Multivariate granulometric filters

Sinan Batman; Edward R. Dougherty

doi:10.1117/12.271129

4 April 1997 Multivariate granulometric filters

Sinan Batman, Edward R. Dougherty

Author Affiliations +

Proceedings Volume 3026, Nonlinear Image Processing VIII; (1997) https://doi.org/10.1117/12.271129
Event: Electronic Imaging '97, 1997, San Jose, CA, United States

Abstract

As introduced by Matheron, granulometries depend on a single sizing parameter for each structuring element. The concept of granulometry has recently been extended in such a way that each structuring element has its own sizing parameter resulting in a filter (Psi) _t depending on the vector parameter t equals (t₁..., t_n). The present paper generalizes the concept of a parameterized reconstructive (tau) -opening to the multivariate setting, where the reconstructive filter (Lambda) _t fully passes any connected component not fully eliminated by (Psi) _t. The problem of minimizing the MAE between the filtered and ideal image processes becomes one of vector optimization in an n- dimensional search space. Unlike the univariate case, the MAE achieved by the optimum filter (Lambda) _t is global in the sense that it is independent of the relative sizes of structuring elements in the filter basis. As a consequence, multivariate granulometries provide a natural environment to study optimality of the choice of structuring elements. If the shapes of the structuring elements are themselves parameterized, the expected error is a deterministic function of the shape and size parameters and its minimization yields the optimal MAE filter.

Citation Download Citation

Sinan Batman and Edward R. Dougherty "Multivariate granulometric filters", Proc. SPIE 3026, Nonlinear Image Processing VIII, (4 April 1997); https://doi.org/10.1117/12.271129

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

;

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
10 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Interference (communication)

Image filtering

Optimal filtering

Error analysis

Image processing

Monte Carlo methods

Statistical modeling

Show All Keywords

Keywords/Phrases

Search In:

Publication Years