home.gif Proj.gif tech.gif Res.gif Publ.gif Pers.gif

Technology

Image processing and recognition

2D-Image processing

  1. Vectorization and other procedures for directional field estimation
  2. Equalization (global, local, fast adaptive techniques)
  3. Isotropic 2D-filtering
  4. Locally adaptive non-isotropic 2D-filtering
  5. Other procedures of image enhancement
  6. Parametric/Semiparametric 2D curve fitting
  7. Wavelet analysis

    Image recognition

  8. Point pattern matching
  9. Image graph matching

    10. Miscellaneous/specific:

  10. Contours
  11. Textures
  12. Segmentation
  13. Position, size and shape estimation
  14. Multiple target tracking
  15. Vector quantization

Analysis of time-series and stochastic processes

  1. Testing/Estimating of change-points
  2. Classification of time sequences
  3. Signal segmentation
  4. Forecasting (exponential, Holt, Winters, regression forecasting, seasonal decomposition, etc).
  5. Spectrum estimation
  6. Estimation of autoregression/moving average models

Speech/signal processing and recognition

Technologies developed:

  1. Speaker independent recognition of isolated words
  2. Text-dependent speaker recognition
  3. Speech animation

Elements of technology:

Pattern recognition and classification

  1. Parametric supervised classification (LDA etc - a lot of techniques)
  2. Nonparametric supervised classification
  3. Unsupervised learning: mixture analysis (multivariate normal mixtures with diagonal, full or tree covariance structure). Time-polinomial models
  4. Cluster analysis (K means, binary tree, etc - a lot of techniques)

Statistics


  • 1. Univariate analysis. 1.1. Univariate estimates, confidence intervals and tests (for mean, variance, median, skew, kurtosis, quantiles, etc) 1.2. Binary data: proportion and confidence interval for the true rate. Exact test of hypothesized value of the true rate (along with the approximate one). 2. Comparison of samples (homogeneity tests and other). 2.1. One-sample problem or comparison of two matched samples: Sign, Wilcoxon signed-rank, Student tests. 2.2. The two-sample problem: Generalized exact two-sample Smirnov, Wilcoxon, Student, Welch tests, Omega-square. 2.3. K-sample problem: Kruskal-Wallis, Jonckheere-Terpstra-Kendall, Spearman. Multiple comparisons for K independent samples. 2.4. K matched samples. Two-way nonparametric ANOVA. Binary samples: Cochran test, Nikiforov/Nikiforova's conditional test. Complete blocks: Friedman, Page tests. General case (incomplete blocks and/ or multiple cases per block per treatment): Benard-van Elteren, Jonckheere-Terpstra-Kendall, (generalized) Mantel-Haenszel tests. Multiple comparisons for K matched samples. 3. Two-way contingency table analysis 3.1. 2x2 table: Exact (Fisher-Irwin), chi-square and chi-square (corrected) tests. Odds ratio, Yule's Q & Y indices, phi- coefficient and attributable risk and the corresponding confidence intervals. 3.2, 3.3. 2xK and Kx2 tables. Test of homogeneity (independence) against ordered and general alternatives: omega-square (Nair, 1987, Taguchi, 1966), Wilcoxon and generalized exact two-sample Smirnov test (Nikiforov, 1994). 3.4. RxC table analysis. Tests: Chi-square, likelihood ratio, Kruskal- Wallis, omega-square, Jonckheere-Terpstra-Kendall, Spearman, tests of marginal homogeneity and symmetry. Multiple comparisons. Estimates of 12 measures of association. 11 intracell characteristics for a contingency table. 4. Correlation analysis. 19 measures of association: measures for 2x2, RxC tables, rank, linear and partial correlations. Two modes of correlation matrix calculation and output. 5. Analysis of several contingency tables. 5.1. Analysis of several contingency tables 2x2. Mantel-Haenszel test, test of homogeneity of association. Odds ratio, confidence interval. 5.2. Analysis of several contingency tables RxC. Benard-van Elteren, Jonckheere-Terpstra-Kendall, (generalized) Mantel-Haenszel tests. Multiple comparisons table. Marginal homogeneity. 6. Expert Agreement analysis. Two kappa tests, Friedman concordance, intraclass rank correlation & the corresponding tests. 7. Regression and Classification. 7.1. Multiple/stepwise regression. Tests & confidence intervals for coefficients, ANOVA), regression prediction table (predictions, residuals, intervals etc). 7.2. Nonparametric discriminant analysis for categorical, numerical or mixed data. 7.3. Cluster-analysis for categorical, numerical or mixed data (three procedures). Data transformations: Functions, standardization, categorization, ranking, sorting/selection operations, operations with two or several columns, random numbers generation; sample simulation using empirical DF etc.

  • Missing data analysis: various EM-algorithms, multivariate tests, etc.

    Graphical analysis, representation and modelings of statistical data

    1. Projection on principal components
    2. Projection on Rao discriminant vectors
    3. Histograms; Multiple/Cumulative function (series) plots etc
    4. Scatter plots (incl. regression scatter plots)
    5. Various nonorthogonal projections of a classified sample

    Graph theory

    1. Minimal spanning tree (Dijkstra) and related
    2. Assignment problem
    3. Inexact graph matching
    4. Other graph related problems

  • Top of the page