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Mathematics for computer vision

Учебный год
Обучение ведется на английском языке


Course Syllabus


The course is devoted to the systematization of the mathematical background of the students necessary for the successful mastering of educational disciplines in the field of computer vision. The course includes sections of mathematical analysis, probability theory, linear algebra.
Learning Objectives

Learning Objectives

  • Systematization of the mathematical background.
  • Preparation for the use of mathematical knowledge in the professional activities of a specialist in the field of computer vision.
Expected Learning Outcomes

Expected Learning Outcomes

  • Understand metrics, norms and orthogonality of vectors in multidimensional space
  • Understand linear operations and linear dependence of vectors in multidimensional space
  • Practically test linear dependence of vectors in multidimensional space
  • Understand the structure of subspaces in multidimensional space
  • Practically find vector representation of images
  • Understand matrix operations, matrix norms
  • Get practical skills to work with matrices
  • Understand linear transformations
  • Get skills to work with square matrices
  • Get practical skills to work with matrix for image processing
  • Understand spectral decomposition of square matrix
  • Get a practical skills in calculation of eigenvalues and eigenvectors
  • Understand SVD decomposition of matrix
  • Get a practical skills in calculation of SVD decomposition
  • Get a practice of the use of SVD decomposition dimension reduction
  • Understand topology of multidimensional space
  • Understand gradient of differentiable functions in multidimensional space
  • Get skills in practical calculation of gradient
  • Understand integral of function in multidimensional space
  • Understand probability space
  • Understand univariate distributions
  • Understand multivariate distributions
  • Get skills to work with distributions in image processing
  • Understand convex functions
  • Get a practice to test convexity of functions
  • Understand general convex optimization problem with constraints
  • Get a practice to solve convex optimization problem
  • Use theoretical knowledge for practical work
  • Be able to solve practical problems in image processing
Course Contents

Course Contents

  • Vectors (specialization)
  • Matrices (specialization)
  • Spectral and SVD decompositions
  • Functions (specialization)
  • Distributions
  • Optimization
  • Project
Assessment Elements

Assessment Elements

  • non-blocking Tests
  • non-blocking Course Project
  • non-blocking Final Exam
Interim Assessment

Interim Assessment

  • Interim assessment (1 module)
    0.5 * Course Project + 0.2 * Final Exam + 0.3 * Tests


Recommended Core Bibliography

  • Cormen, T. H., Leiserson, C. E., Rivest, R. L., Stein, C. Introduction to Algorithms (3rd edition). – MIT Press, 2009. – 1292 pp.

Recommended Additional Bibliography

  • Thompson, S. P., & Hiperlink (Firm). (2014). Calculus Made Easy : Being a Very-simplest Introduction to Those Beautiful Methods of Reckoning Which Are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus. Hiperlink.