June 2014
Intermediate to advanced
464 pages
11h 15m
English
book
Mathematical Foundations of Image Processing and Analysis, Volume 1
by Jean-Charles Jean-Charles Pinoli Pinoli
Content preview from Mathematical Foundations of Image Processing and Analysis, Volume 1Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
11
The Algebraic and Order Functional Framework
The algebraic and order functional framework is the first to be taken into account when addressing mathematical imaging problems.
11.1. Paradigms
Within the algebraic and order functional framework, a gray-tone image is considered as a gray-tone function that will be treated as a partially ordered vector. Therefore, gray-tone images will be combined through their gray-tone functions, which will be submitted to the natural partial order relation. Roughly speaking, it will be allowed to manipulate and modify gray-tone images, as well as to combine and compare them.
11.2. Mathematical structures and notions for IPA
The mathematical disciplines of reference are the theory of sets, for short Set Theory [RUB 67, DEV 93, BOU 04c], and Algebra [LAN 04; 1st ed., 1971] [STR 05; 1st ed., 1976].
11.2.1. Gray-tone functions
A gray-tone function, denoted f, is a mapping defined on the spatial domain 
n and valued in the tonal domain 
, namely:
[11.1] 
where x denotes an arbitrary pixel in n (see Chapter 9), and f(x) is a gray-tone value belonging to ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.