Equivalent weighting functions to equivalent contraction kernels

Walter G. Kropatsch

doi:10.1117/12.301380

1 February 1998 From equivalent weighting functions to equivalent contraction kernels

Walter G. Kropatsch

Proceedings Volume 3346, Sixth International Workshop on Digital Image Processing and Computer Graphics: Applications in Humanities and Natural Sciences; (1998) https://doi.org/10.1117/12.301380
Event: Sixth International Workshop on Digital Image Processing and Computer Graphics, 1997, Vienna, Austria

Abstract

Burt introduced 1983 'equivalent weighting function': 'Iterative pyramid generation is equivalent to convolving the image g₀ with a set of 'equivalent weighting functions' h_l' g_l equals h_l * g₀ equals h * g_l-1, l > 1. It allowed him to study the effects of iterated reduction using the single parameter h_l without giving up the efficient iterative computation. A similar concept applies to graph pyramids built by dual graph contraction. This new algorithm reduces the number of vertices and of edges of a pair of dual image graphs while, at he same time, the topological relations among the 'surviving' components are preserved. Repeated application produces a stack of successively smaller graphs: a pari of dual irregular pyramids. The process is controlled by selected decimation parameters which consist of a subset of surviving vertices and associated contraction kernels. These pay a similar role for graph pyramids than the convolution kernels of Gaussian pyramids. Equivalent contraction kernels combine two or more contraction kernels int one single dual contraction. The basic concepts are elaborated and discussed. The new theory opens a large variety of possibilities to explore the domain of 'all' graph pyramids.

Citation Download Citation

Walter G. Kropatsch "From equivalent weighting functions to equivalent contraction kernels", Proc. SPIE 3346, Sixth International Workshop on Digital Image Processing and Computer Graphics: Applications in Humanities and Natural Sciences, (1 February 1998); https://doi.org/10.1117/12.301380

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