Mathematics for computer vision

2024/2025

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Кафедра прикладной математики и информатики (Нижний Новгород) (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:

Курс обязательный

Когда читается:

1-й курс, 1 модуль

Course Syllabus

Abstract

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

• 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

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

Course Contents

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

Assessment Elements

• weekly tests
• Final project

Interim Assessment

• 2024/2025 1st module
  0.6 * Final project + 0.4 * weekly tests

Bibliography

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.

Authors

• Kaliagin Valerii ALEKSANDROVICH