Direct Parallel–Hierarchical Transformation Based on Evolutionary Development Models: Application to Laser Beam Spot Image Processing with a Prospective Extension to Railway Track Infrastructure Maintenance
- 1Educational and Research Kyiv Institute of Railway Transport, National Transport University, Mykhaila Omelianovycha—Pavlenka Str. 1, 01010 Kyiv, Ukraine
- 2Department of Transport Engineering, Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentų Str. 56, 51424 Kaunas, Lithuania
Abstract
Signal processing systems operating in noisy or dynamically changing environments require computational architectures capable of multilevel parallel information processing. Biological sensory systems have naturally evolved such architectures through hierarchical organization, providing inspiration for efficient computational models. This paper presents a mathematical model of the direct parallel–hierarchical transformation (PHT), its FPGA implementation, and an application to laser-beam spot processing. The original experiment yielded an average coordinate-determination error of 0.47%, a maximum error of 1.6%, and a standard deviation of 0.36%. The 269-frame tr0_269 dataset constitutes one sequentially acquired frame sequence; its 70/199 division is therefore treated as an internal functional division within that sequence rather than as a separation of independent laser tracks. For the subsequent 199-frame segment, the complete modified PHT chain gave a mean coordinate-determination error of 0.567 pixels; the repeated calculation gave 0.569 pixels, supporting reproducibility within this frame sequence. For an additional check, separate completed frame sequences were used without overlap: TRASSA00 and FRAME02-FRAME05 were used for implementation checks and parameter definition, whereas FRAME06-FRAME11 were not used for parameter selection and were used only for subsequent evaluation of the method. The FMT headers show that FRAME02-FRAME11 are separate completed acquisition sequences with individual start and end times; the gaps between successive sequences substantially exceed the 40 ms inter-frame period, excluding their interpretation as contiguous fragments of one continuously stored FMT file. No sequence and no frame contributed to both groups. The 38-section method produced a lower mean coordinate-determination error than the six-section method in all six evaluation sequences, with means across the six sequences of 0.815 and 1.321 pixels, respectively (Wilcoxon statistic 0; one-sided p-value 0.015625; 95% confidence interval from whole-sequence resampling, −1.178 to −0.152 pixels). In an additional evaluation of the complete PHT on FRAME06-FRAME11, the shape-coefficient limits were determined only from TRASSA00 and FRAME02-FRAME05 as the central 95% empirical interval [0.637, 0.862] and then applied unchanged to FRAME06-FRAME11. On the same evaluation frames, the mean same-frame error of the complete PHT was 0.961 pixels versus 0.822 pixels for the direct 38-section stage. The complete method produced a larger same-frame error in all six sequences because its acceptance logic can retain the preceding accepted coordinate. The FPGA implementation reached 7 ms/frame with register memory and 25 ms/frame with serial memory.
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BibTeX
@article{tverdomed2026direct,
title = {{Direct Parallel–Hierarchical Transformation Based on Evolutionary Development Models: Application to Laser Beam Spot Image Processing with a Prospective Extension to Railway Track Infrastructure Maintenance}},
author = {Volodymyr Tverdomed and Natalia Kokriatska and Leonid Tymchenko and Yurii Didenko and Mykhailo Braikovskyi and Mariia Demchenko and Vaidas Lukoševičius and Ramūnas Skvireckas and Rolandas Makaras},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203807},
url = {https://www.mdpi.com/2227-7390/14/20/3807},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Direct Parallel–Hierarchical Transformation Based on Evolutionary Development Models: Application to Laser Beam Spot Image Processing with a Prospective Extension to Railway Track Infrastructure Maintenance
AU - Volodymyr Tverdomed
AU - Natalia Kokriatska
AU - Leonid Tymchenko
AU - Yurii Didenko
AU - Mykhailo Braikovskyi
AU - Mariia Demchenko
AU - Vaidas Lukoševičius
AU - Ramūnas Skvireckas
AU - Rolandas Makaras
PY - 2026
DA - 2026/10/20
JO - Mathematics
DO - 10.3390/math14203807
UR - https://www.mdpi.com/2227-7390/14/20/3807
AB - Signal processing systems operating in noisy or dynamically changing environments require computational architectures capable of multilevel parallel information processing. Biological sensory systems have naturally evolved such architectures through hierarchical organization, providing inspiration for efficient computational models. This paper presents a mathematical model of the direct parallel–hierarchical transformation (PHT), its FPGA implementation, and an application to laser-beam spot processing. The original experiment yielded an average coordinate-determination error of 0.47%, a maximum error of 1.6%, and a standard deviation of 0.36%. The 269-frame tr0_269 dataset constitutes one sequentially acquired frame sequence; its 70/199 division is therefore treated as an internal functional division within that sequence rather than as a separation of independent laser tracks. For the subsequent 199-frame segment, the complete modified PHT chain gave a mean coordinate-determination error of 0.567 pixels; the repeated calculation gave 0.569 pixels, supporting reproducibility within this frame sequence. For an additional check, separate completed frame sequences were used without overlap: TRASSA00 and FRAME02-FRAME05 were used for implementation checks and parameter definition, whereas FRAME06-FRAME11 were not used for parameter selection and were used only for subsequent evaluation of the method. The FMT headers show that FRAME02-FRAME11 are separate completed acquisition sequences with individual start and end times; the gaps between successive sequences substantially exceed the 40 ms inter-frame period, excluding their interpretation as contiguous fragments of one continuously stored FMT file. No sequence and no frame contributed to both groups. The 38-section method produced a lower mean coordinate-determination error than the six-section method in all six evaluation sequences, with means across the six sequences of 0.815 and 1.321 pixels, respectively (Wilcoxon statistic 0; one-sided p-value 0.015625; 95% confidence interval from whole-sequence resampling, −1.178 to −0.152 pixels). In an additional evaluation of the complete PHT on FRAME06-FRAME11, the shape-coefficient limits were determined only from TRASSA00 and FRAME02-FRAME05 as the central 95% empirical interval [0.637, 0.862] and then applied unchanged to FRAME06-FRAME11. On the same evaluation frames, the mean same-frame error of the complete PHT was 0.961 pixels versus 0.822 pixels for the direct 38-section stage. The complete method produced a larger same-frame error in all six sequences because its acceptance logic can retain the preceding accepted coordinate. The FPGA implementation reached 7 ms/frame with register memory and 25 ms/frame with serial memory.
SN - 2227-7390
ER -