Model-fitting Problem Research Articles

Radiation-Variation Insensitive Coarse-to-Fine Image Registration for Infrared and Visible Remote Sensing Based on Zero-Shot Learning

Infrared and visible remote sensing image registration is significant for utilizing remote sensing images to obtain scene information. However, it is difficult to establish a large number of correct matches due to the difficulty in obtaining similarity metrics due to the presence of radiation variation between heterogeneous sensors, which is caused by different imaging principles. In addition, the existence of sparse textures in infrared images as well as in some scenes and the small number of relevant trainable datasets also hinder the development of this field. Therefore, we combined data-driven and knowledge-driven methods to propose a Radiation-variation Insensitive, Zero-shot learning-based Registration (RIZER). First, RIZER, as a whole, adopts a detector-free coarse-to-fine registration framework, and the data-driven methods use a Transformer based on zero-shot learning. Next, the knowledge-driven methods are embodied in the coarse-level matches, where we adopt the strategy of seeking reliability by introducing the HNSW algorithm and employing a priori knowledge of local geometric soft constraints. Then, we simulate the matching strategy of the human eye to transform the matching problem into a model-fitting problem and employ a multi-constrained incremental matching approach. Finally, after fine-level coordinate fine tuning, we propose an outlier culling algorithm that only requires very few iterations. Meanwhile, we propose a multi-scene infrared and visible remote sensing image registration dataset. After testing, RIZER achieved a correct matching rate of 99.55% with an RMSE of 1.36 and had an advantage in the number of correct matches, as well as a good generalization ability for other multimodal images, achieving the best results when compared to some traditional and state-of-the-art multimodal registration algorithms.

Sparse Signal Models for Data Augmentation in Deep Learning ATR

Automatic target recognition (ATR) algorithms are used to classify a given synthetic aperture radar (SAR) image into one of the known target classes by using the information gleaned from a set of training images that are available for each class. Recently, deep learning methods have been shown to achieve state-of-the-art classification accuracy if abundant training data are available, especially if they are sampled uniformly over the classes and in their poses. In this paper, we consider the ATR problem when a limited set of training images are available. We propose a data-augmentation approach to incorporate SAR domain knowledge and improve the generalization power of a data-intensive learning algorithm, such as a convolutional neural network (CNN). The proposed data-augmentation method employs a physics-inspired limited-persistence sparse modeling approach, which capitalizes on the commonly observed characteristics of wide-angle synthetic aperture radar (SAR) imagery. Specifically, we fit over-parametrized models of scattering to limited training data, and use the estimated models to synthesize new images at poses and sub-pixel translations that are not available in the given data in order to augment the limited training data. We exploit the sparsity of the scattering centers in the spatial domain and the smoothly varying structure of the scattering coefficients in the azimuthal domain to solve the ill-posed problem of the over-parametrized model fitting. The experimental results show that, for the training on the data-starved regions, the proposed method provides significant gains in the resulting ATR algorithm’s generalization performance.

A Maximally Split and Adaptive Relaxed Alternating Direction Method of Multipliers for Regularized Extreme Learning Machines

One of the significant features of extreme learning machines (ELMs) is their fast convergence. However, in the big data environment, the ELM based on the Moore–Penrose matrix inverse still suffers from excessive calculation loads. Leveraging the decomposability of the alternating direction method of multipliers (ADMM), a convex model-fitting problem can be split into a set of sub-problems which can be executed in parallel. Using a maximally splitting technique and a relaxation technique, the sub-problems can be split into multiple univariate sub-problems. On this basis, we propose an adaptive parameter selection method that automatically tunes the key algorithm parameters during training. To confirm the effectiveness of this algorithm, experiments are conducted on eight classification datasets. We have verified the effectiveness of this algorithm in terms of the number of iterations, computation time, and acceleration ratios. The results show that the method proposed by this paper can greatly improve the speed of data processing while increasing the parallelism.

Improved model fitting approaches under ranked set sampling schemes with application to forest data

In this paper, we address the problem of fitting probabilistic models based on several sampling designs that originated from the ranked set sampling (RSS) scheme. Although these sampling designs have been proved to be efficient and/or economical alternatives to simple random sampling (SRS) and RSS, the problem of model fitting still should be properly studied for a complete understanding of their advantages. In this study, we investigated the performance of eight RSS-based designs, among them the recently proposed modified neoteric RSS (Taconeli & Cabral, 2019), combined with six estimation methods in model fitting. Through extensive simulations, we could identify the combinations that provided higher efficiency. The simulated results showed that the RSS-based designs outperformed SRS in model fitting, whereas the Anderson-Darling and maximum product of spacings were the most efficient among the estimation methods. In addition, the Anderson-Darling and maximum product of spacings estimation, combined with the neoteric RSS design and its variants, allowed the highest efficiency under both perfectand imperfect ranking. Additional simulations based on real data set from a forest inventory corroborated these findings.

A Model-Independent Characterisation of Strong Gravitational Lensing by Observables

When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie in its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly distorted images of the source are observed. This strong gravitational lensing effect has so far been treated as a model-fitting problem. Using the observed multiple images as constraints yields a self-consistent model of the deflecting mass density and the source object. As several models meet the constraints equally well, we develop a lens characterisation that separates data-based information from model assumptions. The observed multiple images allow us to determine local properties of the deflecting mass distribution on any mass scale from one simple set of equations. Their solution is unique and free of model-dependent degeneracies. The reconstruction of source objects can be performed completely model-independently, enabling us to study galaxy evolution without a lens-model bias. Our approach reduces the lens and source description to its data-based evidence that all models agree upon, simplifies an automated treatment of large datasets, and allows for an extrapolation to a global description resembling model-based descriptions.

Hypergraph Optimization for Multi-Structural Geometric Model Fitting

Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However, a hypergraph becomes extremely complicated when the input data include a large number of data points (usually contaminated with noises and outliers), which will significantly increase the computational burden. In order to overcome the above problem, we propose a novel hypergraph optimization based model fitting (HOMF) method to construct a simple but effective hypergraph. Specifically, HOMF includes two main parts: an adaptive inlier estimation algorithm for vertex optimization and an iterative hyperedge optimization algorithm for hyperedge optimization. The proposed method is highly efficient, and it can obtain accurate model fitting results within a few iterations. Moreover, HOMF can then directly apply spectral clustering, to achieve good fitting performance. Extensive experimental results show that HOMF outperforms several state-of-the-art model fitting methods on both synthetic data and real images, especially in sampling efficiency and in handling data with severe outliers.

Fast and highly efficient pseudo-likelihood methodology for large and complex ordinal data.

In longitudinal studies, continuous, binary, categorical, and survival outcomes are often jointly collected, possibly with some observations missing. However, when it comes to modeling responses, the ordinal ones have received less attention in the literature. In a longitudinal or hierarchical context, the univariate proportional odds mixed model (POMM) can be regarded as an instance of the generalized linear mixed model (GLMM). When the response of the joint multivariate model encompass ordinal responses, the complexity further increases. An additional problem of model fitting is the size of the collected data. Pseudo-likelihood based methods for pairwise fitting, for partitioned samples and, as introduced in this paper, pairwise fitting within partitioned samples allow joint modeling of even larger numbers of responses. We show that that pseudo-likelihood methodology allows for highly efficient and fast inferences in high-dimensional large datasets.

A statistical shape model of the human second cervical vertebra.

Statistical shape and appearance models play an important role in reducing the segmentation processing time of a vertebra and in improving results for 3D model development. Here, we describe the different steps in generating a statistical shape model (SSM) of the second cervical vertebra (C2) and provide the shape model for general use by the scientific community. The main difficulties in its construction are the morphological complexity of the C2 and its variability in the population. The input dataset is composed of manually segmented anonymized patient computerized tomography (CT) scans. The alignment of the different datasets is done with the procrustes alignment on surface models, and then, the registration is cast as a model-fitting problem using a Gaussian process. A principal component analysis (PCA)-based model is generated which includes the variability of the C2. The SSM was generated using 92 CT scans. The resulting SSM was evaluated for specificity, compactness and generalization ability. The SSM of the C2 is freely available to the scientific community in Slicer (an open source software for image analysis and scientific visualization) with a module created to visualize the SSM using Statismo, a framework for statistical shape modeling. The SSM of the vertebra allows the shape variability of the C2 to be represented. Moreover, the SSM will enable semi-automatic segmentation and 3D model generation of the vertebra, which would greatly benefit surgery planning.

Using evolutionary algorithms for model-based clustering

In mixture model-based clustering, parameter estimation is generally carried out using the expectation–maximization algorithm, or some closely related variant. We present a new approach by casting the model-fitting problem as a single-objective evolutionary algorithm that focuses on searching the cluster-membership space. The appeal of an evolutionary algorithm is its ability to more thoroughly search the parameter space, providing an approach inherently more robust with respect to local maxima. This approach is illustrated through application to both simulated and real clustering data sets where comparisons are drawn with traditional model-fitting algorithms.

Computational auditory induction as a missing-data model-fitting problem with Bregman divergence

The human auditory system has the ability, known as auditory induction, to estimate the missing parts of a continuous auditory stream briefly covered by noise and perceptually resynthesize them. In this article, we formulate this ability as a model-based spectrogram analysis and clustering problem with missing data, show how to solve it using an auxiliary function method, and explain how this method is generally related to the expectation–maximization (EM) algorithm for a certain type of divergence measures called Bregman divergences, thus enabling the use of prior distributions on the parameters. We illustrate how our method can be used to simultaneously analyze a scene and estimate missing information with two algorithms: the first, based on non-negative matrix factorization (NMF), performs analysis of polyphonic multi-instrumental musical pieces. Our method allows this algorithm to cope with gaps within the audio data, estimating the timbre of the instruments and their pitch, and reconstructing the missing parts. The second, based on a recently introduced technique for the analysis of complex acoustical scenes called harmonic-temporal clustering (HTC), enables us to perform robust fundamental frequency estimation from incomplete speech data.

Stable Iterative Methods for the Inversion of Geophysical Data

Interpretation of earth electrical measurements can often be assisted by inversion, which is a non-linear model-fitting problem in these cases. Iterative methods are normally used, and the solution is defined by ‘best fit’ in the sense of generalized least-squares. The inverse problems we describe are ill-posed. That is, small changes in the data can lead to large changes in both the solution and in the iterative process that finds the solution. Through an analysis of the problem, based on local linearization, we define a class of methods that stabilize the iteration, and provide a robust solution. These methods are seen as generalizations of the well-known Singular Value Truncation and Marquardt Methods of iterative inversion. Here, and in a companion paper, we give examples illustrating the successful application of the method to ill-posed problems relating to the resistivity of the Earth.

A New Platform for Modeling Ferroelectric Devices

High-performance models are required during the design (phase) of sensing devices in order to take their physical behavior into account and to include these models in calculations and simulations aimed at optimizing the performance of devices in fixed operating conditions. In this paper, the problem of model fitting for ferroelectric devices is addressed; in particular, a model of the behavior of a ferroelectric capacitor is accomplished. The static behavior of such devices is investigated, and an experimental setup for both characterization and model estimation is proposed. The model obtained is assessed, and the uncertainty introduced by the measurement system is estimated

An efficient statistical method for subpixel optical flow detection

In this paper, we show that the randomized sampling and voting process detects optical flow. We introduce a random sampling method for solving the least-squares model-fitting problem using a mathematical property for the construction of pseudo-inverse. Using an appropriate number of images from a sequence of images, our method detects subpixel motion in this sequence. It is possible to compute subpixel motions from a long-time interval. We use the accumulator space for the unification of these flow vectors which are computed from different time intervals. Numerical examples for the test image sequences show the performance of our method.

Evolution of the discrepancy between a universe and its model

We study a fundamental issue in cosmology: whether we can rely on a cosmological model to understand the real history of the Universe. This fundamental, still unresolved issue is often called the ‘model-fitting problem (or averaging problem) in cosmology’. Here we analyse this issue with the help of the spectral scheme prepared in the preceding studies. Choosing two specific spatial geometries \U0001d4a2, and, \U0001d4a2′ that are very close to each other, we investigate explicitly the time evolution of the spectral distance between them; as two spatial geometries \U0001d4a2, and, \U0001d4a2′, we choose a flat 3-torus and a perturbed geometry around it, mimicking the relation of a ‘model universe’ and the ‘real Universe’. Then we estimate the spectral distance between them, dN(\U0001d4a2, \U0001d4a2′), and investigate its time evolution explicitly. This analysis is done efficiently by making use of the basic results of the standard linear structure-formation theory. We observe that, as far as the linear approximation of the geometrical perturbation is valid, dN(\U0001d4a2, \U0001d4a2′) does not increase with time prominently, rather it shows a tendency to decrease. This result is compatible with the general belief in the reliability of describing the Universe by means of a model and calls for more detailed studies along the same lines including the investigation of a wider class of spacetimes and analysis beyond the linear regime.

Spectral evolution of the Universe

We derive the evolution equations for the spectra of the Universe. Here "spectra" means the eigenvalues of the Laplacian defined on a space, which contain the geometrical information on the space. These equations are expected to be useful to analyze the evolution of the geometrical structures of the Universe. As an application, we investigate the time evolution of the spectral distance between two Universes that are very close to each other; it is the first necessary step for the detailed analysis of the model-fitting problem in cosmology with the spectral scheme. We find out a universal formula for the spectral distance between two very close Universes, which turns out to be independent of the detailed form of the distance nor the gravity theory. Then we investigate its time evolution with the help of the evolution equations we derive. We also formulate the criteria for a good cosmological model in terms of the spectral distance.

An inverse problem approach to optical homodyne tomography

The problem of optical homodyne tomography is considered in the context of a Bayesian model-fitting or inverse problem approach. An algorithm is formulated, based on matrix computation rather than the numerical approximation of an analytic inverse transform. This automatically takes into account the effects of noise, detector inefficiencies and incomplete sampling of the data. The relationships with conventional reconstruction schemes, methods for including various forms of prior information and for calculating error estimates are discussed. The process of reconstructing the photon number distribution and the density matrix are illustrated using both simulated and experimental data.

MODEL SELECTION AND ORDER DETERMINATION FOR TIME SERIES BY INFORMATION BETWEEN THE PAST AND THE FUTURE

Abstract. In this paper, the information between the past and the future of a Gaussian stationary sequence is calculated either by its spectral density or by its autocovariances, and is related to the problem of model fitting. It is demonstrated that the criterion of minimum mutual information is the generalization of that of maximum entropy. By employing the above information quantity, we propose a procedure, which is called LIC for simplicity, to obtain consistent estimate of the order of the Bloomfield model or the autoregressive model. In Monte Carlo studies, we illustrate the LIC procedure by several examples, and also estimate the spectral density of time series by the Bloomfield model and LIC method.

Bayesian analysis of time-domain magnetic resonance signals

Although the discrete Fourier transform remains the dominant means of processing NMR data (l-4), other methods of analyzing time-domain signals exist (5), and there has been recent interest among magnetic resonance scientists in applying alternative analysis techniques in an effort to improve signal-to-noise and resolution of the resulting frequency-domain spectrum. Recently, Bretthorst (6) and Jaynes ( 7) introduced a novel approach to the general time-domain signal analysis problem utilizing the techniques of Bayesian probability theory. Their approach is particularly suited to the class of time-domain signals characteristic of pulsed magnetic resonance spectroscopy, namely, a sum of decaying sinusoids. An especially attractive feature of Bayesian spectrum analysis lies in its ability to integrate out of the parameteroptimization-search procedure many of the parameters that define the model (socalled “nuisance” parameters), This greatly reduces the complexity of the optimization-search process. These nuisance parameters, such as sinusoid amplitude and phase, are then readily estimated, if needed, once the primary model parameters (e.g., frequencies and decay rates) are found via standard optimization-search algorithms. In this communication we demonstrate the application of Bayesian spectrum analysis to a time-domain (Bloch decay) 13C NMR signal from a standard ASTM reference sample of 1,4-dioxane in benzenede. Generally, a substantial amount of prior information is available regarding the “true” signal resulting from an NMR experiment. Making use of this information ought to improve our results. However, simply taking the Fourier transform of the data affords no way to take it into account. This information can be incorporated advantageously into the time-domain analysis, yielding a more powerful parameter determination. In the Bayesian spectrum-analysis and parameter-estimation technique, one analyzes the data in terms of some model which expresses the prior information. The data are fitted to the model using probability theory to obtain the “best” estimated parameters. The residuals are then reviewed to see if there is any coherent characteristic that has not been accounted for in the model. If there is, the model is updated and the entire process repeated until all coherent characteristics are removed from the residuals, that is, until the data accurately map onto the model. The Bayesian analysis gives a simple and elegant interpretation to the model-fitting problem and places the discrete Fourier transform in a new light. When fitting data to a model, the data may be thought of as a vector in an N-dimensional vector space

Square root covariance ladder algorithms

Square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting. A simplified derivation of the general update formulas for such ladder forms is presented, and is used to develop the growing memory and sliding memory covariance ladder algorithms. New ladder form realizations for the identified models are presented, leading to convenient methods for computing the model parameters from estimated reflection coefficients. A complete solution to the problem of possible singularity in the ladder update equations is also presented.

Estimating quartz fabrics from piezoelectric measurements

An aggregate of piezoelectric minerals may itself be piezoelectric if the minerals are suitably aligned. Thus quartz-bearing rocks may be piezoelectric, since quartz is one such mineral. It has been shown that some rocks do possess this effect, termed a piezoelectric fabric (Bishop, 1981). The type of piezoelectric fabric may be determined by matching experimental data to theoretical models of piezoelectric fabrics. These theoretical models of pure quartz aggregates are derived by considering the symmetry of the preferred crystallographic directions of the aggregate grains. From the symmetry, the piezoelectric matrix of the model may be determined. The best-fitting model and the orientation of its fabric is obtained by equating the experimental data to each model in turn. For each model, the best fitting fabric orientation is determined by using an inversion routine. If the experimental data are due to a piezoelectric fabric and not to some random or nonpolar distribution of grains, the fabric type (c-axis point maximum or large-circle girdle) and its orientation with respect to the specimen may be determined. The positions and polarities of the quartz a-axes are also specified. A statistical examination of results from a quartz-mylonite shows that the problem of piezoelectric model fitting is well posed, in that the Eulerian angles that specify the fabric orientation are fairly independent “important” parameters and a sufficiently close fit of the model to the data can be obtained to determine the fabric.