Acquisition of image data. Sources and detectors of radiation, cameras and their properties, types of noise. Coding, transferring and storing images. Image formation in optical systems, optical resolution, PSF, optical defects, microscopes and telescopes. Detection of multidimensional image data (3D, spectral, time series). Automation of image acquisition.
Digital filters. Methods of histogram analysis, edge detection, discrete transformation (Fourier, wavelet), Hough / Radon transformation, recursive filtration, deconvolution, image descriptors, image compression, resampling, linear and nonlinear filters.
Digital geometry. Grids, digitization, neighborhood, incidence, component marking, geometric and topological properties of digital sets, digital metrics (Euclidean and geodetic), Euclidean metrics approximation, distance map calculation, Freeman code, description of objects, skeleton.
Mathematical morphology. Properties of morphological operators (arrangement, idempotency, etc.). Dilatation and erosion. Top-hat. Morphological and algebraic opening and closing. Granulometry. Hit-or-miss transformation. Geodetic transformations and morphological reconstruction. Morphological filters. Segmentation using mathematical morphology.
Image analysis. Diffuse filtering, variation filtering, image segmentation. Level set method, active curves and surfaces (geodetic model, Chan-Vese model). Optical flow, image registration, minimization using graphical slices, object classification.
Geometric algorithms. Convex packaging, design in 2D and 3D. Packaging bodies, packaging hierarchy, packaging efficiency. Vorono diagrams, Delaunay triangulations, duality, spatial search (data structures, algorithms).
Graphs and graph algorithms. Formalization of basic graph terms, representation of graphs. Chart Link, Color, Plane Charts. Algorithms (including complexity and basic idea of proof of correctness): scanning the chart to width and depth, shortest distance, skeleton, network flows.
Statistics. Descriptive statistics. Discrete and continuous random variables (NV), basic layout. Numeric characteristics of NV. The Central Limit Theorem. Point estimates, confidence intervals, statistical hypothesis testing, materiality level. Basic parametric and nonparametric tests, ANOVA, NV independence tests. Linear regression, total F-test, partial t-tests.
Algorithms and data structures. Complexity analysis, amortized complexity. Algorithm design techniques (divide and dominate, dynamic programming, hungry strategies). Advanced data structures (heap, union-find structures). String algorithms (Karp-Rabin, KMP, Boyer-Moore algorithms, finite automata).
Powerful computers and intensive calculations. Superscalar and Streaming (GPU) processors, intraprocessor and inter-junctional parallelism. Memory organization, shared and distributed, cache coherence. Code optimization. Distributed systems, task decomposition, basic programming support.