Diffraction Theory of the Knife-Edge Test and its Improved Form, The Phase-Contrast Method

Zernike, F.; Stratton, F. J. M.

doi:10.1093/mnras/94.5.377

Cited by 313 publications

(177 citation statements)

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“…Zernike Moments: The moment formulation of Zernike polynomials [30] appears to be one of the most popular in terms of noise resilience, information redundancy and reconstruction capability. Complex Zernike moments are constructed using a set of complex polynomials which form a complete orthogonal basis set defined on the unit disc.…”

Section: Gray Level Patchmentioning

confidence: 99%

A comparative evaluation of interest point detectors and local descriptors for visual SLAM

Gil

Mozos

Ballesta

2009

Machine Vision and Applications

152

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In this paper we compare the behavior of different interest points detectors and descriptors under the conditions needed to be used as landmarks in visionbased simultaneous localization and mapping (SLAM). We evaluate the repeatability of the detectors, as well as the invariance and distinctiveness of the descriptors, under different perceptual conditions using sequences of images representing planar objects as well as 3D scenes. We believe that this information will be useful when selecting an appropriate landmark detector and descriptor for visual SLAM.

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Section: Gray Level Patchmentioning

confidence: 99%

A comparative evaluation of interest point detectors and local descriptors for visual SLAM

Gil

Mozos

Ballesta

2009

Machine Vision and Applications

152

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“…where ܴ , ሺߩሻ represents the radial polynomials [7]. Thus, ु may now be called the Zernike moment descriptor (ZMD).…”

Section: Construction Of Shape Features -Modified Zernike Momentsmentioning

confidence: 99%

“…However, certain criteria must be met to ensure the retained small number of significant shape features is sufficient to represent the original pattern. Comparing the norm of the reconstructed pattern by retaining the significant terms with the original is a feasible criterion [7].…”

Section: Advances In Experimental Mechanics VIImentioning

confidence: 99%

“…Since only a small number of ZMD terms are significant, the number of shape features needed to recover the original pattern may be determined by comparing the norm of the original shape and reconstructed pattern by the retained ZMD terms [7]. The reconstruction from the 10 largest terms is shown in Fig 3. It is seen that the recovered images are very similar to the original patterns.…”

Section: Full-field Strain Pattern Decomposition Using the Modified Zmentioning

confidence: 99%

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Construction of Shape Features for the Representation of Full-Field Displacement/Strain Data

Wang

Mottershead

Patki

et al. 2010

AMM

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The achievement of high levels of confidence in finite element models involves their validation using measured responses such as static strains or vibration mode shapes. A huge amount of data with a high level of information redundancy is usually obtained in both the detailed finite element prediction and the full-field measurements so that achieving a meaningful validation becomes a challenging problem. In order to extract useful shape features from such data, image processing and pattern recognition techniques may be used. One of the most commonly adopted shape feature extraction procedures is the Fourier transform in which the original data may be expressed as a set of coefficients (coordinates) of the decomposition kernels (bases) in the feature space. Localised effects can be detected by the wavelet transform. The acquired shape features are succinct and therefore simplify the model validation, based on the full-field data, allowing it to be achieved in a more effective and efficient way. In this paper, full-field finite element strain patterns of a plate with a centred circular hole are considered. A special set of orthonormal shape decomposition kernels based on the circular Zernike polynomials are constructed by the Gram-Schmidt orthonormalization process. It is found that the strain patterns can suitably be represented by only a very small number of shape features from the derived kernels.

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“…Optical errors are described by means of the weight coefficients of the Zernike polynomials, 20 following the standards of the Optical society of America (OSA). 21 For the purpose of the present work, SciLab ™ was used for performing calculations and running the simulations, Microsoft ™ Excel for plotting graphs, and Delphi's programming language was used for implementing the modules in the Optimized Refractive Keratectomy (ORK) and the Custom Ablation Manager (CAM).…”

Section: Patients and Materialsmentioning

confidence: 99%

Tissue-Saving Zernike Terms Selection in Customized Treatments for Refractive Surgery

Arba-Mosquera

Ortueta

Merayo‐Lloves

2009

Journal of Optometry

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PURPOSE:To study the possibility of performing customized refractive surgery minimising the amount of ablated tissue without compromising visual quality. METHODS: A new algorithm for the selection of an optimized set of Zernike terms in customized treatments for laser corneal refractive surgery was developed. Its tissue saving attributes have been simulated on 100 different wave aberrations at 6mm diameter. Outcomes were evaluated in terms of how much depth and volume was saved for each condition (in micrometers and in percentage), whether the proposed correction consists of either a full wavefront correction or an aberration-free treatment, and whether the proposed depth or volume was less than the one required for the equivalent aberrationfree treatment. RESULTS: Simulated outcomes showed an average saved depth of 5μm (0-16μm), and an average saved volume of 95μl (0-127μl) or 11% saved tissue (0-66% saved tissue). Proposed corrections were always less deep than full wavefront corrections and in 59% of the cases were less deep than equivalent aberration-free treatments. CONCLUSIONS: Even though Zernike modes decomposition is a mathematical description of the aberration, it is not the aberration itself. Not all Zernike modes affect the optical quality in the same way. The eye does not see through Zernike decomposition but with its own aberration pattern. However, it seems feasible to efficiently perform laser corneal refractive surgery in a customized form minimising the amount of ablated tissue without compromising the visual quality. Further clinical evaluations on human eyes are needed to confirm the preliminary simulated results presented herein. KEY WORDS: refractive surgery; visual quality; Zernike; tissue saving; wavefront; aberrations; depth; volume; time; aberration-free; free of aberrations; diffraction limited. RESUMEN OBJETIVO: Estudiar la posibilidad de realizar tratamientos personalizados de cirugía refractiva donde se minimice la cantidad de tejido ablacionado sin que por ello se vea afectada la calidad visual. MÉTODOS: Se ha desarrollado un nuevo algoritmo para seleccionar un conjunto optimizado de términos de Zernike para su aplicación en tratamientos personalizados de cirugía refractiva corneal. Para 100 mapas de aberración de onda corneal (para un tamaño de pupila de 6 mm de diámetro), se ha simulado la capacidad de dicho algoritmo para preservar tejido corneal. El resultado de dicha simulación se ha analizado en función de cuanto espesor (en micras) o de cuanto volumen (en %) se preserva en cada situación (respecto a otra situación de referencia): si la corrección propuesta logra corregir todo el frente de onda o sólo las aberraciones de segundo orden, y si el espesor o el volumen que hay que ablacionar con esta configuración es menor que para un tratamiento estándar equivalente, donde se traten de corregir únicamente las aberraciones de segundo orden. RESULTADOS: Las simulaciones arrojaron un "ahorro" promedio de tejido ablacionado igual a 5 μm en términos de espesor máximo que se h...

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Diffraction Theory of the Knife-Edge Test and its Improved Form, The Phase-Contrast Method

Cited by 313 publications

References 0 publications

A comparative evaluation of interest point detectors and local descriptors for visual SLAM

A comparative evaluation of interest point detectors and local descriptors for visual SLAM

Construction of Shape Features for the Representation of Full-Field Displacement/Strain Data

Tissue-Saving Zernike Terms Selection in Customized Treatments for Refractive Surgery

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