Karhunen-love expansion of a set of rotated templates

Jogan, Matjaž; Žagar, Emil; Leonardis, A.

doi:10.1109/tip.2003.813141

Cited by 15 publications

(19 citation statements)

References 9 publications

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“…The presented modification combines a View-Based method with the algorithm of minimal eigenvalues of Töeplitz matrices previously used in cursive-character recognition [3], [11] as well as in spoken word recognition [15], [16]. It is certainly worth mentioning that the idea of Toeplitz matrices and their minimal eigenvalues were successfully used by researchers as a tool similar to discrete Fourier transform [17] or for studying the relationship between Karhunen-Loeve expansion and discrete cosine transform DCT [18] and also for computing the eigenvectors of uniformly rotated images [19]. None of these works, however, has discovered the important property of Töeplitz matrices minimal eigenvalues.…”

Section: Discussionmentioning

confidence: 99%

A View-Based T¿eplitz-Matrix-Supported System for Word Recognition without Segmentation

Tabędzki

Saeed

2006

Sixth International Conference on Intelligent Systems Design and Applications

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In this paper, new modifications and experiments for word recognition and classification are presented. The algorithm is based on recognizing the whole words without separating them into letters. The whole word is treated and analyzed as an image. The method is based on the modification of a novel view-based word recognition algorithm -an approach that was successfully used by the authors' in previous works.This method shows how to recognize words without segmentation. The top and bottom views of the word are analyzed in order to create the feature vector. Then the feature vector is processed by the aid of Töeplitz matrices. The obtained series of Töeplitz matrix minimal eigenvalues are used for classification. The results are promising.

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Section: Discussionmentioning

confidence: 99%

A View-Based T¿eplitz-Matrix-Supported System for Word Recognition without Segmentation

Tabędzki

Saeed

2006

Sixth International Conference on Intelligent Systems Design and Applications

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“…Here we give the block diagonalization of M. This can also be found in textbooks on linear algebra [47] and also in [5,3,6]. As Park [3] pointed out, this real block diagonalization is not unique, and there are other ways how it can be done.…”

Section: Appendix a Complex Diagonalization Of Mmentioning

confidence: 97%

“…This diagonalization of M is nothing new, it is just a standard exercise in linear algebra [47]. It can also be found in studies on the analytical Eigenspace approach [5,3,6].…”

Section: Appendix a Complex Diagonalization Of Mmentioning

confidence: 99%

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Representing images of a rotating object with cyclic permutation for view-based pose estimation

Tamaki

Amano

Kaneda

2009

Computer Vision and Image Understanding

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a b s t r a c tIn this paper, we propose a novel approach using a cyclic group to model the appearance change in an image sequence of an object rotated about an arbitrary axis (1DOF out-of-plane rotation). In the sequence, an image x j is followed by an image x jþ1 . We represent the relationship between images by a cyclic group as x jþ1 ¼ Gx j , and obtain the matrix G by real block diagonalization. Then, G to the power of a real number is used to represent the image sequence and also for pose estimation. Two estimation methods are proposed and evaluated with real image sequences from the COIL-20, COIL-100, and ALOI datasets, and also compared to the Parametric Eigenspace method. Additionally, we discuss the relationship of the proposed approach to the pixel-wise Discrete Fourier Transform (DFT) and to linear regression, and also outline several extensions.

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“…Then it is actually possible to compute the eigenvectors of the much smaller matrix AA H and to map them back to those of A H A. This trick has also been proposed in the context of Karhunen-Loéve expansions of rotated templates by Jogan, Zagar, and Leonardis in [6].…”

Section: Theoretical Solution Using the Singular-value Decompositionmentioning

confidence: 99%

Steerable PCA for Rotation-Invariant Image Recognition

Vonesch¹,

Stauber²,

Unser³

2015

SIAM J. Imaging Sci.

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Abstract. In this paper, we propose a continuous-domain version of principal-component analysis, with the constraint that the underlying family of templates appears at arbitrary orientations. We show that the corresponding principal components are steerable. Our method can be used for designing steerable filters so that they best approximate a given collection of reference templates. We apply this framework to the detection and classification of micrometer-sized particles that are used in a microfluidic diagnostics system. This is done in two steps. First, we decompose the particles into a small number of templates and compute their steerable principal components. Then we use these principal components to automatically estimate the orientation and the class of each particle.

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Karhunen-love expansion of a set of rotated templates

Cited by 15 publications

References 9 publications

A View-Based T¿eplitz-Matrix-Supported System for Word Recognition without Segmentation

A View-Based T¿eplitz-Matrix-Supported System for Word Recognition without Segmentation

Representing images of a rotating object with cyclic permutation for view-based pose estimation

Steerable PCA for Rotation-Invariant Image Recognition

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