Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Image Processing I: Fourier Transform and Optical Systems

In course

MICRO-511: Image processing I

Introduction to the basic techniques of image processing. Introduction to the development of image-processing software and to prototyping using Jupyter notebooks. Application to real-world examples in industrial vision and biomedical imaging. ...

Description

This lecture covers the basics of image processing, including orientation estimation, Fourier transform, and the importance of phase. It also discusses the characterization of linear shift-invariant (LSI) systems, 2D convolution theorem, transfer functions, modeling of optical systems, and optical transfer functions. The lecture emphasizes the Fourier transform's role in analyzing spatial frequency content and the significance of the Fourier phase in image perception.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

Dimitri Nestor Alice Van De Ville

Michaël Unser

Official source

Ontological neighbourhood

Information engineering

Signal processing: Fourier analysis

Related concepts (18)

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

Fourier series

A Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.

Convolution

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function () that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity).

Related lectures (34)

Fourier Transform Applications: Image Processing Basics

Covers image processing basics, Fourier transformation, convolution, cross-correlation, and 3D reconstruction using the Radon projection theorem.

Spectral Properties of Fourier Series and Fourier Transforms

Explores the motivation behind Fourier series and transforms, their fundamentals, and applications in solving differential equations.

Fourier Transforms: Dirac Delta, Fourier Integral, and Transform

Explores the Dirac delta, Fourier integral, and Fourier transform applications in solving PDE problems.

Fourier Series and Analysis

Covers Fourier series, analysis, the heat equation, Gibbs phenomenon, and Fourier transform properties.

Fourier Series: Understanding Coefficients and Periodicity