Do We Need a Stack to Erase a Component in a Binary Image?

• Published in: Fun with Algorithms Vol. 6099; pp. 16 - 27
• Main Author: Asano, Tetsuo
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 01.01.2010; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: binary image; component; connectivity; constant work space
• ISBN: 9783642131219; 3642131212
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-13122-6_4

Removing noises in a given binary image is one of common operations. A generalization of the operation is to erase arbitrarily specified component by reversing pixels values in the component. This paper shows that this operation is done without using any data structure like a stack or queue, or without using any extra work space in O(n logn) time for a component consisting of n pixels. This is an in-place algorithm, but the image matrix cannot be used as work space since it has a single bit for each pixel. Whenever we flip pixel value in an objective component, the component shape also changes, which causes some difficulty. An idea for our constant work space algorithm is a conversion keeping its topology.