Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF), which can obtain reliable and consistent results for real images. Specifically, SDF includes three main parts: a deterministic sampling algorithm, a model hypothesis updating strategy and a novel model selection algorithm. The proposed deterministic sampling algorithm generates a set of initial model hypotheses according to the prior information of superpixels. Then the proposed updating strategy further improves the quality of model hypotheses. After that, by analyzing the properties of the updated model hypotheses, the proposed model selection algorithm extends the conventional "fit-and-remove" framework to estimate model instances in multiple-structure data. The three parts are tightly coupled to boost the performance of SDF in both speed and accuracy, and SDF has the deterministic nature. Experimental results show that the proposed SDF has significant advantages over several state-of-the-art fitting methods when it is applied to real images with single-structure and multiple-structure data.
Deterministic sampling based fitting methods (e.g., @cite_26 @cite_35 @cite_34 @cite_4 @cite_17 @cite_16 ) are able to provide consistent and reliable fitting results. For example, Li @cite_35 used a tailored branch-and-bound scheme to deterministically solve the global optimization problem for model fitting. @cite_26 deterministically generated model hypotheses based on the maximum feasible subsystem framework for model fitting. @cite_34 employed a method for inlier rate estimation to compute a globally optimal transformation for model fitting. @cite_4 extended a branch-and-bound scheme to solve the two-view translation estimation problem. @cite_17 proposed to use loss functions to perform model estimation. @cite_16 used the Astar search algorithm @cite_24 to provide a globally optimal solution for the model fitting problem.
@cite_35 @cite_26 @cite_4 @cite_16 @cite_24 @cite_34 @cite_17
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In this paper, an estimation of distribution algorithm (EDA)-based memetic algorithm (MA) is proposed for solving the distributed assembly permutation flow-shop scheduling problem (DAPFSP) with the objective to minimize the maximum completion time. A novel bi-vector-based method is proposed to represent a solution for the DAPFSP. In the searching phase of the EDA-based MA (EDAMA), the EDA-based exploration and the local-search-based exploitation are incorporated within the MA framework. For the EDA-based exploration phase, a probability model is built to describe the probability distribution of superior solutions. Besides, a novel selective-enhancing sampling mechanism is proposed for generating new solutions by sampling the probability model. For the local-search-based exploitation phase, the critical path of the DAPFSP is analyzed to avoid invalid searching operators. Based on the analysis, a critical-path-based local search strategy is proposed to further improve the potential solutions obtained in the EDA-based searching phase. Moreover, the effect of parameter setting is investigated based on the Taguchi method of design-of-experiment. Suitable parameter values are suggested for instances with different scales. Finally, numerical simulations based on 1710 benchmark instances are carried out. The experimental results and comparisons with existing algorithms show the effectiveness of the EDAMA in solving the DAPFSP. In addition, the best-known solutions of 181 instances are updated by the EDAMA. We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support spl Fscr that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landau's (1967) lower bound equal to the measure of spl Fscr . For signals with sparse spl Fscr , this rate can be much smaller than the Nyquist rate. Unfortunately the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a previous study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with spl Fscr that tiles under translation. For signals with nontiling spl Fscr , which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate. In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly overdamped) Langevin diffusion and establish guarantees on its error measured in the Wasserstein-2 distance. Our guarantees improve or extend the state-of-the-art results in three directions. First, we provide an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size. This result has the advantage of being horizon free (we do not need to know in advance the target precision) and to improve by a logarithmic factor the corresponding result for the constant step-size. Second, we study the case where accurate evaluations of the gradient of the log-density are unavailable, but one can have access to approximations of the aforementioned gradient. In such a situation, we consider both deterministic and stochastic approximations of the gradient and provide an upper bound on the sampling error of the first-order LMC that quantifies the impact of the gradient evaluation inaccuracies. Third, we establish upper bounds for two versions of the second-order LMC, which leverage the Hessian of the log-density. We nonasymptotic guarantees on the sampling error of these second-order LMCs. These guarantees reveal that the second-order LMC algorithms improve on the first-order LMC in ill-conditioned settings. In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10 –20 selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates. We consider the problem of the reconstruction of a continuous-time function f(x) spl isin H from the samples of the responses of m linear shift-invariant systems sampled at 1 m the reconstruction rate. We extend Papoulis' generalized sampling theory in two important respects. First, our class of admissible input signals (typ. H=L sub 2 ) is considerably larger than the subspace of band-limited functions. Second, we use a more general specification of the reconstruction subspace V( spl psi ), so that the output of the system can take the form of a band-limited function, a spline, or a wavelet expansion. Since we have enlarged the class of admissible input functions, we have to give up Shannon and Papoulis' principle of an exact reconstruction. Instead, we seek an approximation f spl isin V( spl psi ) that is consistent in the sense that it produces exactly the same measurements as the input of the system. This leads to a generalization of Papoulis' sampling theorem and a practical reconstruction algorithm that takes the form of a multivariate filter. In particular, we show that the corresponding system acts as a projector from H onto V( spl psi ). We then propose two complementary polyphase and modulation domain interpretations of our solution. The polyphase representation leads to a simple understanding of our reconstruction algorithm in terms of a perfect reconstruction filter bank. The modulation analysis, on the other hand, is useful in providing the connection with Papoulis' earlier results for the band-limited case. Finally, we illustrate the general applicability of our theory by presenting new examples of interlaced and derivative sampling using splines. Abstract Modifications of Prony's classical technique for estimating rate constants in exponential fitting problems have many contemporary applications. In this article the consistency of Prony's method and of related algorithms based on maximum likelihood is discussed as the number of observations n → ∞ by considering the simplest possible models for fitting sums of exponentials to observed data. Two sampling regimes are relevant, corresponding to transient problems and problems of frequency estimation, each of which is associated with rather different kinds of behavior. The general pattern is that the stronger results are obtained for the frequency estimation problem. However, the algorithms considered are all scaling dependent and consistency is not automatic. A new feature that emerges is the importance of an appropriate choice of scale in order to ensure consistency of the estimates in certain cases. The tentative conclusion is that algorithms referred to as Objective function Reweighting Algorithms ... We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances. Our analysis allows the number of controls to be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "post-double-selection" method. Our results apply to Lasso-type methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates. Identifying the underlying model in a set of data contaminated by noise and outliers is a fundamental task in computer vision. The cost function associated with such tasks is often highly complex, hence in most cases only an approximate solution is obtained by evaluating the cost function on discrete locations in the parameter (hypothesis) space. To be successful at least one hypothesis has to be in the vicinity of the solution. Due to noise hypotheses generated by minimal subsets can be far from the underlying model, even when the samples are from the said structure. In this paper we investigate the feasibility of using higher than minimal subset sampling for hypothesis generation. Our empirical studies showed that increasing the sample size beyond minimal size ( @math ), in particular up to @math , will significantly increase the probability of generating a hypothesis closer to the true model when subsets are selected from inliers. On the other hand, the probability of selecting an all inlier sample rapidly decreases with the sample size, making direct extension of existing methods unfeasible. Hence, we propose a new computationally tractable method for robust model fitting that uses higher than minimal subsets. Here, one starts from an arbitrary hypothesis (which does not need to be in the vicinity of the solution) and moves until either a structure in data is found or the process is re-initialized. The method also has the ability to identify when the algorithm has reached a hypothesis with adequate accuracy and stops appropriately, thereby saving computational time. The experimental analysis carried out using synthetic and real data shows that the proposed method is both accurate and efficient compared to the state-of-the-art robust model fitting techniques. This paper presents a novel improved RANSAC algorithm based on probability and DS evidence theory to deal with the robust pose estimation in robot 3D map building. In this proposed RANSAC algorithm, a parameter model is estimated by using a random sampling test set. Based on this estimated model, all points are tested to evaluate the fitness of current parameter model and their probabilities are updated by using a total probability formula during the iterations. The maximum size of inlier set containing the test point is taken into account to get a more reliable evaluation for test points by using DS evidence theory. Furthermore, the theories of forgetting are utilized to filter out the unstable inliers and improve the stability of the proposed algorithm. In order to boost a high performance, an inverse mapping sampling strategy is adopted based on the updated probabilities of points. Both the simulations and real experimental results demonstrate the feasibility and effectiveness of the proposed algorithm. We propose a robust fitting framework, called Adaptive Kernel-Scale Weighted Hypotheses (AKSWH), to segment multiple-structure data even in the presence of a large number of outliers. Our framework contains a novel scale estimator called Iterative Kth Ordered Scale Estimator (IKOSE). IKOSE can accurately estimate the scale of inliers for heavily corrupted multiple-structure data and is of interest by itself since it can be used in other robust estimators. In addition to IKOSE, our framework includes several original elements based on the weighting, clustering, and fusing of hypotheses. AKSWH can provide accurate estimates of the number of model instances and the parameters and the scale of each model instance simultaneously. We demonstrate good performance in practical applications such as line fitting, circle fitting, range image segmentation, homography estimation, and two--view-based motion segmentation, using both synthetic data and real images. Recently, it was shown that it is possible to develop exact sampling schemes for a large class of parametric nonbandlimited signals, namely certain signals of finite rate of innovation. A common feature of such signals is that they have a finite number of degrees of freedom per unit of time and can be reconstructed from a finite number of uniform samples. In order to prove sampling theorems, considered the case of deterministic, noiseless signals and developed algebraic methods that lead to perfect reconstruction. However, when noise is present, many of those schemes can become ill-conditioned. In this paper, we revisit the problem of sampling and reconstruction of signals with finite rate of innovation and propose improved, more robust methods that have better numerical conditioning in the presence of noise and yield more accurate reconstruction. We analyze, in detail, a signal made up of a stream of Diracs and develop algorithmic tools that will be used as a basis in all constructions. While some of the techniques have been already encountered in the spectral estimation framework, we further explore preconditioning methods that lead to improved resolution performance in the case when the signal contains closely spaced components. For classes of periodic signals, such as piecewise polynomials and nonuniform splines, we propose novel algebraic approaches that solve the sampling problem in the Laplace domain, after appropriate windowing. Building on the results for periodic signals, we extend our analysis to finite-length signals and develop schemes based on a Gaussian kernel, which avoid the problem of ill-conditioning by proper weighting of the data matrix. Our methods use structured linear systems and robust algorithmic solutions, which we show through simulation results. One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales rows columns of data matrices to reduce the data size before performing computations on the subproblem. This method has been successful in improving computational efficiency of algorithms for matrix problems such as least-squares approximation, least absolute deviations approximation, and low-rank matrix approximation. Existing work has focused on algorithmic issues such as worst-case running times and numerical issues associated with providing high-quality implementations, but none of it addresses statistical aspects of this method. In this paper, we provide a simple yet effective framework to evaluate the statistical properties of algorithmic leveraging in the context of estimating parameters in a linear regression model with a fixed number of predictors. In particular, for several versions of leverage-based sampling, we derive results for the bias and variance, both conditional and unconditional on the observed data. We show that from the statistical perspective of bias and variance, neither leverage-based sampling nor uniform sampling dominates the other. This result is particularly striking, given the well-known result that, from the algorithmic perspective of worst-case analysis, leverage-based sampling provides uniformly superior worst-case algorithmic results, when compared with uniform sampling. Based on these theoretical results, we propose and analyze two new leveraging algorithms: one constructs a smaller least-squares problem with "shrinkage" leverage scores (SLEV), and the other solves a smaller and unweighted (or biased) least-squares problem (LEVUNW). A detailed empirical evaluation of existing leverage-based methods as well as these two new methods is carried out on both synthetic and real data sets. The empirical results indicate that our theory is a good predictor of practical performance of existing and new leverage-based algorithms and that the new algorithms achieve improved performance. For example, with the same computation reduction as in the original algorithmic leveraging approach, our proposed SLEV typically leads to improved biases and variances both unconditionally and conditionally (on the observed data), and our proposed LEVUNW typically yields improved unconditional biases and variances. Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of @math functions over a convex constraint set @math where both @math and @math are large. In such problems, sub-sampling as a way to reduce @math can offer great amount of computational efficiency. Within the context of second order methods, we first give quantitative local convergence results for variants of Newton's method where the Hessian is uniformly sub-sampled. Using random matrix concentration inequalities, one can sub-sample in a way that the curvature information is preserved. Using such sub-sampling strategy, we establish locally Q-linear and Q-superlinear convergence rates. We also give additional convergence results for when the sub-sampled Hessian is regularized by modifying its spectrum or Levenberg-type regularization. Finally, in addition to Hessian sub-sampling, we consider sub-sampling the gradient as way to further reduce the computational complexity per iteration. We use approximate matrix multiplication results from randomized numerical linear algebra (RandNLA) to obtain the proper sampling strategy and we establish locally R-linear convergence rates. In such a setting, we also show that a very aggressive sample size increase results in a R-superlinearly convergent algorithm. While the sample size depends on the condition number of the problem, our convergence rates are problem-independent, i.e., they do not depend on the quantities related to the problem. Hence, our analysis here can be used to complement the results of our basic framework from the companion paper, [38], by exploring algorithmic trade-offs that are important in practice. We propose a shape-based, hierarchical part-template matching approach to simultaneous human detection and segmentation combining local part-based and global shape-template-based schemes. The approach relies on the key idea of matching a part-template tree to images hierarchically to detect humans and estimate their poses. For learning a generic human detector, a pose-adaptive feature computation scheme is developed based on a tree matching approach. Instead of traditional concatenation-style image location-based feature encoding, we extract features adaptively in the context of human poses and train a kernel-SVM classifier to separate human nonhuman patterns. Specifically, the features are collected in the local context of poses by tracing around the estimated shape boundaries. We also introduce an approach to multiple occluded human detection and segmentation based on an iterative occlusion compensation scheme. The output of our learned generic human detector can be used as an initial set of human hypotheses for the iterative optimization. We evaluate our approaches on three public pedestrian data sets (INRIA, MIT-CBCL, and USC-B) and two crowded sequences from Caviar Benchmark and Munich Airport data sets. One central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the net-utility-the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning-is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem, which has a separable structure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the net-utility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of well-conditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions In this paper, we propose a new algorithm for pairwise rigid point set registration with unknown point correspondences. The main properties of our method are noise robustness, outlier resistance and global optimal alignment. The problem of registering two point clouds is converted to a minimization of a nonlinear cost function. We propose a new cost function based on an inverse distance kernel that significantly reduces the impact of noise and outliers. In order to achieve a global optimal registration without the need of any initial alignment, we develop a new stochastic approach for global minimization. It is an adaptive sampling method which uses a generalized BSP tree and allows for minimizing nonlinear scalar fields over complex shaped search spaces like, e.g., the space of rotations. We introduce a new technique for a hierarchical decomposition of the rotation space in disjoint equally sized parts called spherical boxes. Furthermore, a procedure for uniform point sampling from spherical boxes is presented. Tests on a variety of point sets show that the proposed registration method performs very well on noisy, outlier corrupted and incomplete data. For comparison, we report how two state-of-the-art registration algorithms perform on the same data sets. We present a novel probabilistic approach for fitting a statistical model to an image. A 3D Morphable Model (3DMM) of faces is interpreted as a generative (Top-Down) Bayesian model. Random Forests are used as noisy detectors (Bottom-Up) for the face and facial landmark positions. The Top-Down and Bottom-Up parts are then combined using a Data-Driven Markov Chain Monte Carlo Method (DDMCMC). As core of the integration, we use the Metropolis-Hastings algorithm which has two main advantages. First, the algorithm can handle unreliable detections and therefore does not need the detectors to take an early and possible wrong hard decision before fitting. Second, it is open for integration of various cues to guide the fitting process. Based on the proposed approach, we implemented a completely automatic, pose and illumination invariant face recognition application. We are able to train and test the building blocks of our application on different databases. The system is evaluated on the Multi-PIE database and reaches state of the art performance. A constructive solution of the irregular sampling problem for band- limited functions is given. We show how a band-limited function can be com- pletely reconstructed from any random sampling set whose density is higher than the Nyquist rate, and give precise estimates for the speed of convergence of this iteration method. Variations of this algorithm allow for irregular sampling with derivatives, reconstruction of band-limited functions from local averages, and irregular sampling of multivariate band-limited functions. In the irregular sampling problem one is asked whether and how a band- limited function can be completely reconstructed from its irregularly sam- pled values f(xi). This has many applications in signal and image processing, seismology, meteorology, medical imaging, etc. Finding constructive solutions of this problem has received considerable attention among mathematicians and engineers. The mathematical literature provides several uniqueness results (1, 2, 17, 18, 19). It is now part of the folklore that for stable sampling the sampling rate must be at least the Nyquist rate (18). These results, as deep as they are, have had little impact for the applied sciences, because they were not constructive. If the sampling set is just a perturbation of the regular oversampling, then a reconstruction method has been obtained in a seminal paper by Duffin and Schaeffer (6) (see also (29)): if for some L > 0, a > 0, and o > 0 the sampling points xk , k e Z , satisfy (a) - ok a, k ^ I, then the norm equivalence A iR (x) ) with w < n o. This norm equivalence implies that it is possible to reconstruct through an iterative procedure, the so-called frame method. Most of the later work on constructive methods consists of variations of this method (3, 21, 22, 26). The above conditions on the sampling set exclude random irregular sampling sets, e.g., sets with regions of higher sampling density. A partial, but undesirable remedy, to handle highly irregular sampling sets, would be to force the above conditions by throwing away information on part of the points and accept a very slow convergence of the iteration. Currently, unsupervised heterogeneous domain adaptation in a generalized setting, which is the most common scenario in real-world applications, is under insufficient exploration. Existing approaches either are limited to special cases or require labeled target samples for training. This paper aims to overcome these limitations by proposing a generalized framework, named as transfer independently together (TIT). Specifically, we learn multiple transformations, one for each domain (independently) , to map data onto a shared latent space, where the domains are well aligned. The multiple transformations are jointly optimized in a unified framework (together) by an effective formulation. In addition, to learn robust transformations, we further propose a novel landmark selection algorithm to reweight samples, i.e., increase the weight of pivot samples and decrease the weight of outliers. Our landmark selection is based on graph optimization. It focuses on sample geometric relationship rather than sample features. As a result, by abstracting feature vectors to graph vertices, only a simple and fast integer arithmetic is involved in our algorithm instead of matrix operations with float point arithmetic in existing approaches. At last, we effectively optimize our objective via a dimensionality reduction procedure. TIT is applicable to arbitrary sample dimensionality and does not need labeled target samples for training. Extensive evaluations on several standard benchmarks and large-scale datasets of image classification, text categorization and text-to-image recognition verify the superiority of our approach. We introduce efficient margin-based algorithms for selective sampling and filtering in binary classification tasks. Experiments on real-world textual data reveal that our algorithms perform significantly better than popular and similarly efficient competitors. Using the so-called Mammen-Tsybakov low noise condition to parametrize the instance distribution, and assuming linear label noise, we show bounds on the convergence rate to the Bayes risk of a weaker adaptive variant of our selective sampler. Our analysis reveals that, excluding logarithmic factors, the average risk of this adaptive sampler converges to the Bayes risk at rate N ?(1+?)(2+?) 2(3+?) where N denotes the number of queried labels, and ?>0 is the exponent in the low noise condition. For all @math this convergence rate is asymptotically faster than the rate N ?(1+?) (2+?) achieved by the fully supervised version of the base selective sampler, which queries all labels. Moreover, for ??? (hard margin condition) the gap between the semi- and fully-supervised rates becomes exponential.