Skip to main content
Erschienen in: Pattern Recognition and Image Analysis 4/2019

01.10.2019 | MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION AND UNDERSTANDING

Generalized Spectral-Analytical Method and Its Applications in Image Analysis and Pattern Recognition Problems

verfasst von: S. A. Makhortykh, L. I. Kulikova, A. N. Pankratov, R. K. Tetuev

Erschienen in: Pattern Recognition and Image Analysis | Ausgabe 4/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The generalized spectral-analytical method as a new approach to the processing of information arrays is stated. Some theoretical foundations of this method and its applications in different experimental data analysis problems are given. The method is based on the adaptive expansion of initial arrays in the functional bases belonging to the classical algebraic systems of polynomials and functions of continuous and discrete arguments (Jacobi, Chebyshev, Lagrange, Laguerre, Kravchuk, Charlier, and other polynomials). This approach combines analytical and digital data-processing procedures, thus providing a basis for the universal combined technology for the processing of information arrays. An appreciable part of this review is devoted to video data analysis and pattern-recognition problems. In addition, some relevant applications of this method in biomedical and bioinformation data analysis, recognition, classification, and diagnosis problems are described.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat V. L. Goncharov, Theory of Interpolation and Approximation of Functions, 2nd ed. (Gostekhteorizdat, Moscow, 1954) [in Russian]. V. L. Goncharov, Theory of Interpolation and Approximation of Functions, 2nd ed. (Gostekhteorizdat, Moscow, 1954) [in Russian].
2.
Zurück zum Zitat A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics (Nauka, Moscow, 1978; Birkhäuser, Basel, 1988). A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics (Nauka, Moscow, 1978; Birkhäuser, Basel, 1988).
3.
Zurück zum Zitat F. F. Dedus, A. F. Dedus, and M. N. Ustinin, “A new data processing technology for pattern recognition and image analysis problems,” Pattern Recogn. Image Anal. 2 (2), 195–207 (1992). F. F. Dedus, A. F. Dedus, and M. N. Ustinin, “A new data processing technology for pattern recognition and image analysis problems,” Pattern Recogn. Image Anal. 2 (2), 195–207 (1992).
4.
Zurück zum Zitat J. K. Bowmaker, “Evolution of color vision in vertebrates,” Eye 12 (3), 541–547 (1998).CrossRef J. K. Bowmaker, “Evolution of color vision in vertebrates,” Eye 12 (3), 541–547 (1998).CrossRef
5.
Zurück zum Zitat S. Belongie, J. Malik, and J. Puzicha, “Shape matching and object recognition using shape contexts,” IEEE Trans. Pattern Anal. Mach. Intell. 24 (4), 509–522 (2002).CrossRef S. Belongie, J. Malik, and J. Puzicha, “Shape matching and object recognition using shape contexts,” IEEE Trans. Pattern Anal. Mach. Intell. 24 (4), 509–522 (2002).CrossRef
6.
Zurück zum Zitat A. Antoniou, Digital Signal Processing: Signals, Systems, and Filters (McGraw Hill, New York, 2006). A. Antoniou, Digital Signal Processing: Signals, Systems, and Filters (McGraw Hill, New York, 2006).
7.
Zurück zum Zitat A. N. Pankratov, “On the implementation of algebraic operations on orthogonal function series,” Comput. Math. Math. Phys. 44 (12), 2017–2023 (2004).MathSciNet A. N. Pankratov, “On the implementation of algebraic operations on orthogonal function series,” Comput. Math. Math. Phys. 44 (12), 2017–2023 (2004).MathSciNet
8.
Zurück zum Zitat G. Benson, “Tandem repeats finder: a program to analyze DNA sequences,” Nucleic Acids Res. 27 (2), 573–580 (1999).CrossRef G. Benson, “Tandem repeats finder: a program to analyze DNA sequences,” Nucleic Acids Res. 27 (2), 573–580 (1999).CrossRef
9.
Zurück zum Zitat R. Kolpakov, G. Bana, and G. Kucherov, “mreps: efficient and flexible detection of tandem repeats in DNA,” Nucleic Acid Res. 31 (13), 3672–3678 (2003).CrossRef R. Kolpakov, G. Bana, and G. Kucherov, “mreps: efficient and flexible detection of tandem repeats in DNA,” Nucleic Acid Res. 31 (13), 3672–3678 (2003).CrossRef
10.
Zurück zum Zitat A. Y. Ogurtsov, M. A. Roytberg, S. A. Shabalina, and A. S. Kondrashov, “OWEN: aligning long collinear regions of genomes,” Bioinformatics 18 (12), 1703–1704 (2002).CrossRef A. Y. Ogurtsov, M. A. Roytberg, S. A. Shabalina, and A. S. Kondrashov, “OWEN: aligning long collinear regions of genomes,” Bioinformatics 18 (12), 1703–1704 (2002).CrossRef
11.
Zurück zum Zitat G. M. Landau, J. P. Schmidt, and D. Sokol, “An algorithm for approximate tandem repeats,” J. Comput. Biol. 8 (1), 1–18 (2001).CrossRef G. M. Landau, J. P. Schmidt, and D. Sokol, “An algorithm for approximate tandem repeats,” J. Comput. Biol. 8 (1), 1–18 (2001).CrossRef
12.
Zurück zum Zitat F. F. Dedus, L. I. Kulikova, S. A. Makhortykh, N. N. Nazipova, A. N. Pankratov, and R. K. Tetuev, “Analytical recognition methods for repeated structures in genomes,” Dokl. Math. 74 (3), 926–929 (2006).MATHCrossRef F. F. Dedus, L. I. Kulikova, S. A. Makhortykh, N. N. Nazipova, A. N. Pankratov, and R. K. Tetuev, “Analytical recognition methods for repeated structures in genomes,” Dokl. Math. 74 (3), 926–929 (2006).MATHCrossRef
13.
Zurück zum Zitat F. F. Dedus, L. I. Kulikova, S. A. Makhortykh, N. N. Nazipova, A. N. Pankratov, and R. K. Tetuev, “Recognition of the structural-functional organization of genetic sequences,” Moscow Univ. Comput. Math. Cybern. 31 (2), 49–53 (2007).MATHCrossRef F. F. Dedus, L. I. Kulikova, S. A. Makhortykh, N. N. Nazipova, A. N. Pankratov, and R. K. Tetuev, “Recognition of the structural-functional organization of genetic sequences,” Moscow Univ. Comput. Math. Cybern. 31 (2), 49–53 (2007).MATHCrossRef
14.
Zurück zum Zitat A. N. Pankratov, M. A. Gorchakov, F. F. Dedus, N. S. Dolotova, L. I. Kulikova, S. A. Makhortykh, N. N. Nazipova, D. A. Novikova, M. M. Olshevets, M. I. Pyatkov, V. R. Rudnev, R. K. Tetuev, and V. V. Filippov, “Spectral analysis for identification and visualization of repeats in genetic sequences,” Pattern Recogn. Image Anal. 19 (4), 687–692 (2009).CrossRef A. N. Pankratov, M. A. Gorchakov, F. F. Dedus, N. S. Dolotova, L. I. Kulikova, S. A. Makhortykh, N. N. Nazipova, D. A. Novikova, M. M. Olshevets, M. I. Pyatkov, V. R. Rudnev, R. K. Tetuev, and V. V. Filippov, “Spectral analysis for identification and visualization of repeats in genetic sequences,” Pattern Recogn. Image Anal. 19 (4), 687–692 (2009).CrossRef
15.
Zurück zum Zitat R. K. Tetuev, N. N. Nazipova, A. N. Pankratov, and F. F. Dedus, “Search for megasatellite tandem repeats in eukaryotic genomes by estimation of GC-content curve oscillations,” Math. Biolog. Bioinform. 5 (1), 30–42 (2010) [in Russian].CrossRef R. K. Tetuev, N. N. Nazipova, A. N. Pankratov, and F. F. Dedus, “Search for megasatellite tandem repeats in eukaryotic genomes by estimation of GC-content curve oscillations,” Math. Biolog. Bioinform. 5 (1), 30–42 (2010) [in Russian].CrossRef
16.
Zurück zum Zitat R. K. Tetuev and N. N. Nazipova, “Consensus of repeated region of mouse chromosome 6 containing 60 tandem copies of a complex pattern,” Repbase Rep. 10 (5), 776 (2010). R. K. Tetuev and N. N. Nazipova, “Consensus of repeated region of mouse chromosome 6 containing 60 tandem copies of a complex pattern,” Repbase Rep. 10 (5), 776 (2010).
17.
Zurück zum Zitat R. K. Tetuev, F. F. Dedus, and N. N. Nazipova, “Consensus of repeated region of rat chromosome 4 similar to mouse chromosome 6 repeated region, enclosed in the intergenic region between genes Hrh1 and Atg7,” Repbase Rep. 10 (8), 1185 (2010). R. K. Tetuev, F. F. Dedus, and N. N. Nazipova, “Consensus of repeated region of rat chromosome 4 similar to mouse chromosome 6 repeated region, enclosed in the intergenic region between genes Hrh1 and Atg7,” Repbase Rep. 10 (8), 1185 (2010).
18.
Zurück zum Zitat A. N. Pankratov, M. I. Pyatkov, R. K. Tetuev, N. N. Nazipova, and F. F. Dedus, “Search for extended repeats in genomes based on the spectral-analytical method,” Math. Biolog. Bioinform. 7 (2), 476–492 (2012) [in Russian].CrossRef A. N. Pankratov, M. I. Pyatkov, R. K. Tetuev, N. N. Nazipova, and F. F. Dedus, “Search for extended repeats in genomes based on the spectral-analytical method,” Math. Biolog. Bioinform. 7 (2), 476–492 (2012) [in Russian].CrossRef
19.
Zurück zum Zitat M. I. Pyatkov, V. V. Filippov, and A. N. Pankratov, “Consensus of repeated region of rabbit chromosome 17 containing over 15 huge approximate tandem repeats,” Repbase Rep. 12 (3), 256 (2012). M. I. Pyatkov, V. V. Filippov, and A. N. Pankratov, “Consensus of repeated region of rabbit chromosome 17 containing over 15 huge approximate tandem repeats,” Repbase Rep. 12 (3), 256 (2012).
20.
Zurück zum Zitat A. N. Pankratov, R. K. Tetuev, M. I. Pyatkov, V. P. Toigildin, and N. N. Popova, “Spectral analytical method of recognition of inexact repeats in character sequences,” Proc. Inst. Syst. Program. Russ. Acad. Sci., 27 (6), 335–344 (2015) [in Russian]. A. N. Pankratov, R. K. Tetuev, M. I. Pyatkov, V. P. Toigildin, and N. N. Popova, “Spectral analytical method of recognition of inexact repeats in character sequences,” Proc. Inst. Syst. Program. Russ. Acad. Sci., 27 (6), 335–344 (2015) [in Russian].
21.
Zurück zum Zitat M. I. Pyatkov and A. N. Pankratov, “SBARS: fast creation of dotplots for DNA sequences on different scales using GA-, GC-content,” Bioinformatics 30 (12), 1765–1766 (2014).CrossRef M. I. Pyatkov and A. N. Pankratov, “SBARS: fast creation of dotplots for DNA sequences on different scales using GA-, GC-content,” Bioinformatics 30 (12), 1765–1766 (2014).CrossRef
22.
Zurück zum Zitat K. Katoh, K. Misawa, K. Kuma, and T. Miyata, “MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform,” Nucleic Acids Res. 30 (14), 3059–3066 (2002).CrossRef K. Katoh, K. Misawa, K. Kuma, and T. Miyata, “MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform,” Nucleic Acids Res. 30 (14), 3059–3066 (2002).CrossRef
23.
Zurück zum Zitat D. Sharma, B. Issac, G. P. S. Raghava, and R. Ramaswamy, “Spectral Repeat Finder (SRF): Identification of repetitive sequences using Fourier transformation,” Bioinformatics 20 (9), 1405–1412 (2004).CrossRef D. Sharma, B. Issac, G. P. S. Raghava, and R. Ramaswamy, “Spectral Repeat Finder (SRF): Identification of repetitive sequences using Fourier transformation,” Bioinformatics 20 (9), 1405–1412 (2004).CrossRef
24.
Zurück zum Zitat L. Du, H. Zhou, and H. Yan, “OMWSA: detection of DNA repeats using moving window spectral analysis,” Bioinformatics 23 (5), 631–633 (2007).CrossRef L. Du, H. Zhou, and H. Yan, “OMWSA: detection of DNA repeats using moving window spectral analysis,” Bioinformatics 23 (5), 631–633 (2007).CrossRef
25.
Zurück zum Zitat J. Krumsiek, R. Arnold, and T. Rattei, “Gepard: a rapid and sensitive tool for creating dotplots on genome scale,” Bioinformatics 23 (8), 1026–1028 (2007).CrossRef J. Krumsiek, R. Arnold, and T. Rattei, “Gepard: a rapid and sensitive tool for creating dotplots on genome scale,” Bioinformatics 23 (8), 1026–1028 (2007).CrossRef
26.
Zurück zum Zitat R. K. Tetuev, M. I. Pyatkov, and A. N. Pankratov, “Parallel algorithm for global alignment of long aminoacid and nucleotide sequences,” Math. Biolog. Bioinform. 12 (1), 137–150 (2017) [in Russian].CrossRef R. K. Tetuev, M. I. Pyatkov, and A. N. Pankratov, “Parallel algorithm for global alignment of long aminoacid and nucleotide sequences,” Math. Biolog. Bioinform. 12 (1), 137–150 (2017) [in Russian].CrossRef
27.
Zurück zum Zitat A. N. Pankratov, R. K. Tetuev, and M. I. Pyatkov, “LSCGAT: Long sequences customizable global alignment tool,” J. Bioinf. Genomics No. 1 (10), 3 pages (2019). A. N. Pankratov, R. K. Tetuev, and M. I. Pyatkov, “LSCGAT: Long sequences customizable global alignment tool,” J. Bioinf. Genomics No. 1 (10), 3 pages (2019).
28.
Zurück zum Zitat E. V. Brazhnikov and A. V. Efimov, “Structure of α-α-hairpins with short connections in globular proteins,” Mol. Biol. 35 (1), 89–97 (2001).CrossRef E. V. Brazhnikov and A. V. Efimov, “Structure of α-α-hairpins with short connections in globular proteins,” Mol. Biol. 35 (1), 89–97 (2001).CrossRef
29.
Zurück zum Zitat A. V. Efimov, “A new super-secondary protein structure: the alpha alpha-angle,” Mol. Biol. (Mosk.) 18 (6), 1524–1537 (1984) [in Russian]. A. V. Efimov, “A new super-secondary protein structure: the alpha alpha-angle,” Mol. Biol. (Mosk.) 18 (6), 1524–1537 (1984) [in Russian].
30.
Zurück zum Zitat A. V. Efimov, “Standard structures in proteins,” Prog. Biophys. Mol. Biol. 60 (3), 201–239 (1993).CrossRef A. V. Efimov, “Standard structures in proteins,” Prog. Biophys. Mol. Biol. 60 (3), 201–239 (1993).CrossRef
31.
Zurück zum Zitat A. V. Efimov, “L-shaped structure from two alpha-helices with a proline residue between them,” Mol. Biol. (Mosk.) 26 (6), 1370–1376 (1992) [in Russian]. A. V. Efimov, “L-shaped structure from two alpha-helices with a proline residue between them,” Mol. Biol. (Mosk.) 26 (6), 1370–1376 (1992) [in Russian].
32.
Zurück zum Zitat C. Chothia, M. Levitt, and D. Richardson, “Structure of proteins: Packing of α-helices and pleated sheets,” Proc. Natl. Acad. Sci. U. S. A. 74 (10), 4130–4134 (1977).CrossRef C. Chothia, M. Levitt, and D. Richardson, “Structure of proteins: Packing of α-helices and pleated sheets,” Proc. Natl. Acad. Sci. U. S. A. 74 (10), 4130–4134 (1977).CrossRef
33.
Zurück zum Zitat C. Chothia, M. Levitt, and D. Richardson, “Helix to helix packing in proteins,” J. Mol. Biol. 145 (1), 215–250 (1981).CrossRef C. Chothia, M. Levitt, and D. Richardson, “Helix to helix packing in proteins,” J. Mol. Biol. 145 (1), 215–250 (1981).CrossRef
34.
Zurück zum Zitat D. Walther, F. Eisenhaber, and P. Argos, “Principles of helix-helix packing in proteins: The helical lattice superposition model,” J. Mol. Biol. 255 (3), 536–553 (1996).CrossRef D. Walther, F. Eisenhaber, and P. Argos, “Principles of helix-helix packing in proteins: The helical lattice superposition model,” J. Mol. Biol. 255 (3), 536–553 (1996).CrossRef
35.
Zurück zum Zitat A. Trovato and F. Seno, “A new perspective on analysis of helix-helix packing preferences in globular proteins,” Proteins: Struct., Funct., Bioinf. 55 (4), 1014–102 (2004). A. Trovato and F. Seno, “A new perspective on analysis of helix-helix packing preferences in globular proteins,” Proteins: Struct., Funct., Bioinf. 55 (4), 1014–102 (2004).
36.
Zurück zum Zitat H. Bateman and A. Erdélyi, Higher transcendental functions, Vol. II (McGraw Hill, New York, 1953; Nauka, Moscow, 1966). H. Bateman and A. Erdélyi, Higher transcendental functions, Vol. II (McGraw Hill, New York, 1953; Nauka, Moscow, 1966).
37.
Zurück zum Zitat A. F. Nikiforov, V. B. Uvarov, and S. K. Suslov, Classical Orthogonal Polynomials of a Discrete Variable, in Springer Series in Computational Physics (Springer, Berlin, Heidelberg, 1991). A. F. Nikiforov, V. B. Uvarov, and S. K. Suslov, Classical Orthogonal Polynomials of a Discrete Variable, in Springer Series in Computational Physics (Springer, Berlin, Heidelberg, 1991).
38.
Zurück zum Zitat H. Jeffreys and B. Swirles, Methods of Mathematical Physics, 3rd ed. (Cambridge Univ. Press, Cambridge, 1966; Mir, Moscow, 1970) [Vol. 3 of the Russian translation]. H. Jeffreys and B. Swirles, Methods of Mathematical Physics, 3rd ed. (Cambridge Univ. Press, Cambridge, 1966; Mir, Moscow, 1970) [Vol. 3 of the Russian translation].
39.
Zurück zum Zitat E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton Univ. Press, Princeton, NJ, 1971); Introduction to Harmonic Analysis on Euclidean Spaces (Mir, Moscow, 1974) [in Russian]. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton Univ. Press, Princeton, NJ, 1971); Introduction to Harmonic Analysis on Euclidean Spaces (Mir, Moscow, 1974) [in Russian].
40.
Zurück zum Zitat N. Ya. Vilenkin, Special Functions and Theory of Group Representations (Nauka, Moscow, 1991) [in Russian].CrossRef N. Ya. Vilenkin, Special Functions and Theory of Group Representations (Nauka, Moscow, 1991) [in Russian].CrossRef
41.
Zurück zum Zitat W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea Publ., New York, 1954).MATH W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea Publ., New York, 1954).MATH
42.
Zurück zum Zitat M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, Vol. 55 (U.S. Government Printing Office, Washington, D.C., 1964) [Chapter 8].MATH M. Abramowitz and I. A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, Vol. 55 (U.S. Government Printing Office, Washington, D.C., 1964) [Chapter 8].MATH
43.
Zurück zum Zitat F. F. Dedus, S. A. Makhortykh, M. N. Ustinin, and A. F. Dedus, Generalized Spectral-Analytic Method for Data File Processing. Problems of Image Analysis and Pattern Recognition (Mashinostroenie, Moscow, 1999) [in Russian]. F. F. Dedus, S. A. Makhortykh, M. N. Ustinin, and A. F. Dedus, Generalized Spectral-Analytic Method for Data File Processing. Problems of Image Analysis and Pattern Recognition (Mashinostroenie, Moscow, 1999) [in Russian].
44.
Zurück zum Zitat S. A. Makhortykh, “Generalized spectral-analytical method for biomedical data processing,” Math. Montisnigri XXXVI, 104–113 (2016).MathSciNetMATH S. A. Makhortykh, “Generalized spectral-analytical method for biomedical data processing,” Math. Montisnigri XXXVI, 104–113 (2016).MathSciNetMATH
45.
Zurück zum Zitat M. N. Ustinin, S. A. Makhortykh, A. M. Molchanov, et al., “Problems of the analysis of magnetic encephalography data,” in Computers and Supercomputers in Biology, Ed. by V. D. Lakhno and M. N. Ustinin (Inst. Komp. Issled., Izhevsk, Moscow, 2002), pp. 327–349 [in Russian]. M. N. Ustinin, S. A. Makhortykh, A. M. Molchanov, et al., “Problems of the analysis of magnetic encephalography data,” in Computers and Supercomputers in Biology, Ed. by V. D. Lakhno and M. N. Ustinin (Inst. Komp. Issled., Izhevsk, Moscow, 2002), pp. 327–349 [in Russian].
46.
Zurück zum Zitat L. I. Kulikova and S. A. Makhortykh, “Mathematical operations on two-dimensional signals in bases of spherical harmonics,” Investigated in Russia 9, 598–608 (2006) [Electronic journal, in Russian]. L. I. Kulikova and S. A. Makhortykh, “Mathematical operations on two-dimensional signals in bases of spherical harmonics,” Investigated in Russia 9, 598–608 (2006) [Electronic journal, in Russian].
47.
Zurück zum Zitat A. V. Derguzov and S. A. Makhortykh, “Spectral analysis and data classification in magnetoencephalography,” Pattern Recogn. Image Anal. 16 (3), 497–505 (2006).CrossRef A. V. Derguzov and S. A. Makhortykh, “Spectral analysis and data classification in magnetoencephalography,” Pattern Recogn. Image Anal. 16 (3), 497–505 (2006).CrossRef
48.
Zurück zum Zitat T. Boraud, E. Bezard, B. Bioulac, and C. E. Gross, “From single extracellular unit recording in experimental and human Parkinsonism to the development of a functional concept of the role played by the basal ganglia in motor control,” Prog. Neurobiol. 66 (4), 265–283 (2002).CrossRef T. Boraud, E. Bezard, B. Bioulac, and C. E. Gross, “From single extracellular unit recording in experimental and human Parkinsonism to the development of a functional concept of the role played by the basal ganglia in motor control,” Prog. Neurobiol. 66 (4), 265–283 (2002).CrossRef
49.
Zurück zum Zitat M. B. H. Youdim and P. Riederer, “Understanding Parkinson’s disease,” Sci. Am. 276 (1), 52–59 (1997).CrossRef M. B. H. Youdim and P. Riederer, “Understanding Parkinson’s disease,” Sci. Am. 276 (1), 52–59 (1997).CrossRef
50.
Zurück zum Zitat R. K. Tetouev, “Contour recognition based on spectral methods. Solution of the problem of choice of the start-point,” Pattern Recogn. Image Anal. 17 (2), 243–251 (2007).CrossRef R. K. Tetouev, “Contour recognition based on spectral methods. Solution of the problem of choice of the start-point,” Pattern Recogn. Image Anal. 17 (2), 243–251 (2007).CrossRef
51.
Zurück zum Zitat H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne, “The protein Data Bank,” Nucleic Acids Res. 28 (1), 235–242 (2000).CrossRef H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne, “The protein Data Bank,” Nucleic Acids Res. 28 (1), 235–242 (2000).CrossRef
52.
Zurück zum Zitat V. R. Rudnev, A. N. Pankratov, L.I. Kulikova, F. F. Dedus, D. A. Tikhonov, and A. V. Efimov, “Recognition and stability analysis of structural motifs of α-α-corner type in globular proteins,” Mat. Biolog. Bioinform. 8 (2), 398–406 (2013) [in Russian].CrossRef V. R. Rudnev, A. N. Pankratov, L.I. Kulikova, F. F. Dedus, D. A. Tikhonov, and A. V. Efimov, “Recognition and stability analysis of structural motifs of α-α-corner type in globular proteins,” Mat. Biolog. Bioinform. 8 (2), 398–406 (2013) [in Russian].CrossRef
53.
Zurück zum Zitat V. R. Rudnev, A. N. Pankratov, L.I. Kulikova, F. F. Dedus, D. A. Tikhonov, and A. V. Efimov, “Conformational analysis of structural motifs of α-α-corner in the computational experiment of molecular dynamics,” Mat. Biolog. Bioinform. 9 (2), 575–584 (2014) [in Russian].CrossRef V. R. Rudnev, A. N. Pankratov, L.I. Kulikova, F. F. Dedus, D. A. Tikhonov, and A. V. Efimov, “Conformational analysis of structural motifs of α-α-corner in the computational experiment of molecular dynamics,” Mat. Biolog. Bioinform. 9 (2), 575–584 (2014) [in Russian].CrossRef
54.
Zurück zum Zitat D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “Statistical analysis of internal distances of helical pairs in protein molecules,” Mat. Biolog. Bioinform. 11 (2), 170–190 (2016) [in Russian].CrossRef D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “Statistical analysis of internal distances of helical pairs in protein molecules,” Mat. Biolog. Bioinform. 11 (2), 170–190 (2016) [in Russian].CrossRef
55.
Zurück zum Zitat D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “The study of interhelical angles in the structural motifs formed by two helices,” Mat. Biolog. Bioinform. 12 (1), 83–101 (2017) [in Russian].CrossRef D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “The study of interhelical angles in the structural motifs formed by two helices,” Mat. Biolog. Bioinform. 12 (1), 83–101 (2017) [in Russian].CrossRef
56.
Zurück zum Zitat D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “Analysis of torsion angles between helical axes in pairs of helices in protein molecules,” Mat. Biolog. Bioinform. 12 (2), 398–410 (2017) [in Russian].CrossRef D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “Analysis of torsion angles between helical axes in pairs of helices in protein molecules,” Mat. Biolog. Bioinform. 12 (2), 398–410 (2017) [in Russian].CrossRef
57.
Zurück zum Zitat D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “Analysis of the areas and perimeters of polygons of the helices projections intersection in helical pairs of protein molecules,” Keldysh Institute of Applied Mathematics Preprint No. 59 (2018) [in Russian]. D. A. Tikhonov, L. I. Kulikova, and A. V. Efimov, “Analysis of the areas and perimeters of polygons of the helices projections intersection in helical pairs of protein molecules,” Keldysh Institute of Applied Mathematics Preprint No. 59 (2018) [in Russian].
Metadaten
Titel
Generalized Spectral-Analytical Method and Its Applications in Image Analysis and Pattern Recognition Problems
verfasst von
S. A. Makhortykh
L. I. Kulikova
A. N. Pankratov
R. K. Tetuev
Publikationsdatum
01.10.2019
Verlag
Pleiades Publishing
Erschienen in
Pattern Recognition and Image Analysis / Ausgabe 4/2019
Print ISSN: 1054-6618
Elektronische ISSN: 1555-6212
DOI
https://doi.org/10.1134/S1054661819040102

Weitere Artikel der Ausgabe 4/2019

Pattern Recognition and Image Analysis 4/2019 Zur Ausgabe

MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION AND UNDERSTANDING

Descriptive Image Analysis: Part II. Descriptive Image Models

MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION AND UNDERSTANDING

Research on Improvement of Stagewise Weak Orthogonal Matching Pursuit Algorithm