Morphological pyramids with alternating sequential filters

Aldo Morales, Raj Acharya, Sung-Jea Ko

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The aim of this paper is to find a relationship between alternating sequential filters (ASF) and the morphological sampling theorem (MST) developed by Haralick et a. The motivation behind this approach is to take advantage of the computational efficiency offered by the MST to implement morphological operations. First, we show alternative proofs for opening and closing in the sampled and unsampled domain using the basis functions. These proofs are important because they show that it possible to obtain any level of a morphological pyramid in one step rather than the traditional two-step procedure. This decomposition is then used to show the relationship of the open-closing in the sampled and unsampled domain. An upper and a lower bound, for the above relationships, are presented. Under certain circumstances, an equivalence is shown for open-closing between the sampled and the unsampled domain. An extension to more complicated algorithms using a union of openings and an intersection of closings is also proposed. Using the Hausdorff metric, it is shown that a morphologically reconstructed image cannot have a better accuracy than twice the radius of the reconstruction structuring element. Binary and gray scale examples are presented.

Original languageEnglish
Pages (from-to)965-977
Number of pages13
JournalIEEE Transactions on Image Processing
Volume4
Issue number7
DOIs
Publication statusPublished - 1995 Jul 1

Fingerprint

Pyramid
Sampling Theorem
Filter
Sampling
Computational efficiency
Morphological Operations
Hausdorff Metric
Decomposition
Computational Efficiency
Basis Functions
Union
Intersection
Radius
Equivalence
Binary
Lower bound
Decompose
Alternatives
Relationships

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Software
  • Electrical and Electronic Engineering
  • Theoretical Computer Science

Cite this

Morphological pyramids with alternating sequential filters. / Morales, Aldo; Acharya, Raj; Ko, Sung-Jea.

In: IEEE Transactions on Image Processing, Vol. 4, No. 7, 01.07.1995, p. 965-977.

Research output: Contribution to journalArticle

Morales, Aldo ; Acharya, Raj ; Ko, Sung-Jea. / Morphological pyramids with alternating sequential filters. In: IEEE Transactions on Image Processing. 1995 ; Vol. 4, No. 7. pp. 965-977.
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