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C. Walter - One of the best experts on this subject based on the ideXlab platform.
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ICASSP - Signal compression model interrelationships in the time, frequency, principal component and Canonical Coordinate domains
ICASSP '82. IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: C. Walter, J. TardelliAbstract:This paper describes the use of a Canonical signal compression and modelling technique that permits the minimization of certain non-euclidean types of signal resynthesis error criteria. The technique is based on the construction of a non-orthogonal transformation from the original sampled signal representation, in either the time, frequency or spatial domain, to a special Canonical Coordinate domain. The parameters characterizing this transformation are then chosen to minimize the specified error criterion, for each level of truncation of the Canonical Coordinate based signal representation. A mechanism for factoring this Canonical Coordinate transformation into an eigenvector-eigenvalue based correlation simplification process and an error metric simplification process, is described. This mechanism is shown to involve principal component (or Loeve-Karhunen) analysis as an intermediate step in the complete Canonical Coordinate determination process, and can lead to a substantial simplification in the computational complexity that is entailed in handling a class of non-euclidean error criteria.
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ICASSP - Geometrical characterization of the Canonical Coordinate basis underlying a family of error minimizing signal compression techniques
ICASSP '79. IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: C. WalterAbstract:A geometrical interpretation is used to illustrate the interrelationships that exist between autoregressive analysis, principal component analysis, and certain Canonical Coordinate-based non-euclidean error minimization procedures. The generalized eigenvector approach to these error minimization problems has a geometrical characterization, in N-space, that provides insight into their performance. This applies to the error bound interrelationships that exist between these signal representation procedures and also to the stability of the error minimizing transformation coefficients obtained from the different procedures. The geometrical interpretation also provides insight into the effects of eigenvalue degeneracy in introducing ambiguities into the analysis coefficient determination process.
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ICASSP - Application of Canonical Coordinate methods to the characterization of a family of error minimizing signal compression techniques
ICASSP '78. IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: C. WalterAbstract:Mean-square-error minimizing signal compression techniques, such as Autoregressive Analysis or Linear Predictive Coding and Principal Component or Karhunen-Loeve Analysis, can be systematically characterized in terms of Canonical Coordinate or generalized eigenvector procedures. This approach provides considerable insight into the interrelationships between a variety of seemingly different signal compression methods. The approach also provides a convenient mechanism for introducing the types of non-Euclidean error measures that are needed to adjust the signal performance optimization criteria to take into account different types of a priori statistical and dynamical information relating to both the desired signal and to various interference processes.
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ICASSP - A speech waveform analysis and reconstruction process based on non-euclidean error minimization and matrix array procesing techniques
ICASSP '86. IEEE International Conference on Acoustics Speech and Signal Processing, 1Co-Authors: J. Tardelli, C. WalterAbstract:This paper describes the implementation of a matrix array processor oriented technique that can transform time sampled speech waveform data, by way of the frequency domain, into a psendo-Canonical Coordinate domain whose components can be ordered in such a manner as to commit the smallest signal reconstruction error, relative to a given non-euclidean quadratic error criterion, when certain ordered components are not used in the reconstruction process. The error metric can be specified, in either the time or frequency domain, in the form of a complex valued hermitian matrix, thus allowing a very large number of degrees of freedom that can be used to incorporate certain statistical, dynamical and psychoacoustic attributes of the speech data into the analysis and reconstruction process. For the case of a simple euclidean error metric, the pseudo-Canonical Coordinate process is shown to reduce to the well known principal component, or Loeve-Karhunen, signal representation technique.
Andrzej Derdzinski - One of the best experts on this subject based on the ideXlab platform.
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connections with skew symmetric ricci tensor on surfaces
Results in Mathematics, 2008Co-Authors: Andrzej DerdzinskiAbstract:Some known results on torsionfree connections with skew-symmetric Ricci tensor on surfaces are extended to connections with torsion, and Wong’s Canonical Coordinate form of such connections is simplified.
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Connections with Skew-Symmetric Ricci Tensor on Surfaces
Results in Mathematics, 2008Co-Authors: Andrzej DerdzinskiAbstract:Some known results on torsionfree connections with skew-symmetric Ricci tensor on surfaces are extended to connections with torsion, and Wong's Canonical Coordinate form of such connections is simplified.Comment: 22 page
Iasonas Kokkinos - One of the best experts on this subject based on the ideXlab platform.
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Deforming Autoencoders: Unsupervised Disentangling of Shape and Appearance
2018Co-Authors: Zhixin Shu, Mihir Sahasrabudhe, Rıza Güler, Dimitris Samaras, Nikos Paragios, Iasonas KokkinosAbstract:In this work we introduce Deforming Autoencoders, a generative model for images that disentangles shape from appearance in an unsupervised manner. As in the deformable template paradigm, shape is represented as a deformation between a Canonical Coordinate system ('template') and an observed image, while appearance is modeled in 'Canonical', template, Coordinates, thus discarding variability due to deformations. We introduce novel techniques that allow this approach to be deployed in the setting of autoencoders and show that this method can be used for unsupervised group-wise image alignment. We show experiments with expression morphing in humans, hands, and digits, face manipulation, such as shape and appearance interpolation, as well as unsupervised landmark local-ization. A more powerful form of unsupervised disentangling becomes possible in template Coordinates, allowing us to successfully decompose face images into shading and albedo, and further manipulate face images. Latent Representation Input Image Generated Deformation Generated Texture Decoder Decoder Spatial Warping Reconstructed Image Encoder Fig. 1. Deforming Autoencoders follow the deformable template paradigm and model image generation through a cascade of appearance (or, 'texture') synthesis in a Canonical Coordinate system and a spatial deformation that warps the texture to the observed image Coordinates. By keeping the latent vector for texture short the network is forced to model shape variability through the deformation branch, so as to minimize a reconstruction loss. This allows us to train a deep gen-erative image model that disentangles shape and appearance in an entirely unsupervised manner.
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deforming autoencoders unsupervised disentangling of shape and appearance
European Conference on Computer Vision, 2018Co-Authors: Mihir Sahasrabudhe, Dimitris Samaras, Nikos Paragios, Riza Alp Guler, Iasonas KokkinosAbstract:In this work we introduce Deforming Autoencoders, a generative model for images that disentangles shape from appearance in an unsupervised manner. As in the deformable template paradigm, shape is represented as a deformation between a Canonical Coordinate system (‘template’) and an observed image, while appearance is modeled in deformation-invariant, template Coordinates. We introduce novel techniques that allow this approach to be deployed in the setting of autoencoders and show that this method can be used for unsupervised group-wise image alignment. We show experiments with expression morphing in humans, hands, and digits, face manipulation, such as shape and appearance interpolation, as well as unsupervised landmark localization. We also achieve a more powerful form of unsupervised disentangling in template Coordinates, that successfully decomposes face images into shading and albedo, allowing us to further manipulate face images.
Mahmood R. Azimi-sadjadi - One of the best experts on this subject based on the ideXlab platform.
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Dual-Satellite Cloud Product Generation Using Temporally Updated Canonical Coordinate Features
IEEE Transactions on Geoscience and Remote Sensing, 2007Co-Authors: A.k. Falcone, Mahmood R. Azimi-sadjadi, J.a. KankiewiczAbstract:State-of-the-art cloud products are typically generated using scientific polar orbiting satellites such as the Moderate Resolution Imaging Spectroradiometer (MODIS). However, they do not allow for observation of the same region at a regular temporal frequency, rendering them ineffectual for nowcasting problems. Operational satellites such as Meteosat-8 SEVIRI, in contrast, are geostationary and provide continual data at a regular temporal frequency over a much larger region. MODIS-like cloud products cannot be directly generated from operational satellites as they typically have a smaller number of spectral bands and different wavelengths and spatial resolution. This paper applies the Canonical Coordinate decomposition method to estimate scientific cloud products using imagery from operational satellites. Using the proposed method features of the Meteosat-8 imagery data that are maximally coherent with the data from the MODIS are generated. These features are temporally updated at times and locations where MODIS data are unavailable using the alternating block power method. A subset of the Canonical Coordinates of Meteosat-8 SEVIRI is then used to create MODIS-like cloud products using several neural networks. The quality of the generated cloud products and their temporal consistency have been demonstrated on several data sets from July 2004. A benchmarking with an independent Meteosat-8-based algorithm is also provided, which shows the promise of our approach in generating MODIS-like cloud products
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Two-channel constrained least squares problems: solutions using power methods and connections with Canonical Coordinates
IEEE Transactions on Signal Processing, 2005Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. Scharf, Yingbo HuaAbstract:The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered, and a general set of solutions is derived. For each set of constraints, the solution is determined by a coupled (asymmetric) generalized eigenvalue problem. This eigenvalue problem establishes a connection between two-channel CLS filtering and transform methods for resolving channel measurements into Canonical or half-Canonical Coordinates. Based on this connection, a unified framework for reduced-rank Wiener filtering is presented. Then, various representations of reduced-rank Wiener filters in Canonical and half-Canonical Coordinates are introduced. An alternating power method is proposed to recursively compute the Canonical Coordinate and half-Canonical Coordinate mappings. A deflation process is introduced to extract the mappings associated with the dominant Coordinates. The correctness of the alternating power method is demonstrated on a synthesized data set, and conclusions are drawn.
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Coherence Analysis using Canonical Coordinate Decomposition with Applications to Sparse Processing and Optimal Array Deployment
Unattended Unmanned Ground Ocean and Air Sensor Technologies and Applications VI, 2004Co-Authors: Mahmood R. Azimi-sadjadi, Ali Pezeshki, Robert L. WadeAbstract:ABSTRACT Sparse array processing methods are typically used to improve the spatial resolution of sensor arrays for theestimation of direction of arrival (DOA). The fundamental assumption behind these methods is that signals thatare received by the sparse sensors (or a group of sensors) are coherent. However, coherence may vary signicantlywith the changes in environmental, terrain, and, operating conditions. In this paper Canonical correlation analysisis used to study the variations in coherence between pairs of sub-arrays in a sparse array problem. The dataset for this study is a subset of an acoustic signature data set, acquired from the US Army TACOM-ARDEC,Picatinny Arsenal, NJ. This data set is collected using three wagon-wheel type arrays with ve microphones.The results show that in nominal operating conditions, i.e. no extreme wind noise or masking eects by trees,building, etc., the signals collected at dierent sensor arrays are indeed coherent even at distant node separation.Keywords: DOA estimation, sparse sensor arrays, signal coherence, Canonical Coordinates.
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A network for recursive extraction of Canonical Coordinates
2003Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. ScharfAbstract:A network structure for Canonical Coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that together extract the Canonical Coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections perform a deflation process that subtracts the contributions of the already extracted Coordinates from the input data subspace. This structure allows for adding new nodes for extracting additional Canonical Coordinates without the need for retraining the previous nodes. The performance of the network is evaluated on a synthesized data set.
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A Canonical Coordinate decomposition network
Proceedings of the International Joint Conference on Neural Networks 2003., 1Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. ScharfAbstract:A network structure for Canonical Coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that together extract the Canonical Coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections perform a deflation process that subtracts the contribution of the already extracted Coordinates from the input data subspace. This structure allows for adding new nodes for extracting additional Canonical Coordinates without the need for retraining the previous nodes. The performance of the network is evaluated on a synthesized data set.
Louis L. Scharf - One of the best experts on this subject based on the ideXlab platform.
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ACSSC - Scaled Canonical Coordinates for compression and transmission of noisy sensor measurements
2013 Asilomar Conference on Signals Systems and Computers, 2013Co-Authors: Yuan Wang, Haonan Wang, Louis L. ScharfAbstract:This paper is motivated by sensing and wireless communication, where data compression or dimension reduction may be used to reduce the required communication bandwidth. High-dimensional measurements are converted into low-dimensional representations through linear compression. Our aim is to compress a noisy sensor measurement, allowing for the fact that the compressed measurement will then be transmitted over a noisy channel. We give the closed-form expression for the optimal compression matrix that minimizes the trace or determinant of the error covariance matrix. We show that the solutions share a common architecture consisting of a Canonical Coordinate transformation, scaling by coefficients which account for Canonical correlations and channel noise variance, followed by a Coordinate transformation into the sub-dominant invariant subspace of the channel noise.
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Two-channel constrained least squares problems: solutions using power methods and connections with Canonical Coordinates
IEEE Transactions on Signal Processing, 2005Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. Scharf, Yingbo HuaAbstract:The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered, and a general set of solutions is derived. For each set of constraints, the solution is determined by a coupled (asymmetric) generalized eigenvalue problem. This eigenvalue problem establishes a connection between two-channel CLS filtering and transform methods for resolving channel measurements into Canonical or half-Canonical Coordinates. Based on this connection, a unified framework for reduced-rank Wiener filtering is presented. Then, various representations of reduced-rank Wiener filters in Canonical and half-Canonical Coordinates are introduced. An alternating power method is proposed to recursively compute the Canonical Coordinate and half-Canonical Coordinate mappings. A deflation process is introduced to extract the mappings associated with the dominant Coordinates. The correctness of the alternating power method is demonstrated on a synthesized data set, and conclusions are drawn.
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A network for recursive extraction of Canonical Coordinates
2003Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. ScharfAbstract:A network structure for Canonical Coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that together extract the Canonical Coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections perform a deflation process that subtracts the contributions of the already extracted Coordinates from the input data subspace. This structure allows for adding new nodes for extracting additional Canonical Coordinates without the need for retraining the previous nodes. The performance of the network is evaluated on a synthesized data set.
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A Canonical Coordinate decomposition network
Proceedings of the International Joint Conference on Neural Networks 2003., 1Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. ScharfAbstract:A network structure for Canonical Coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that together extract the Canonical Coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections perform a deflation process that subtracts the contribution of the already extracted Coordinates from the input data subspace. This structure allows for adding new nodes for extracting additional Canonical Coordinates without the need for retraining the previous nodes. The performance of the network is evaluated on a synthesized data set.
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A Canonical correlation-based feature extraction method for underwater target classification
Oceans '02 MTS IEEE, 1Co-Authors: Ali Pezeshki, Mahmood R. Azimi-sadjadi, Louis L. Scharf, M. RobinsonAbstract:A new feature extraction method for underwater target detection and classification is developed. This is accomplished by applying a Canonical Coordinate decomposition to the backscattered signals to maximize the mutual information between the outputs of the channels associated with consecutive aspects/pings. As a consequence of this information maximization the most coherent target features are extracted while reverberation effects are removed. The classification of targets/nontargets can then be made based on the extracted Canonical Coordinate features. Test results presented in this paper are based on a wideband data set that has been collected at Applied Research Lab (ARL), University of Texas (UT)-Austin. This data set consists of the backscattered signals of four different objects: two mine-like objects and two non-mine-like objects for several aspect angles and both smooth and rough bottom conditions. The extracted Canonical Coordinate features from every other aspect angle of backscattered signals in smooth bottom condition are used to train a back-propagation neural network (BPNN) classifier. The generalization ability of the trained network is then demonstrated by computing the classification rate statistics on the rest of the smooth data set. The performance of the classifier is investigated against environmental changes by testing the trained network on the rough bottom condition data. The results demonstrate the potential of the proposed method for feature extraction in difficult bottom/buried conditions.