Morphological Decomposition and Compression of Binary Images via a Minimum Set Cover Algorithm

Morphological Decomposition and Compression of Binary Images via a Minimum Set Cover Algorithm In this paper, by a novel morphological decomposition method, we propose an efficient compression approach. Our presented decomposition arises from solving a minimum set cover problem (MSCP) obtained from the image skeleton data. We first use the skeleton pixels to create a collection of blocks which cover the foreground. The given blocks are both overlapped and too many. Hence, in order to find the minimum number of the blocks that cover the foreground, we form an MCSP. To solve this problem, we present a new algorithm of which accuracy is better than those of the known methods in the literatures. Also, its error analysis is studied to obtain an error bound. In the sequel, we present a fast algorithm which include an extra parameter by which the relation between the accuracy and CPU time can be controlled. Finally, several examples are given to confirm the efficiency of our approach. Keywords Decomposition · Compression · Minimum set cover algorithm Mathematics Subject Classification 68U10 · 94A08 1 Introduction The difference is substantial. While minimal decomposi- tion into non-overlapping blocks is polynomial, the one into It is well known that there are several methods for com- overlapping blocks is NP complete. The http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Imaging and Vision Springer Journals

Morphological Decomposition and Compression of Binary Images via a Minimum Set Cover Algorithm

Loading next page...
 
/lp/springer_journal/morphological-decomposition-and-compression-of-binary-images-via-a-x6uygbqZIN
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Computer Science; Image Processing and Computer Vision; Applications of Mathematics; Signal,Image and Speech Processing; Mathematical Methods in Physics
ISSN
0924-9907
eISSN
1573-7683
D.O.I.
10.1007/s10851-018-0825-x
Publisher site
See Article on Publisher Site

Abstract

In this paper, by a novel morphological decomposition method, we propose an efficient compression approach. Our presented decomposition arises from solving a minimum set cover problem (MSCP) obtained from the image skeleton data. We first use the skeleton pixels to create a collection of blocks which cover the foreground. The given blocks are both overlapped and too many. Hence, in order to find the minimum number of the blocks that cover the foreground, we form an MCSP. To solve this problem, we present a new algorithm of which accuracy is better than those of the known methods in the literatures. Also, its error analysis is studied to obtain an error bound. In the sequel, we present a fast algorithm which include an extra parameter by which the relation between the accuracy and CPU time can be controlled. Finally, several examples are given to confirm the efficiency of our approach. Keywords Decomposition · Compression · Minimum set cover algorithm Mathematics Subject Classification 68U10 · 94A08 1 Introduction The difference is substantial. While minimal decomposi- tion into non-overlapping blocks is polynomial, the one into It is well known that there are several methods for com- overlapping blocks is NP complete. The

Journal

Journal of Mathematical Imaging and VisionSpringer Journals

Published: May 29, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off