Sinusoidal Siemens star spatial frequency response measurement errors due to misidentified target centers

Birch, Gabriel C.; Griffin, John

doi:10.1117/1.oe.54.7.074104

Cited by 12 publications

(7 citation statements)

References 11 publications

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“…The SSS consists of sinusoidal oscillations in a polar coordinate system such that the spatial frequency varies for concentric circles of different sizes. The SSS pattern is given by: 36

I\left(\theta \right)=a+b\sin \left(\omega \theta -\phi \right),

where

I

represents the image intensity,

\theta

the polar angle for the sinusoidal function,

a

is the mean intensity value,

b

represents the amplitude of the intensity oscillation,

\omega

depicts the number of cycles, and

\phi

is the offset of the potential phase. In the experiment, two test images are utilized with the following parameters:

a=0

b=255

\phi =0

, and

\omega =200

and 400.…”

Section: Resultsmentioning

confidence: 99%

Fast and accurate computation of high‐order Tchebichef polynomials

Abdulhussain

Mahmmod

Baker

et al. 2022

Concurrency and Computation

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Summary Discrete Tchebichef polynomials (DTPs) and their moments are effectively utilized in different fields such as video and image coding, pattern recognition, and computer vision due to their remarkable performance. However, when the moments order becomes large (high), DTPs prone to exhibit numerical instabilities. In this article, a computationally efficient and numerically stable recurrence algorithm is proposed for high order of moment. The proposed algorithm is based on combining two recurrence algorithms, which are the recurrence relations in the n$$ n $$ and x$$ x $$‐directions. In addition, an adaptive threshold is used to stabilize the generation of the DTP coefficients. The designed algorithm can generate the DTP coefficients for high moment's order and large signal size. By large signal size, we mean the samples of the discrete signal are large. To evaluate the performance of the proposed algorithm, a comparison study is performed with state‐of‐the‐art algorithms in terms of computational cost and capability of generating DTPs with large polynomial size and high moment order. The results show that the proposed algorithm has a remarkably low computation cost and is numerically stable, where the proposed algorithm is 27prefix×$$ \times $$ times faster than the state‐of‐the‐art algorithm.

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“…The SSS consists of sinusoidal oscillations in a polar coordinate system such that the spatial frequency varies for concentric circles of different sizes. The SSS pattern is given by: 36

I\left(\theta \right)=a+b\sin \left(\omega \theta -\phi \right),

where

I

represents the image intensity,

\theta

the polar angle for the sinusoidal function,

a

is the mean intensity value,

b

represents the amplitude of the intensity oscillation,

\omega

depicts the number of cycles, and

\phi

is the offset of the potential phase. In the experiment, two test images are utilized with the following parameters:

a=0

b=255

\phi =0

, and

\omega =200

and 400.…”

Section: Resultsmentioning

confidence: 99%

Fast and accurate computation of high‐order Tchebichef polynomials

Abdulhussain

Mahmmod

Baker

et al. 2022

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

“…Sinusoidal Siemens star involves of sinusoidal oscillations patterns in a polar coordinate system such that the spatial frequency varies for concentric circles of different sizes. The Sinusoidal Siemens star is defined as [15]:…”

Section: Performance Evaluation Of the Proposed Methodsmentioning

confidence: 99%

where I represent the intensity represented by a sinusoidal function with an angle

. In addition, a, b,

, and

are the intensity mean, the intensity amplitude, the number of cycles, and the phase offset, respectively.…”

Section: Performance Evaluation Of the Proposed Methodsmentioning

confidence: 99%

On Computational Aspects of Krawtchouk Polynomials for High Orders

et al. 2020

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Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods.

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“…In [54], the significant influence of a misidentified centre on the determined D LIM following the radial measurement and evaluation was proved. However, there is also a significant impact of the profile extraction on the determined D LIM when following the NPL Good Practice Guide [55].…”

Section: Introduction and Literature Reviewmentioning

confidence: 96%

Effect of a Misidentified Centre of a Type ASG Material Measure on the Determined Topographic Spatial Resolution of an Optical Point Sensor

2022

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The article presents the determination of the topographic spatial resolution of an optical point sensor. It is quantified by the lateral period limit DLIM measured on a type ASG material measure, also called (topographic) Siemens star, with a confocal sensor following both a radial measurement and evaluation, as proposed by ISO 25178-70, and the measurement and subsequent evaluation of two line scans, proposed by the NPL Good Practice Guide. As will be shown, for the latter, an only slightly misidentified target centre of the Siemens star leads to quite significant errors of the determined DLIM. Remarkably, a misidentified target centre does not necessarily result in an overestimation of DLIM, but lower values might also be obtained. Therefore, a modified Good Practice Guide is proposed to determine DLIM more accurately, as it includes a thorough determination of the centre of the Siemens star as well. While the measurement and evaluation effort is increased slightly compared to the NPL Good Practice Guide, it is still much faster than a complete radial measurement and evaluation.

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Sinusoidal Siemens star spatial frequency response measurement errors due to misidentified target centers

Cited by 12 publications

References 11 publications

Fast and accurate computation of high‐order Tchebichef polynomials

Fast and accurate computation of high‐order Tchebichef polynomials

On Computational Aspects of Krawtchouk Polynomials for High Orders

Effect of a Misidentified Centre of a Type ASG Material Measure on the Determined Topographic Spatial Resolution of an Optical Point Sensor

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