Morphological Operations and Spaces of Sequences | Mathematical Image Processing |  Exercise 04
Channel: Fabian Gabel
Date: 02/10/2022

This is Exercise 04 of the course "Mathematical Image Processing" held at #tuhh in 2021/2022. 

Watch the full series at
https://www.youtube.com/playlist?list=PLqB7maHdRHhNdx1QX7kUNediGlGqo8NGw

You find the exercise sheet on the webpage
https://math.fabian-gabel.de/teaching/improc/ex04.pdf

Further Resources to books, lecture notes, and software are linked below. Let me know if anything is unclear.

Chapters
0:00 Intro
0:38 Definition and Examples for the Morphological Operations Dilation and Erosion
5:30 Proving Set Theoretical Monotonicity Properties of Closing and Opening
12:28 Octave Example for Morphological Denoising Background with Salt and Pepper Noise 
17:15 Definition of Structure Elements / Masks for Morphological Operations
22:52 Intro to lp-Spaces as Normed Vector Spaces of Infinite Sequences 
26:09 Calculating the lp-Norm of Example Sequences (Canonical Unit Vector and Geometric Sequence) 
36:05 Examples for Sequences in l2 that are not l1
38:54 Vector Space Structure of lp-Spaces of Infinite Sequences (Addition of Sequences, Scalar Multiples)
42:48 Showing that the lp-Norm Actually Defines a Norm Making lp  a Banach Space
44:51 Outro

===References===

==Book==
 "Mathematical Image Processing" by K. Bredies and D. Lorenz:
https://doi.org/10.1007/978-3-030-01458-2

==Lecture Notes==
https://bit.ly/math-improc-script

==Software==
GNU Octave is free software licensed under the terms of the GNU General Public License (GPL).
Get Octave:  https://octave.org/
License: https://www.gnu.org/licenses/gpl-3.0.html

===Credits===
Thumbnail uses a photo by Jannet Corgi: https://bit.ly/3feoSEn (also converted to black&white using Otsu's algorithm, further processed with imopen, imclose, and imerode).
Outro music titled "Motion Blur" by "http://www.nihilore.com/synthwave" is licensed under a Creative Commons Attribution 4.0 license (https://creativecommons.org/licenses/by/4.0/legalcode).

#math #imageprocessing #octave #matlab #morphological-operations #vectorspace #lp-space #norm #dilation #erosion #opening #closing #denoising #geometricseries #lpspace #banachspace #hilbertspace