Image moments and reconstruction by Krawtchouk via Clenshaw's reccurence formula

Jahid, Tarik; Karmouni, Hicham; Hmimid, Abdeslam; Sayyouri, Mhamed; Qjidaa, Hassan

doi:10.1109/eitech.2017.8255265

Cited by 15 publications

(10 citation statements)

References 13 publications

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“…where i = 1, N , n = 3, N , 0 < p < 1. In [22], [26], [27], [28], [29], [30], [31], [32], [33] recurrence algorithms for fast computation of the Krawtchouk functions are presented. The symmetry relation (1) for the polynomials turns into an analogous formula for the Krawtchouk functions…”

Section: The Model Of Shift Invariant Image Recognition Of the Visual...mentioning

confidence: 99%

“…N ♢ with respect to the binomial distribution were introduced by Mykhailo Krawtchouk, hence the denomination Krawtchouk functions. They are also called normalized Krawtchouk polynomials [3], [22], [26], [27] in analogy with Hermite functions referring the fact that Krawtchouk polynomials are the discrete analogues of Hermite polynomials [1], [15], or weighted Krawtchouk polynomials [28], [29], [30], weighted and normalized Krawtchouk polynomials [31], [32], [33] or Krawtchouk functions [45].…”

Section: The Model Of Shift Invariant Image Recognition Of the Visual...mentioning

confidence: 99%

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A method for determining the time-frequency characteristics of localized impulse components in continuous signals

Filimonova,

Specovius-Neugebauer,

Friedmann

2024

Preprint

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Background: We propose a method for analyzing the dynamics of signals of different nature. The method aims to find the time-frequency characteristics of the local impulse components for continuous signals. Thereby, we separate the information about the impulse shape from the time of its appearance. The method is based on a mathematical model of invariant pattern recognition by a visual system combined with a wavelet analysis method. Here we use Krawtchouk functions to model the response of the receptive fields of the lateral geniculate nucleus and, in addition, as the mother wavelet. Results: The inclusion of saccades in the model of the visual system allows us to extract invariant features of the signals. In addition, a parameter is included in the model that controls the front-to-back ratio of the basis functions. This means that the signal decomposition is not solely based on one particular set of basis functions, but on a family of basis functions parametrized by the shift transformation and an asymmetry parameter, which allows a better approximation of asymmetric impulse components. Conclusion: Our method makes it possible to study both the time of emergence of the impulse components of continuous signals and their spectral characteristics, which in turn can be used for their identification. Applying the method to biological signals of various nature, we could identify and localize a blinking, a muscle response due to emotions and find times of changes in a driver’s stress state, etc. Potentially, other applications of nonstationary signals with impulse components can also be considered.

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Section: The Model Of Shift Invariant Image Recognition Of the Visual...mentioning

confidence: 99%

Section: The Model Of Shift Invariant Image Recognition Of the Visual...mentioning

confidence: 99%

A method for determining the time-frequency characteristics of localized impulse components in continuous signals

Filimonova,

Specovius-Neugebauer,

Friedmann

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore, it is essential to note that in complex industrial scenarios, there is an increase in noise within camera images. Preprocessing [ 11 , 12 ] of these images can be performed to mitigate errors in point cloud reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Quaternary Categorization Strategy for Reconstructing High-Reflectivity Surface in Structured Light Illumination

Xu,

Qu,

et al. 2023

Sensors

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Structured light illumination is widely applied for surface defect detection due to its advantages in terms of speed, precision, and non-contact capabilities. However, the high reflectivity of metal surfaces often results in the loss of point clouds, thus reducing the measurement accuracy. In this paper, we propose a novel quaternary categorization strategy to address the high-reflectivity issue. Firstly, we classify the pixels into four types according to the phase map characteristics. Secondly, we apply tailored optimization and reconstruction strategies to each type of pixel. Finally, we fuse point clouds from multi-type pixels to accomplish precise measurements of high-reflectivity surfaces. Experimental results show that our strategy effectively reduces the high-reflectivity error when measuring metal surfaces and exhibits stronger robustness against noise compared to the conventional method.

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“…In theory, the moment approach is divided into three main categories: The non-orthogonal moments, such as geometric and complex moments [5,6], the continuous orthogonal moments [7][8][9][10][11][12][13], and the discrete orthogonal moments (DOMs). We are going to focus mainly on DOMs such as the moments of Tchebichef [14,15], Krawtchouk [14][15][16][17], Hahn [18], Charlier [19][20][21], and last but not least Meixner [21,22], as these have concrete advantages over 3D image analysis. However, it has been noted that the computation of moments is a complex and costly task in terms of time.…”

mentioning

confidence: 99%

“…However, it has been noted that the computation of moments is a complex and costly task in terms of time. Therefore, several algorithms are implemented into the literature to reduce the cost of moment calculation; Most of the algorithms are either centered on the use of the image new representations [23][24][25][26], or the acceleration of time calculating values of polynomials [16][17][18][19]22].…”

mentioning

confidence: 99%

Partial 3D Image Reconstruction by Cuboids Using Stable Computation of Hahn Polynomials

Tahiri

Karmouni

Tahiri

et al. 2021

Lecture Notes in Electrical Engineering

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In this paper, we will present a new method of partial reconstruction of the 3D image. The latter is based on the following two concepts: one is the stable discrete orthogonal Hahn polynomials (DOHPs), which significantly reduces numerical defects. The other is the 3D image cuboid representation (ICR) to accelerate the computation time of discrete orthogonal Hahn moments (DOHMs) and improve the quality of 3D image reconstruction. The results of the simulation confirm the ability of the 3D image reconstruction using the proposed process. IntroductionResearch on 3D image reconstruction has always been a difficult challenge. The latter can be used for evaluating an object's 3D profile, as well as for defining a profile 3D coordinate at any given point. The reconstruction of 3D objects constitutes a

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Image moments and reconstruction by Krawtchouk via Clenshaw's reccurence formula

Cited by 15 publications

References 13 publications

A method for determining the time-frequency characteristics of localized impulse components in continuous signals

A method for determining the time-frequency characteristics of localized impulse components in continuous signals

Quaternary Categorization Strategy for Reconstructing High-Reflectivity Surface in Structured Light Illumination

Partial 3D Image Reconstruction by Cuboids Using Stable Computation of Hahn Polynomials

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