Optimal approximation of uniformly rotated images: relationship between Karhunen-Loeve expansion and discrete cosine transform

Uenohara, Michihiro; Kanade, Takeo

doi:10.1109/83.650856

Cited by 42 publications

(34 citation statements)

References 9 publications

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“…As a word of caution, several authors including [9] and [10], mistakenly reported the formula for the eigenvectors proportional to ( )…”

Section: Eigenvalues and Eigenvectors Of Symmetric Circulantmentioning

confidence: 99%

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Applications of Symmetric Circulant Matrices to Isotropic Markov Chain Models and Electrical Impedance Tomography

Demidenko¹

2017

APM

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Symmetric circulant matrices (or shortly symmetric circulants) are a very special class of matrices sometimes arising in problems of discrete periodic convolutions with symmetric kernel. First, we collect major properties of symmetric circulants scattered through the literature. Second, we report two new applications of these matrices to isotropic Markov chain models and electrical impedance tomography on a homogeneous disk with equidistant electrodes. A new special function is introduced for computation of the Ohm's matrix. The latter application is illustrated with estimation of the resistivity of gelatin using an electrical impedance tomography setup.

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“…As a word of caution, several authors including [9] and [10], mistakenly reported the formula for the eigenvectors proportional to ( )…”

Section: Eigenvalues and Eigenvectors Of Symmetric Circulantmentioning

confidence: 99%

“…For example, a SC matrix is used in physical applications [6] and image processing to describe the Karhunen-Loève type rotations of image templates [9] [11]. Generally, the SC matrix may be useful in modeling rotationinvariant systems in equilibrium.…”

Section: Applicationsmentioning

confidence: 99%

Applications of Symmetric Circulant Matrices to Isotropic Markov Chain Models and Electrical Impedance Tomography

Demidenko¹

2017

APM

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“…See Han and Vasconcelos (2010). The accuracy of the stereo matching is measured by the ratio of the number of correct matches to the total number of matches obtained using (23), as R(1) varies in I (1). Let this ratio be r esd (m, k 1 ).…”

Section: Stereo Matchingmentioning

confidence: 99%

A probabilistic definition of salient regions for image matching

Maybank

2013

Neurocomputing

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Abstract. A probabilistic definition of saliency is given in a form suitable for applications to image matching. In order to make this definition, the values of the pixels in pairs of matching regions are modeled using an elliptically symmetric distribution (ESD). The values of the pixels in background pairs of regions are also modeled using an ESD. If a region is given in one image, then the conditional probability density function for the pixel values in a matching region can be calculated. The saliency of the given region is defined to be the Kullback-Leibler divergence between this conditional pdf and a background conditional pdf. Experiments carried out using images in the Middlebury stereo database show that if the salience of a given image region is high, then there are relatively few background regions that have a better match to the given region than the true matching region.

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“…In [71] it was already shown that the result of applying PCA to a set of rotated images has some remarkable effects: although there is only one changing source (the angle of rotation) multiple intensity sources are estimated from this data set. Moreover, the eigenvalues do not have the be estimated with an eigenvalue decomposition, they can also be found using Discrete Cosine Transform (DCT).…”

Section: Modeling Introductionmentioning

confidence: 99%

“…In [71] it was already shown that model errors can determine the characteristics of the eigenvalue plots: Uenohara and Kanade showed that the eigenvalues of a training set composed of rotated versions of one image can be determined using DCT as well as by doing an eigenvalue decomposition.…”

Section: Introductionmentioning

confidence: 99%

SOS, lost in a high dimensional space

Hendrikse¹

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Optimal approximation of uniformly rotated images: relationship between Karhunen-Loeve expansion and discrete cosine transform

Cited by 42 publications

References 9 publications

Applications of Symmetric Circulant Matrices to Isotropic Markov Chain Models and Electrical Impedance Tomography

Applications of Symmetric Circulant Matrices to Isotropic Markov Chain Models and Electrical Impedance Tomography

A probabilistic definition of salient regions for image matching

SOS, lost in a high dimensional space

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