Global Consistency Constraints Research Articles

3D reconstruction from cryo-EM projection images using two spherical embeddings

Single-particle analysis (SPA) in cryo-electron microscopy has become a powerful tool for determining and studying the macromolecular structure at an atomic level. However, since the SPA problem is a non-convex optimization problem with enormous search space and there is high level of noise in the input images, the existing methods may produce biased or even wrong final models. In this work, to deal with the problem, consistent constraints from the input data are explored in an embedding space, a 3D spherical surface. More specifically, the orientation of a projection image is represented by two intersection points of the normal vector and the local X-axis vector of the projection image on the unit spherical surface. To determine the orientations of the projection images, the global consistency constraints of the relative orientations of all the projection images are satisfied by two spherical embeddings which estimate the normal vectors and the local X-axis vectors of the projection images respectively. Compared to the traditional methods, the proposed method is shown to be able to rectify the initial computation errors and produce a more accurate estimation of the projection angles, which results in a better final model reconstruction from the noisy image data.

Surface Map Homology Inference

AbstractA homeomorphism between two surfaces not only defines a (continuous and bijective) geometric correspondence of points but also (by implication) an identification of topological features, i.e. handles and tunnels, and how the map twists around them. However, in practice, surface maps are often encoded via sparse correspondences or fuzzy representations that merely approximate a homeomorphism and are therefore inherently ambiguous about map topology. In this work, we show a way to infer topological information from an imperfect input map between two shapes. In particular, we compute a homology map, a linear map that transports homology classes of cycles from one surface to the other, subject to a global consistency constraint. Our inference robustly handles imperfect (e.g., partial, sparse, fuzzy, noisy, outlier‐ridden, non‐injective) input maps and is guaranteed to produce homology maps that are compatible with true homeomorphisms between the input shapes. Homology maps inferred by our method can be directly used to transfer homological information between shapes, or serve as foundation for the construction of a proper homeomorphism guided by the input map, e.g., via compatible surface decomposition.

Toward semantic image inpainting: where global context meets local geometry

Image inpainting attempts to fill the missing areas of an image with plausible content that is visually coherent with the image context. Semantic image inpainting has remained a challenging task even with the emergence of deep learning-based approaches. We propose a deep semantic inpainting model built upon a generative adversarial network and a dense U-Net network. Such a design helps achieve feature reuse while avoiding feature explosion along the upsampling path of the U-Net. The model also uses a composite loss function for the generator network to enforce a joint global and local content consistency constraint. More specifically, our new loss function combines the global reconstruction loss characterizing the semantic similarity between the missing and known image regions with the local total variation loss characterizing the natural transitions among adjacent regions. Experimental results on CelebA-HQ and Paris StreetView datasets have demonstrated encouraging performance when compared with other state-of-the-art methods in terms of both quantitative and qualitative metrics. For the CelebA-HQ dataset, the proposed method can more faithfully infer the semantics of human faces; for the StreetView dataset, our method achieves improved inpainting results in terms of more natural texture transitions, better structural consistency, and enriched textural details.

Online collaborative filtering with local and global consistency

Collaborative Filtering (CF) is one of the most popular technologies used in online recommendation systems. Most of the existing CF studies focus on the offline algorithms, a major drawback of these algorithms is the lack of ability to use the latest user feedbacks to update the learned model in realtime, due to the high cost of the offline training procedure. In this work, we propose Logo, an online CF algorithm. Our proposed method is based on a hierarchical generative model, with which, we derive a set of local and global consistency constraints for the prediction targets, and eventually obtain the design of the learning algorithm. We conduct comprehensive experiments to evaluate the proposed algorithm, the results show that: (1) Under the online setting, our algorithm achieves notably better prediction results than the benchmark algorithms; (2) Under the offline setting, our algorithm attains comparable accurate prediction results with the best performed competitors; (3) In all the experiments, our algorithm performs tens or even hundreds of times faster than the comparison algorithms.

Transferred Knowledge Aided Positioning via Global and Local Structural Consistency Constraints

The fluctuation of received signal strength (RSS) induced by changing environment is the main hindrance from practical applications of the fingerprint-based indoor positioning methods. Transfer learning can mitigate the fluctuation of RSS by transferring knowledge from a source domain (off-line RSS data) to a target domain (online RSS data). However, the existing transfer learning approaches do not fully take into account the full constraints in Global and LOcal Structural conSistency (GLOSS), thus resulting in insufficient knowledge transfer. To overcome the above drawback, we propose a Transferred knowlEdge-Aided POsiTioning (TEAPOT) approach via GLOSS constraints in this paper. TEAPOT imposes the global structural consistency by minimizing the differences between the marginal and conditional distributions of the source and target domains and maximizing the samples variance in a latent subspace. Simultaneously, it also imposes the local structural consistency by minimizing within class variance and maximizing between class variance to retain the source discriminative information and preserving the local neighborhood relationship by using manifold regularization. Furthermore, a nonlinear TEAPOT is derived to improve the ability of TEAPOT to alleviate the limitation of linear projection. Compared with the existing methods, two of our proposed TEAPOT approaches via GLOSS constraints show higher accuracy and better ability in handling out-of-sample generalization. The experimental results verify that the proposed method significantly outperforms the existing methods.

Group-Based Asynchronous Distributed Alternating Direction Method of Multipliers in Multicore Cluster

The distributed alternating direction method of multipliers (ADMM) algorithm is one of the effective methods to solve the global consensus optimization problem. Considering the differences between the communication of intra-nodes and inter-nodes in multicore cluster, we propose a group-based asynchronous distributed ADMM (GAD-ADMM) algorithm: based on the traditional star topology network, the grouping layer is added. The workers are grouped according to the process allocation in nodes and model similarity of datasets, and the group local variables are used to replace the local variables to compute the global variable. The algorithm improves the communication efficiency of the system by reducing communication between nodes and accelerates the convergence speed by relaxing the global consistency constraint. Finally, the algorithm is used to solve the logistic regression problem in a multicore cluster. The experiments on the Ziqiang 4000 showed that the GAD-ADMM reduces the system time cost by 35 % compared with the AD-ADMM.

Projection learning with local and global consistency constraints for scene classification

Besides the problem of high within-class variation and between-class ambiguity in high spatial resolution (HSR) remote sensing images, the dimension of data representation is very high, which poses a challenge for scene classification. To achieve high scene classification performance, it is important to uncover a discriminative subspace for data representation and scene classification. In this paper, we propose a projection learning framework with local and global consistency constraints for aerial scene classification. During the learning process, the within-class compactness and between-class separation of the data representation are enforced. To guarantee the subspace to be locally smooth, we obtain the local geometric structures of data including the similarity of features and geospatial adjacency of image patches. We utilize the global label consistency constraint to enforce the discrimination of the subspace. To make the projection optimal for classification, the projection learning with local and global constraints is integrated with the classification error to form a unified objective function. An efficient iteration algorithm is employed to solve the objective function. Experimental results demonstrate the superior performance of our method over state-of-the-art algorithms on aerial scene classification tasks.

Hierarchical motion consistency constraint for efficient geometrical verification in UAV stereo image matching

This paper proposes a strategy for efficient geometrical verification in unmanned aerial vehicle (UAV) image matching. First, considering the complex transformation model between correspondence set in the image-space, feature points of initial candidate matches are projected onto an elevation plane in the object-space, with assistant of UAV flight control data and camera mounting angles. Spatial relationships are simplified as a 2D-translation, in which a motion establishes the relation of two correspondence points. Second, a hierarchical motion consistency constraint, termed HMCC, is designed to eliminate outliers from initial candidate matches, which includes three major steps, namely the global direction consistency constraint, the local direction-change consistency constraint and the global length consistency constraint. To cope with scenarios with high outlier ratios, the HMCC is achieved by using a voting scheme. Finally, an efficient geometrical verification strategy is proposed by using the HMCC as a pre-processing step to increase inlier ratios before the consequent application of the basic RANSAC algorithm. The performance of the proposed strategy is verified through comprehensive comparison and analysis by using real UAV datasets captured with different photogrammetric systems. Experimental results demonstrate that the generated motions have noticeable separation ability, and the HMCC-RANSAC algorithm can efficiently eliminate outliers based on the motion consistency constraint, with a speedup ratio reaching to 6 for oblique UAV images. Even though the completeness sacrifice of approximately 7% of points is observed from image orientation tests, competitive orientation accuracy is achieved from all used datasets. For geometrical verification of both nadir and oblique UAV images, the proposed method can be a more efficient solution.

Cluster-based image super-resolution via jointly low-rank and sparse representation

In this paper, we propose a novel algorithm for single image super-resolution by developing a concept of cluster rather than using patch as the basic unit. For the proposed algorithm, all patches are splitted into numerous subspaces, and the optimal representation problem is solved with jointly low-rank and sparse regularization for each subspace. By enforcing global consistency constraint of each subspace with nuclear norm regularization and capturing local linear structure of each patch with ℓ1-norm regularization, effective matching functions for test and exemplar patches can be created. Accordingly, the desirable results with low computational complexity are obtained. Experimental results show that the proposed algorithm generates high-quality images in comparison with other state-of-the-art methods.

Tight Relaxation of Quadratic Matching

AbstractEstablishing point correspondences between shapes is extremely challenging as it involves both finding sets of semantically persistent feature points, as well as their combinatorial matching. We focus on the latter and consider the Quadratic Assignment Matching (QAM) model. We suggest a novel convex relaxation for this NP‐hard problem that builds upon a rank‐one reformulation of the problem in a higher dimension, followed by relaxation into a semidefinite program (SDP). Our method is shown to be a certain hybrid of the popular spectral and doubly‐stochastic relaxations of QAM and in particular we prove that it is tighter than both.Experimental evaluation shows that the proposed relaxation is extremely tight: in the majority of our experiments it achieved the certified global optimum solution for the problem, while other relaxations tend to produce sub‐optimal solutions. This, however, comes at the price of solving an SDP in a higher dimension. Our approach is further generalized to the problem of Consistent Collection Matching (CCM), where we solve the QAM on a collection of shapes while simultaneously incorporating a global consistency constraint. Lastly, we demonstrate an application to metric learning of collections of shapes.

Symmetric smoothing filters from global consistency constraints.

Many patch-based image denoising methods can be viewed as data-dependent smoothing filters that carry out a weighted averaging of similar pixels. It has recently been argued that these averaging filters can be improved using their doubly stochastic approximation, which are symmetric and stable smoothing operators. In this paper, we introduce a simple principle of consistency that argues that the relative similarities between pixels as imputed by the averaging matrix should be preserved in the filtered output. The resultant consistency filter has the theoretically desirable properties of being symmetric and stable, and is a generalized doubly stochastic matrix. In addition, we can also interpret our consistency filter as a specific form of Laplacian regularization. Thus, our approach unifies two strands of image denoising methods, i.e., symmetric smoothing filters and spectral graph theory. Our consistency filter provides high-quality image denoising and significantly outperforms the doubly stochastic version. We present a thorough analysis of the properties of our proposed consistency filter and compare its performance with that of other significant methods for image denoising in the literature.

A Scale Independent Selection Process for 3D Object Recognition in Cluttered Scenes

During the last years a wide range of algorithms and devices have been made available to easily acquire range images. The increasing abundance of depth data boosts the need for reliable and unsupervised analysis techniques, spanning from part registration to automated segmentation. In this context, we focus on the recognition of known objects in cluttered and incomplete 3D scans. Locating and fitting a model to a scene are very important tasks in many scenarios such as industrial inspection, scene understanding, medical imaging and even gaming. For this reason, these problems have been addressed extensively in the literature. Several of the proposed methods adopt local descriptor-based approaches, while a number of hurdles still hinder the use of global techniques. In this paper we offer a different perspective on the topic: We adopt an evolutionary selection algorithm that seeks global agreement among surface points, while operating at a local level. The approach effectively extends the scope of local descriptors by actively selecting correspondences that satisfy global consistency constraints, allowing us to attack a more challenging scenario where model and scene have different, unknown scales. This leads to a novel and very effective pipeline for 3D object recognition, which is validated with an extensive set of experiments and comparisons with recent techniques at the state of the art.

Multiview Metric Learning with Global Consistency and Local Smoothness

In many real-world applications, the same object may have different observations (or descriptions) from multiview observation spaces, which are highly related but sometimes look different from each other. Conventional metric-learning methods achieve satisfactory performance on distance metric computation of data in a single-view observation space, but fail to handle well data sampled from multiview observation spaces, especially those with highly nonlinear structure. To tackle this problem, we propose a new method called Multiview Metric Learning with Global consistency and Local smoothness (MVML-GL) under a semisupervised learning setting, which jointly considers global consistency and local smoothness. The basic idea is to reveal the shared latent feature space of the multiview observations by embodying global consistency constraints and preserving local geometric structures. Specifically, this framework is composed of two main steps. In the first step, we seek a global consistent shared latent feature space, which not only preserves the local geometric structure in each space but also makes those labeled corresponding instances as close as possible. In the second step, the explicit mapping functions between the input spaces and the shared latent space are learned via regularized locally linear regression. Furthermore, these two steps both can be solved by convex optimizations in closed form. Experimental results with application to manifold alignment on real-world datasets of pose and facial expression demonstrate the effectiveness of the proposed method.

Discarding wide baseline mismatches with global and local transformation consistency

A novel method called global and local transformation consistency constraints, which combines the scale, orientation and spatial layout information of ‘scale invariant feature transform’ (SIFT) features, is proposed for discarding mismatches from given putative point correspondences. Experiments show that the proposed method can efficiently extract high-precision matches from low-precision putative SIFT matches for wide baseline image pairs, and outperforms or performs close to state-of-the-art approaches.

Improving Strand Pairing Prediction through Exploring Folding Cooperativity

The topology of beta-sheets is defined by the pattern of hydrogen-bonded strand pairing. Therefore, predicting hydrogen bonded strand partners is a fundamental step towards predicting beta-sheet topology. At the same time, finding the correct partners is very difficult due to long range interactions involved in strand pairing. Additionally, patterns of amino acids involved, in beta-sheet formations are very general and therefore difficult to use for computational recognition of specific contacts between strands. In this work, we report a new strand pairing algorithm. To address above mentioned difficulties, our algorithm attempts to mimic elements of the folding process. Namely, in addition to ensuring that the predicted hydrogen bonded strand pairs satisfy basic global consistency constraints, it takes into account hypothetical folding pathways. Consistently with this view, introducing hydrogen bonds between a pair of strands changes the probabilities of forming hydrogen bonds between other pairs of strand. We demonstrate that this approach provides an improvement over previously proposed algorithms. We also compare the performance of this method to that of a global optimization algorithm that poses the problem as integer linear programming optimization problem and solves it using ILOG CPLEX package.

Theoretical description of phase coexistence in model C60.

We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.

Computing on anonymous networks with sense of direction

Sense of direction refers to a set of global consistency constraints of the local labeling of the edges of a network. Sense of direction has a large impact on the communication complexity of many distributed problems. In this paper, we study the impact that sense of direction has on computability and we focus on anonymous networks. We establish several results. In particular, we prove that with weak sense of direction, the intuitive knowledge-computability hierarchy between levels of a priori structural knowledge collapses. A powerful implication is the formal proof that shortest path routing is possible in anonymous networks with sense of direction. We prove that weak sense of direction is computationally stronger than topological awareness. We also consider several fundamental problems; for each, we provide a complete characterization of the anonymous networks on which it is computable with sense of direction.

A model of binocular stereopsis including a global consistency constraint.

The binocular correspondence problem was solved by implementing the uniqueness constraint and the continuity constraint, as proposed by Marr and Poggio [Marr D, PoggioT (1976) Science 194: 283-287]. However, these constraints are not sufficient to define the proper correspondence uniquely. With these constraints, random-dot stereograms (RDSs), consisting of the periodic textures in each image, are treated as a correspondence of surfaces composed of patches of alternating values of disparity. This is quite different from the surface we perceive through the RDSs, that is a surface characterized by a single depth. Because these constraints are local, they cannot produce the global optimum of correspondence. To obtain the global optimum of correspondence, we propose a model of binocular stereopsis in which a global measure of correspondence is explicitly employed. The model consists of two hierarchical systems. First, the lower system processes various correspondences based on the uniqueness constraint. Second, the higher system provides a global measure of correspondence for the disparity in question. The higher system uniquely determines the global optimum of correspondence in the lower system through the recurrent loop between hierarchical systems. The convergence of the recurrent loop is determined by the consistency between the hierarchical systems. The condition is termed the 'global consistency constraint.

Minimal sense of direction in regular networks

A network is said to have Sense of Direction when the port labeling satisfies a particular set of global consistency constraints. In this paper we study the link between the topology of a system and the number of labels that are necessary to have a Sense of Direction in that system. We consider systems whose topology is a regular graph and we study the relationship between structural properties of d-regular graphs and existence of a Sense of Direction which uses exactly d labels ( minimal SD). In particular, we identify a property ( cycle symmetricity) which we show is a necessary condition for minimal SD. Among regular graphs, we then focus on Cayley graphs and we prove that they always have a minimal Sense of Direction.