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 II: Optimal Transforms and Applications

In course

MICRO-512: Image processing II

Study of advanced image processing; mathematical imaging. Development of image-processing software and prototyping in Jupyter Notebooks; application to real-world examples in industrial vision and biomedical imaging. ...

Description

This lecture by the instructor covers the introduction to optimal transforms, classical 2D transforms, wavelet transforms, generalized filtering, and image coding. It also explores applications such as data processing, image enhancement, denoising, Wiener filter, data compression, data analysis, feature extraction, and transform types. The lecture delves into linear algebra, basis vectors, transforms, inner product, dual basis, orthogonal transforms, and 2nd-order statistics in image processing.

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 (4)

Daniel Sage

Michael Stefan Daniel Liebling

Dimitri Nestor Alice Van De Ville

Michaël Unser

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related concepts (32)

Wavelet transform

In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.

Image compression

Image compression is a type of data compression applied to s, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data. Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics.

Digital image processing

Digital image processing is the use of a digital computer to process s through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over . It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the form of multidimensional systems.

Orthonormal basis

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for arises in this fashion.

Discrete wavelet transform

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.

Related lectures (44)

JPEG 2000: Image Compression

Explores image compression principles, focusing on JPEG 2000, covering transform-based coding, quantization, entropy coding, region of interest, error resilience, and software implementations.

Watermarking II

Covers advanced topics in watermarking, including resisting scaling and rotations, self-referenced watermarking, and types of attacks.

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Orthogonal/Orthonormal Bases and Polynomials