Incremental Fourier interpolation of 2-D fractional Brownian motion
Zhaojin Han; Denney, T.S., Jr.
Industrial Electronics, IEEE Transactions on
Volume 48, Issue 5, Oct 2001 Page(s):920 - 925
Digital Object Identifier 10.1109/41.954556
Summary:This paper presents a new method to interpolate two-dimensional
fractional Brownian motion (fBm), fBm interpolation can be used in
multimedia applications such as landscape synthesis or zooming into a
synthetic scene, where the objective is to generate an fBm field that
passes through a sparse set of known points. The fBm interpolation
problem differs from standard image interpolation because noise must be
added to the interpolated points to obtain an interpolated image with
the proper second-order statistics. Our interpolation method is based on
the first-order increments of both the original fBm and interpolated
fBm. These increments are stationary and yield interpolation equations
with a Toeplitz-block-Toeplitz structure which can be approximated by a
circulant-block-circulant matrix. By taking advantage of fast Fourier
transform, the computational complexity is
O(N2log2N) for N×N image interpolation.
Simulation shows this method achieves good second-order statistics, even
for small-size images
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