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Journal ArticleDOI

Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode

01 May 1934-Physica D: Nonlinear Phenomena (North-Holland)-Vol. 1, Iss: 7, pp 689-704
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.
About: This article is published in Physica D: Nonlinear Phenomena.The article was published on 1934-05-01. It has received 967 citations till now.
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Journal ArticleDOI
TL;DR: A systematic reconstruction-based method for deciding the highest-order ZERNike moments required in a classification problem is developed and the superiority of Zernike moment features over regular moments and moment invariants was experimentally verified.
Abstract: The problem of rotation-, scale-, and translation-invariant recognition of images is discussed. A set of rotation-invariant features are introduced. They are the magnitudes of a set of orthogonal complex moments of the image known as Zernike moments. Scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments. A systematic reconstruction-based method for deciding the highest-order Zernike moments required in a classification problem is developed. The quality of the reconstructed image is examined through its comparison to the original one. The orthogonality property of the Zernike moments, which simplifies the process of image reconstruction, make the suggest feature selection approach practical. Features of each order can also be weighted according to their contribution to the reconstruction process. The superiority of Zernike moment features over regular moments and moment invariants was experimentally verified. >

1,971 citations

Journal ArticleDOI
TL;DR: Various types of moments have been used to recognize image patterns in a number of applications and some fundamental questions are addressed, such as image-representation ability, noise sensitivity, and information redundancy.
Abstract: Various types of moments have been used to recognize image patterns in a number of applications. A number of moments are evaluated and some fundamental questions are addressed, such as image-representation ability, noise sensitivity, and information redundancy. Moments considered include regular moments, Legendre moments, Zernike moments, pseudo-Zernike moments, rotational moments, and complex moments. Properties of these moments are examined in detail and the interrelationships among them are discussed. Both theoretical and experimental results are presented. >

1,522 citations

Journal ArticleDOI
TL;DR: In this paper, a method for finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region was given, and the solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x-ray absorption coefficient in two dimensions, (2) the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter, and (3) a variable density of matter with constant chemical composition, using the energy loss
Abstract: A method is given of finding a real function in a finite region of a plane given its line integrals along all straight lines intersecting the region. The solution found is applicable to three problems of interest for precise radiology and radiotherapy: (1) the determination of a variable x‐ray absorption coefficient in two dimensions; (2) the determination of the distribution of positron annihilations when there is an inhomogeneous distribution of the positron emitter in matter; and (3) the determination of a variable density of matter with constant chemical composition, using the energy loss of charged particles in the matter.

1,409 citations

Book
19 Mar 2001
TL;DR: In this article, the authors considered the properties of orthogonal polynomials on the unit sphere, root systems and Coxeter groups, and the Summability of Orthogonal expansions.
Abstract: Preface to the second edition Preface to the first edition 1. Background 2. Orthogonal polynomials in two variables 3. General properties of orthogonal polynomials in several variables 4. Orthogonal polynomials on the unit sphere 5. Examples of orthogonal polynomials in several variables 6. Root systems and Coxeter groups 7. Spherical harmonics associated with reflection groups 8. Generalized classical orthogonal polynomials 9. Summability of orthogonal expansions 10. Orthogonal polynomials associated with symmetric groups 11. Orthogonal polynomials associated with octahedral groups and applications References Author index Symbol index Subject index.

1,026 citations

Journal ArticleDOI
01 Mar 2020-IUCrJ
TL;DR: Methods are presented that estimate symmetrical and antisymmetrical optical aberrations, as well as magnification anisotropy, in a cryo-EM data set, and considering these effects improves the resolution of the 3D reconstruction when these effects are present.

504 citations