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   -> Volume 4, Issue 8

Preprint: B-spline wavelet for multiscale edge detection
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Wang Yuping (

PostPosted: Tue Dec 03, 2002 1:30 pm    
Subject: Preprint: B-spline wavelet for multiscale edge detection
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Preprint: B-spline wavelet for multiscale edge detection

Title: Construction and properties of B-spline wavelet
for multiscale edge detection

Authors: Yu Ping Wang, Yuan Long Cai.,

Part of the paper will appear at 1995 IEEE international conferences
on image processing. For details,refer to <<Science in China>>(in
English) Series A,vol.38,no.4,pp.499-512.


B-spline plays a very important role in wavelet theory.Starting from
B-splne, one can construct orthonomal spline wavelet and
non-orthogonal wavelet. One can derive fast implementaion of
continous wavelet transform.etc.All seems in that polynomial spline
function space as the basis of translated and dilated B-spline
constitutes a multiresolution or multiscale approximation of L^2(R)
space. Many authors such as M.Unser,C.K.Chui,J.Z.Wang have made
contribution to this subject. In this paper we aim to use B-spline to
construct wavelet for multiscale edge detection inclulding both the
zero-crossing detection and the maximum detection. Such a transform
is called dyadic wavelet transform originally proposed by S.Mallt.
The edges of a signal can be efficienctly represented and detected
through its zero-crossing or maximum.For B-spline of any order n,the
fast algorithm for decomposition and reconstruction have been
derived.Also the impulse and frequency responses of the corresponding
decomposition and reconstruction filters are given explicitly.We will
show Mallat's wavelet for maximum detection is just one example of the
wavelet designed by us.In terms of time/frequency localization we will
show cubic B-spline is nearly optimal for most applictions.One has the
freedom using the proposed B-spline wavelet to do many applications
such as multiedge-based compression,stereo matching,denosing,conner
detection.etc. To our knowledge,Gaussian functon or its molulation as
Gabor function has occupied a great position in computer vision and
image processing for a long time. Most scale-space approaches are
based on these functions.For its good properties and similarity to
Gaussian function,we believe that B-spline combinaitng wavelet theory
will have great potentiality in computer vision.

Comments are welcome,please contact with the authors.

Wang Yuping or Cai Yuanlong

Image Processing Center
School of Electronic & Information Engineering
Xi'an Jiaotong University,Shaanxi,710049


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