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   -> Volume 7, Issue 8

Preprint: Computer vision and image analysis (Y.P-Wang)
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Wang Yu-Ping (

PostPosted: Sat Aug 08, 1998 8:30 am    
Subject: Preprint: Computer vision and image analysis (Y.P-Wang)
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#3 Preprint: Computer vision and image analysis (Y.P-Wang)

1. Title: Scale-space derived from B-splines,

to be published in IEEE Trans. Pattern Analysis and
Machine Intelligence

Authors: Yu-Ping Wang, S. L. Lee

Abstract: It is well-known that linear scale-space theory in computer
vision is mainly based on the Gaussian kernel. The purpose of the
paper is to propose a scale-space theory based on B-spline
kernels. Our aim is twofold. On one hand, we present a general
framework and show how B-splines provide a flexible tool to design
various scale-space representations: continuous scale-space, dyadic
scale-space frame, and compact scale-space representation. In
particular, we focus on the design of continuous scale-space and
dyadic scale-space frame representation. A general algorithm is
presented for fast implementation of continuous scale-space at
rational scales. In the dyadic case, efficient frame algorithms are
derived using B-spline techniques to analyze the geometry of an
image. Moreover, the image can be synthesized from its multiscale
local partial derivatives. Also the relationship between several
scale-space approaches is explored. In particular, the evolution of
wavelet theory from traditional scale-space filtering can be well
understood in terms of B-splines. On the other hand, the behavior of
edge models, the properties of completeness, causality, and other
properties in such a scale-space representation are examined in the
framework of B-splines. It is shown that, besides the good properties
inherited from the Gaussian kernel, the B-spline derived scale-space
exhibits many advantages for modeling visual mechanism with regard to
the efficiency, compactness, orientation feature and parallel

Index terms: Image modeling, B-spline, wavelet, scale-space, scaling
theorem, fingerprint theorem.

2. Title: Image representations using multiscale differential operators

Author: Yu-Ping Wang

Abstract: Differential operators have been widely used for multiscale
geometric descriptions of images. The efficient computation of these
differential operators is always desirable. Moreover, it has not been
clear whether such representations are invertible. In this paper, such
problems are studied. We consider multiscale differential
representations of images using different types of operators such as
the directional derivative operators and Laplacian operators. In
particular, we provide a general approach to represent images by their
multiscale and multi-directional derivative components. For practical
implementation, efficient pyramid-like algorithms are derived using
spline technique for both the decomposition and reconstruction of
images. It is shown that using these representations various
meaningful geometric information of images can be extracted at
multiple scales; therefore, these representations can be used for edge
based image processing purposes. Furthermore, the intrinsic
relationships of the proposed representations with the compact wavelet
models, and some classical multiscale approaches are also elucidated
in the paper.

Keywords: Computer vision, Image representation, Edge detection,
B-splines, Wavelet, Scale-space

The above preprints are available at the URL:

Thanks for your comments and suggestions.

WANG Yu-Ping Email:
Dept. of Math. Fax: (65)7795452
National University of Singapore Phone:(65)8742773(lab)
10 Kent Ridge Crescent (65)8745005(office)
Singapore 119260
All times are GMT + 1 Hour
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