Representing local structure using tensors II
01 May 2011-pp 545-556
TL;DR: It is shown how higher order tensors can be estimated using a generalization of the same simple formulation as a number of known structure tensor algorithms by formulating them in monomial filter set terms.
Abstract: Estimation of local spatial structure has a long history and numerous analysis tools have been developed. A concept that is widely recognized as fundamental in the analysis is the structure tensor. However, precisely what it is taken to mean varies within the research community. We present a new method for structure tensor estimation which is a generalization of many of it's predecessors. The method uses filter sets having Fourier directional responses being monomials of the normalized frequency vector, one odd order sub-set and one even order sub-set. It is shown that such filter sets allow for a particularly simple way of attaining phase invariant, positive semi-definite, local structure tensor estimates. We continue to compare a number of known structure tensor algorithms by formulating them in monomial filter set terms. In conclusion we show how higher order tensors can be estimated using a generalization of the same simple formulation.
Citations
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TL;DR: This paper introduces a novel framework for adaptive enhancement and spatiotemporal upscaling of videos containing complex activities without explicit need for accurate motion estimation based on multidimensional kernel regression, which significantly widens the applicability of super-resolution methods to a broad variety of video sequences containing complex motions.
Abstract: The need for precise (subpixel accuracy) motion estimates in conventional super-resolution has limited its applicability to only video sequences with relatively simple motions such as global translational or affine displacements. In this paper, we introduce a novel framework for adaptive enhancement and spatiotemporal upscaling of videos containing complex activities without explicit need for accurate motion estimation. Our approach is based on multidimensional kernel regression, where each pixel in the video sequence is approximated with a 3-D local (Taylor) series, capturing the essential local behavior of its spatiotemporal neighborhood. The coefficients of this series are estimated by solving a local weighted least-squares problem, where the weights are a function of the 3-D space-time orientation in the neighborhood. As this framework is fundamentally based upon the comparison of neighboring pixels in both space and time, it implicitly contains information about the local motion of the pixels across time, therefore rendering unnecessary an explicit computation of motions of modest size. The proposed approach not only significantly widens the applicability of super-resolution methods to a broad variety of video sequences containing complex motions, but also yields improved overall performance. Using several examples, we illustrate that the developed algorithm has super-resolution capabilities that provide improved optical resolution in the output, while being able to work on general input video with essentially arbitrary motion.
415 citations
Cites methods from "Representing local structure using ..."
...First, the local (spatiotemporal) gradients in the window of interest are used to calculate a covariance matrix, sometimes referred to as the “local structure tensor” [ 23 ]....
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TL;DR: The usefulness of the proposed tissue classification method is demonstrated by comparisons with conventional single-channel classification using both synthesized data and clinical data acquired with CT (computed tomography) and MRI (magnetic resonance imaging) scanners.
Abstract: This paper describes a novel approach to tissue classification using three-dimensional (3D) derivative features in the volume rendering pipeline. In conventional tissue classification for a scalar volume, tissues of interest are characterized by an opacity transfer function defined as a one-dimensional (1D) function of the original volume intensity. To overcome the limitations inherent in conventional 1D opacity functions, we propose a tissue classification method that employs a multidimensional opacity function, which is a function of the 3D derivative features calculated from a scalar volume as well as the volume intensity. Tissues of interest are characterized by explicitly defined classification rules based on 3D filter responses highlighting local structures, such as edge, sheet, line, and blob, which typically correspond to tissue boundaries, cortices, vessels, and nodules, respectively, in medical volume data. The 3D local structure filters are formulated using the gradient vector and Hessian matrix of the volume intensity function combined with isotropic Gaussian blurring. These filter responses and the original intensity define a multidimensional feature space in which multichannel tissue classification strategies are designed. The usefulness of the proposed method is demonstrated by comparisons with conventional single-channel classification using both synthesized data and clinical data acquired with CT (computed tomography) and MRI (magnetic resonance imaging) scanners. The improvement in image quality obtained using multichannel classification is confirmed by evaluating the contrast and contrast-to-noise ratio in the resultant volume-rendered images with variable opacity values.
378 citations
TL;DR: This review presents the past and present work on GPU accelerated medical image processing, and is meant to serve as an overview and introduction to existing GPU implementations.
360 citations
Cites background or methods from "Representing local structure using ..."
...In each iteration, the local structure tensor (Knutsson, 1989; Knutsson et al., 2011) is used to improve the registration....
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...More advanced cases include edge detection or applying several non-separable filters to estimate a local structure tensor (Knutsson, 1989; Knutsson et al., 2011)....
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...Just as Langs and Biedermann (2007), Malm et al. (2007) applied 3D denoising to a video sequence, but instead used an adaptive filtering approach....
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...The tensor itself is estimated by combining filter responses from another set of filters (Knutsson, 1989; Knutsson et al., 2011)....
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...tensor (Knutsson et al., 2011) theoretically requires 131 GB of memory....
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01 Jan 1993
TL;DR: In this article, it is shown how false operator responses due to missing or uncertain data can be signiflcantly reduced or eliminated using simple combinations of appropriately chosen convolutions, such as Normalized convolution, Difierential convolution and Normalized differential convolution.
Abstract: In this paper it is shown how false operator responses due to missing or uncertain data can be signiflcantly reduced or eliminated. Perhaps the most well-knownofsuchefiectsarethevarious‘edgeefiects’ which invariably occur at the edges of the input data set. Further,itisshownhowoperatorshavingahigher degreeofselectivityandhighertoleranceagainstnoise can be constructed using simple combinations of appropriately chosen convolutions. The theory is based on linear operations and is general in that it allows for both data and operators to be scalars, vectors or tensors of higher order. Threenewmethodsarepresented: Normalized convolution, Difierential convolutionand Normalized Differential convolution. All three methods are examples of the power of the signal/certainty - philosophy, i.e. the separation of both data and operator into a signal part and a certainty part. Missing data is simply handled by setting the certainty to zero. In the case of uncertain data, an estimate of the certainty must accompany the data. Localization or ‘windowing’ of operators is done using an applicability function, the operator equivalent to certainty, not by changing the actual operator coe‐cients. Spatially or temporally limited operators are handled by setting the applicability function to zero outside the window. Consistentwiththephilosophyofthispaperallalgorithms produce a certainty estimate to be used if further processing is needed. Spectrum analysis is discussed and examples of the performance of gradient, divergence and curl operators are given.
238 citations
15 Jun 1993
TL;DR: It is shown how false operator responses due to missing or uncertain data can be significantly reduced or eliminated and how operators having a higher degree of selectivity and higher tolerance against noise can be constructed using simple combinations of appropriately chosen convolutions.
Abstract: It is shown how false operator responses due to missing or uncertain data can be significantly reduced or eliminated. It is shown how operators having a higher degree of selectivity and higher tolerance against noise can be constructed using simple combinations of appropriately chosen convolutions. The theory is based on linear operations and is general in that it allows for both data and operators to be scalars, vectors or tensors of higher order. Three new methods are represented: normalized convolution, differential convolution and normalized differential convolution. All three methods are examples of the power of the signal/certainty-philosophy, i.e., the separation of both data and operator into a signal part and a certainty part. Missing data are handled simply by setting the certainty to zero. In the case of uncertain data, an estimate of the certainty must accompany the data. Localization or windowing of operators is done using an applicability function, the operator equivalent to certainty, not by changing the actual operator coefficients. Spatially or temporally limited operators are handled by setting the applicability function to zero outside the window. >
222 citations
References
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TL;DR: It is shown that recognition of geometrical patterns and alphabetical characters independently of position, size and orientation can be accomplished and it is indicated that generalization is possible to include invariance with parallel projection.
Abstract: In this paper a theory of two-dimensional moment invariants for planar geometric figures is presented. A fundamental theorem is established to relate such moment invariants to the well-known algebraic invariants. Complete systems of moment invariants under translation, similitude and orthogonal transformations are derived. Some moment invariants under general two-dimensional linear transformations are also included. Both theoretical formulation and practical models of visual pattern recognition based upon these moment invariants are discussed. A simple simulation program together with its performance are also presented. It is shown that recognition of geometrical patterns and alphabetical characters independently of position, size and orientation can be accomplished. It is also indicated that generalization is possible to include invariance with parallel projection.
7,963 citations
"Representing local structure using ..." refers background in this paper
...The first steps towards analysis of digital images were taken more then four decades ago [4]....
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01 Jan 1946
5,910 citations
"Representing local structure using ..." refers background in this paper
...Riesz transforms,[1], Zernike moments, [2], and Gabor signals,[3]....
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Dissertation•
22 May 1963
TL;DR: Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1963.
Abstract: Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1963.
1,753 citations
TL;DR: In this paper, ausammenfassung auf Grundlage der A b b eschen Beugungstheorie der optischen Abbildung wird das Aussehen eines Hohlspiegels mit willkurlich verlaufenden kleinen Abweichungen beim Foucaul tschen Schneidenverfahren and beim neuen Phasenkontrastverfhren berechnet.
967 citations