Unified Scale Theorem: A Mathematical Formulation of Scale in the Frame of Earth Observation Image Classification

Karydas, Christos

doi:10.3390/fractalfract5030127

“…In addition, Berke 22 supplemented the equation, proposing a spatial and spectral resolution range factor applicable to digital images produced by CCD/CMOS sensors with finite resolution, which includes all three important sensor characteristics (number of pixels, spectral resolution and number of channels). Equation ( 5 ) has also been used successfully to detect the effect of pollution on corn via the examination of proximity-derived pollutants (cadmium and carbon black) 25 . Berke 26 , 27 applied the equation to recognise potato varieties that cannot be distinguished by eye and to measure leaf damage.…”

Section: Discussionmentioning

confidence: 99%

“…Berke 26 , 27 applied the equation to recognise potato varieties that cannot be distinguished by eye and to measure leaf damage. Karydas 25 used Eq. ( 5 ) in the mathematical presentation of natural processes containing scale changes.…”

Section: Discussionmentioning

confidence: 99%

Unique algorithm for the evaluation of embryo photon emission and viability

Berke,

Gulyás,

Bognár

et al. 2024

Sci Rep

0

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Living cells have spontaneous ultraweak photon emission derived from metabolic reactions associated with physiological conditions. The ORCA-Quest CMOS camera (Hamamatsu Photonics, Japan) is a highly sensitive and essential tool for photon detection; its use with a microscope incubator (Olympus) enables the detection of photons emitted by embryos with the exclusion of harmful visible light. With the application of the second law of thermodynamics, the low-entropy energy absorbed and used by embryos can be distinguished from the higher-entropy energy released and detectable in their environment. To evaluate higher-entropy energy data from embryos, we developed a unique algorithm for the calculation of the entropy-weighted spectral fractal dimension, which demonstrates the self-similar structure of the energy (photons) released by embryos. Analyses based on this structure enabled the distinction of living and degenerated mouse embryos, and of frozen and fresh embryos and the background. This novel detection of ultra-weak photon emission from mouse embryos can provide the basis for the development of a photon emission embryo control system. The ultraweak photon emission fingerprints of embryos may be used for the selection of viable specimens in an ideal dark environment.

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“…Eq. 5 has also been used successfully to detect the effect of pollution on corn via the examination of proximity-derived pollutants (cadmium and carbon black) 25 .…”

Section: Discussionmentioning

confidence: 99%

Unique algorithm for the evaluation of embryo photon emission and viability

Berke,

Gulyás,

Bognár

et al. 2023

Preprint

1

0

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Living cells have spontaneous ultraweak photon emission derived from metabolic reactions associated with physiological conditions. The ORCA-Quest CMOS camera (Hamamatsu Photonics, Japan) is a highly sensitive and essential tool for photon detection; its use with a microscope incubator (Olympus) enables the detection of photons emitted by embryos with the exclusion of harmful visible light. With the application of the second law of thermodynamics, the low-entropy energy absorbed and used by embryos can be distinguished from the higher-entropy energy released and detectable in their environment. To evaluate higher-entropy energy data from embryos, we developed a unique algorithm for the calculation of the entropy-weighted spectral fractal dimension, which demonstrates the self-similar structure of the energy (photons) released by embryos. Analyses based on this structure enabled the distinction of living and degenerated mouse embryos, and of frozen and fresh embryos and the background. This novel detection of ultra-weak photon emission from mouse embryos can provide the basis for the development of a photon emission embryo control system. The ultraweak photon emission fingerprints of embryos may be used for the selection of viable specimens in an ideal dark environment.

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“…Besides, there are a lot of other potential applications of the theory of fractal surfaces like geology [3], oceanography [51], geosciences [52][53][54] and so on. Relevant interested researchers can further explore these applications in the future.…”

Section: Applications In Other Fieldsmentioning

confidence: 99%

An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces

Wang

2023

Fractal Fract

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In this paper, we conduct research on the fractal characteristics of the superposition of fractal surfaces from the view of fractal dimension. We give the upper bound of the lower and upper box dimensions of the graph of the sum of two bivariate continuous functions and calculate the exact values of them under some particular conditions. Further, it has been proven that the superposition of two continuous surfaces cannot keep the fractal dimensions invariable unless both of them are two-dimensional. A concrete example of a numerical experiment has been provided to verify our theoretical results. This study can be applied to the fractal analysis of metal fracture surfaces or computer image surfaces.

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Unified Scale Theorem: A Mathematical Formulation of Scale in the Frame of Earth Observation Image Classification

Cited by 8 publications

References 25 publications

Unique algorithm for the evaluation of embryo photon emission and viability

Unique algorithm for the evaluation of embryo photon emission and viability

Unique algorithm for the evaluation of embryo photon emission and viability

An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces

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