288 research outputs found

    Regularized pointwise map recovery from functional correspondence

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    The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases

    Multireference Alignment using Semidefinite Programming

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    The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment problem. Although we show that the MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for the MLE appears to perform quite well in typical instances, outperforming existing methods. In an attempt to explain this behavior we provide stability guarantees for our SDP under a random noise model on the observations. This case is more challenging to analyze than traditional semi-random instances of Unique-Games: the noise model is on vertices of a graph and translates into dependent noise on the edges. Interestingly, we show that if certain positivity constraints in the SDP are dropped, its solution becomes equivalent to performing phase correlation, a popular method used for pairwise alignment in imaging applications. Finally, we show how symmetry reduction techniques from matrix representation theory can simplify the analysis and computation of the SDP, greatly decreasing its computational cost

    Feature Reduction using a Singular Value Decomposition for the Iterative Guided Spectral Class Rejection Hybrid Classifier

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    Feature reduction in a remote sensing dataset is often desirable to decrease the processing time required to perform a classification and improve overall classification accuracy. This work introduces a feature reduction method based on the singular value decomposition (SVD). This feature reduction technique was applied to training data from two multitemporal datasets of Landsat TM/ETM+ imagery acquired over a forested area in Virginia, USA and Rondonia, Brazil. Subsequent parallel iterative guided spectral class rejection (pIGSCR) forest/nonforest classifications were performed to determine the quality of the feature reduction. The classifications of the Virginia data were five times faster using SVDbased feature reduction without affecting the classification accuracy. Feature reduction using the SVD was also compared to feature reduction using principal components analysis (PCA). The highest average accuracies for the Virginia dataset (88.34%) and for the Rondonia dataset (93.31%) were achieved using the SVD. The results presented here indicate that SVDbased feature reduction can produce statistically significantly better classifications than PCA

    A Bayesian alternative to mutual information for the hierarchical clustering of dependent random variables

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    The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering

    A Hybrid Approach of Using Wavelets and Fuzzy Clustering for Classifying Multispectral Florescence In Situ Hybridization Images

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    Multicolor or multiplex fluorescence in situ hybridization (M-FISH) imaging is a recently developed molecular cytogenetic diagnosis technique for rapid visualization of genomic aberrations at the chromosomal level. By the simultaneous use of all 24 human chromosome painting probes, M-FISH imaging facilitates precise identification of complex chromosomal rearrangements that are responsible for cancers and genetic diseases. The current approaches, however, cannot have the precision sufficient for clinical use. The reliability of the technique depends primarily on the accurate pixel-wise classification, that is, assigning each pixel into one of the 24 classes of chromosomes based on its six-channel spectral representations. In the paper we introduce a novel approach to improve the accuracy of pixel-wise classification. The approach is based on the combination of fuzzy clustering and wavelet normalization. Two wavelet-based algorithms are used to reduce redundancies and to correct misalignments between multichannel FISH images. In comparison with conventional algorithms, the wavelet-based approaches offer more advantages such as the adaptive feature selection and accurate image registration. The algorithms have been tested on images from normal cells, showing the improvement in classification accuracy. The increased accuracy of pixel-wise classification will improve the reliability of the M-FISH imaging technique in identifying subtle and cryptic chromosomal abnormalities for cancer diagnosis and genetic disorder research

    Improving quality and combustion control in pyrometallurgical processes using multivariate image analysis of flames

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    La combustion est utilisé dans l’industrie chimique et du traitement des minéraux dans le but de produire de la vapeur dans les chaudières, de sécher les concentrés dans les fours rotatifs, et d’appliquer des traitements thermiques dans les fours pyrométallurgiques. Le contrôle serré de la combustion dans ces fours est très important parce que les conditions de combustion affectent directement la qualité du produit fini. Arriver à un contrôle serré de la combustion n’est pas facile à cause du fait que les flammes qu’on retrouve dans ces industries sont obtenues avec des combustibles non pré-mélangés et aussi parce que la combustion est affectée par des perturbations non-mesurées comme l’utilisation fréquente de plusieurs combustibles, certains étant des sous-produits de l’usine, et de débit et composition variables. Une nouvelle méthode est proposée dans cette étude afin d’améliorer le contrôle de la qualité des produits de ces fours tout en réduisant la consommation de carburants. Cette méthode s’appuie sur l’extraction d’information provenant d’images de flammes. La méthode d’analyse et de régression sur les images multivariées est utilisée pour l’extraction des caractéristiques de couleur de la flamme qui sont ensuite utilisées pour prédire la température de décharge des solides d’un four rotatif (qualité). Cette étude démontre que cette méthode est capable de très bien prédire la température de décharge du solide 20, 40, et jusqu’à 80 minutes dans le futur. Ceci devrait permettre une réduction substantielle de la variabilité de la qualité du produit et de la consommation de combustible.Combustion is used throughout the mineral processing industry to produce steam in boilers, to dry concentrates in rotary dryers, and to apply heat treatments in pyrometallurgical furnaces. Tight combustion control is very important in the latter type of furnace since the combustion conditions directly affect final ore quality. However, achieving tight combustion control is not straightforward since most of the flames encountered in industry are turbulent non-premixed flames, they are affected by several unmeasured disturbances, various flow rates, continuous variation in the mix between fuels since they are often produced by simultaneously burning several types of fuel, some of them coming from other parts of the plant. A novel method is proposed in this study to improve process and product quality control as well as to optimize the combustion conditions based on digital flame color images. Multivariate Image Analysis and Regression is used to extract the flame color characteristics from images to predict the solids discharge temperature of an industrial rotary kiln related to product quality. It is shown that this method yield extremely good 20 minutes, 40 minutes as well as 80 minutes ahead forecasts of the discharge temperature of mineral ore. This should lead to a substantial reduction in product quality variability as well as in fuel consumption

    Statistical Methods for Polarimetric Imagery

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    Estimation theory is applied to a physical model of incoherent polarized light to address problems in polarimetric image registration, restoration, and analysis for electro-optical imaging systems. In the image registration case, the Cramer-Rao lower bound on unbiased joint estimates of the registration parameters and the underlying scene is derived, simplified using matrix methods, and used to explain the behavior of multi-channel linear polarimetric imagers. In the image restoration case, a polarimetric maximum likelihood blind deconvolution algorithm is derived and tested using laboratory and simulated imagery. Finally, a principal components analysis is derived for polarization imaging systems. This analysis expands upon existing research by including an allowance for partially polarized and unpolarized light
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