Mr. Jucheng Zhao Profile

Jucheng Zhao

SPIE Involvement:

Author

Publications (1)

This will count as one of your downloads.

You will have access to both the presentation and article (if available).

DOWNLOAD NOW

This content is available for download via your institution's subscription. To access this item, please sign in to your personal account.

Email or Username Forgot your username?

Password Forgot your password?

Show

Keep me signed in

No SPIE account? Create an account

Proceedings Article | 17 September 2005 Paper

PHLFT5: a practical and improved version of polyharmonic local Fourier transform

Jucheng Zhao, Naoki Saito, Katsu Yamatani

Proceedings Volume 5914, 59141N (2005) https://doi.org/10.1117/12.618584

KEYWORDS: Algorithm development, Statistical analysis, Fourier transforms, Tolerancing, Image quality, Image analysis, Eye, Image segmentation, Mathematics, Systems engineering

Read Abstract +

We introduce a practical and improved version of the Polyharmonic Local Fourier transform (PHLFT) called PHLFT5. After partitioning an input image into a set of rectangular blocks, the original PHLFT decomposes each block into the polyharmonic component and the residual. The polyharmonic component solves the polyharmonic equation with the boundary condition that matches the values and normal derivatives of first order up to higher order of the solution along the block boundary with those of the original image block. Thanks to this boundary condition, the residual component can be expanded into a complex Fourier series without facing the Gibbs phenomenon and its Fourier coefficients decay faster than those of the original block. Due to the difficulty of estimating the higher order normal derivatives, however, only the harmonic case (i.e., Laplace's equation) has been implemented to date. In that case, the Fourier coefficients of the residual decay as O (||k||^-2) where k is the frequency index vector. Unlike the original version, PHLFT5 only imposes the boundary values and the first order normal derivatives as the boundary condition, which can be estimated using our robust algorithm. We then derive a fast algorithm to compute a fifth degree polyharmonic function that satisfies such boundary condition. The Fourier coefficients of the residual now decay as O (||k||^-3). We shall also show our preliminary numerical experiments that demonstrates the superiority of PHLFT5 over the original PHLFT of harmonic case in terms of the decay rate of the residual and interpretability of oriented textures.

My Library

You currently do not have any folders to save your paper to! Create a new folder below.

Folder Name

Folder Description

View contact details

UPDATE YOUR PROFILE

Is this your profile? Update it now.

Sign into your SPIE.org account

Don’t have a profile and want one?

Create an account on SPIE.org

Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks. You are receiving this notice because your organization may not have SPIE eBooks access.*

*Shibboleth/Open Athens users─please sign in to access your institution's subscriptions.

To obtain this item, you may purchase the complete book in print or electronic format on SPIE.org.

ORGANIZATIONAL
Sign in with credentials provided by your organization.

Organizational Username

Organizational Password

Show/Hide Password

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:

Non-members: ADD TO CART

Keywords/Phrases

Search In:

Publication Years