Optimal structuring elements for the morphological pattern restoration of binary images

Author

Schonfeld, Dan

Author_Institution

Signal & Image Res. Lab., Illinois Univ., Chicago, IL, USA

Volume

16

Issue

6

fYear

1994

fDate

6/1/1994 12:00:00 AM

Firstpage

589

Lastpage

601

Abstract

In this paper, we derive the optimal structuring elements of morphological filters in image restoration. The expected pattern transformation of random sets is presented. An estimation theory framework for random sets is subsequently proposed. This framework is based on the least mean difference (LMD) estimator. The LMD estimator is defined to minimize the cardinality of the expected pattern transformation of the set-difference of the parameter and the estimate. Several important results for the determination of the LMD estimator are derived. The LMD structuring elements of morphological filters in image restoration are finally derived

Keywords

estimation theory; filtering and prediction theory; image reconstruction; mathematical morphology; random processes; set theory; binary images; cardinality; estimation theory; image restoration; least mean difference estimator; morphological filters; morphological pattern restoration; optimal structuring elements; random sets; Computational complexity; Data mining; Estimation theory; Filtering theory; Filters; Image analysis; Image restoration; Morphology; Parameter estimation; Set theory;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.295904

Filename

295904