Point-Spread Functions, Line-Spread Functions, and Edge-Response Functions Associated with MTFs of the Form exp [−(ω/ωc)n]

Cb, Johnson

doi:10.1364/ao.12.001031

Cited by 27 publications

(17 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following, an alternative to (9) and (13) is suggested focusing on increasing resolution in intensity profiles while limiting computational effort. The approach is inspired by Verbeek and van Vliet, 18 where the accuracy of higher order derivative based edge detection methodologies is assessed.…”

Section: Geometric Interpretation Of Convolution Principlementioning

confidence: 99%

“…[3][4][5] Although the majority of detection algorithms are based on recorded intensity patterns, be it in terms of Hough transforms, 6 intensity gradients 7 or higher order derivatives, 8 so far neither an inherent analytical model of the ellipse image nor an easy way of modelling intensity profiles has to the best of the author's knowledge been presented. While analytical models exist for the straight edge response function 9 involving the error function, an analytical solution is not as straightforward for curved edges.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling of imaged ellipse intensity profiles using Euclidean geometry

Theunissen

2015

The Imaging Science Journal

View full text Add to dashboard Cite

To model the evolution in intensity of an ellipse image along randomly oriented profiles, this paper starts with the derivation of an analytical solution involving infinite summations of products of Hermite polynomials, which is consequently argued to be impractical. Generation of profiles adopting Fourier analyses hampers the extraction of arbitrarily located intensity distributions as a direct result of equidistant spatial sampling, and an alternative procedure is therefore presented to calculate the sought for intensity at isolated spatial locations. The algorithm introduced is based on the overlap area between the ellipse and concentric circles, which can be performed using basic trigonometric properties. The simplicity of the proposed method allows, contrary to Fourier based analyses, the modelling of intensity profiles with high resolution while demanding minimal computational memory. The proficiency of the method is demonstrated numerically, and its generality and applicability to real images in terms of motion induced image blurring and digitisation are discussed.

show abstract

Section: Geometric Interpretation Of Convolution Principlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling of imaged ellipse intensity profiles using Euclidean geometry

Theunissen

2015

The Imaging Science Journal

View full text Add to dashboard Cite

show abstract

“…It has been suggested that MTF's can be fitted to a curve of the form e "'' [18]. For reasonable MTF's the exponent will be a number between 1 and 2.…”

Section: -I-> Nmentioning

confidence: 99%

Performance of a pressurized multiwire proportional chamber for neutron radiography

Director¹

1979

View full text Add to dashboard Cite

A study was made of the effect of gas density on resolution and efficiency of a neutron sensitive multiwire proportional chamber. Increasing the density will shorten the reaction products range. A pressure vessel was designed and constructed for 4 atm thereby reducing the range of the reaction products from the neutron converter by a factor of 4, compared to 1 atm. Pressurizing the chamber to 4 atm resulted in a spatial resolution of 1mm under the most favor able operating conditions. For the type of neutron converters used improving the efficiency is lim ited to a choice of material. Two different materials were tried, gadolinium and boron, with effici.ncies of 6.3 and 2.3%, respectively.

show abstract

“…Recall that from (7), the system otf satisfies logĥ(ρ) ∼ (1 − c)p(ρ), ρ ≫ 1, for some unknown positive constant c < 1. Continuation all the way to t = 0 in (22), withĥ(ξ, η, t) as in (23), is equivalent to falsely setting c = 0 in (7). This necessarily produces oversharpening.…”

mentioning

confidence: 99%

Bochner subordination, logarithmic diffusion equations, and blind deconvolution of hubble space telescope imagery and other scientific data

Carasso¹

2009

View full text Add to dashboard Cite

Abstract. Generalized Linnik processes and associated logarithmic diffusion equations can be constructed by appropriate Bochner randomization of the time variable in Brownian motion and the related heat conduction equation. Remarkably, over a large but finite frequency range, generalized Linnik characteristic functions can exhibit almost Gaussian behavior near the origin, while behaving like low exponent isotropic Lévy stable laws away from the origin. Such behavior matches Fourier domain behavior in a large class of real blurred images of considerable scientific interest, including Hubble space telescope imagery and scanning electron micrographs. This paper develops a powerful blind deconvolution procedure based on postulating system optical transfer functions (otf) in the form of generalized Linnik characteristic functions. The system otf and 'true' sharp image are then reconstructed by solving a related logarithmic diffusion equation backwards in time, using the blurred image as data at time t = 1. The present methodology significantly improves upon previous work based on system otfs in the form of Lévy stable characteristic functions. Such improvement is validated by the substantially smaller image Lipschitz exponents that ensue, confirming increased fine structure recovery. These results resolve the unexplained appearance of exceptionally low Lévy stable exponents in previous work on the same class of images. The paper is illustrated with striking enhancements of gray scale and colored images.

show abstract

Point-Spread Functions, Line-Spread Functions, and Edge-Response Functions Associated with MTFs of the Form exp [−(ω/ωc)n]

Cited by 27 publications

References 1 publication

Modelling of imaged ellipse intensity profiles using Euclidean geometry

Modelling of imaged ellipse intensity profiles using Euclidean geometry

Performance of a pressurized multiwire proportional chamber for neutron radiography

Bochner subordination, logarithmic diffusion equations, and blind deconvolution of hubble space telescope imagery and other scientific data

Contact Info

Product

Resources

About