallel transport that can be based on various connection types is necessary to perform such kind of data centering usually the levi civita connection is used for interpolation of curves in a riemannian space it can also be used to transport a deformation we demonstrate that this procedure does not preserve some important characters of the deformation even in the affine case we propose a novel procedure called tps direct transport which is able to perfectly transport deformation in the affine case and to better approximate non affine deformation in comparison to existing tools we recommend to center shape data using the methods described here when the differences in deformation rather than in shape are under study

genus zero surface conformal mapping and its application to brain surface mapping we developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one forms for surfaces with or without boundaries gu and yau 2002 gu and yau 2003 for genus zero surfaces our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map in this paper we apply the algorithm to the cortical surface matching problem we use a mesh structure to represent the brain surface further constraints are added to ensure that the conformal map is unique empirical tests on magnetic resonance imaging mri data show that the mappings preserve angular relationships are stable in mris acquired at different times and are robust to differences in data triangulation and resolution compared with other brain surface conformal mapping algorithms our algorithm is more stable and has good extensibility