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Summary: Holomorphic Filters for Object Detection
Marco Reisert, Olaf Ronneberger and Hans Burkhardt
University of Freiburg, Computer Science Department,
79110 Freiburg i.Br., Germany
reisert@informatik.uni-freiburg.de
Abstract. It is well known that linear filters are not powerful enough
for many low-level image processing tasks. But it is also very difficult
to design robust non-linear filters that respond exclusively to features
of interest and that are at the same time equivariant with respect to
translation and rotation. This paper proposes a new class of rotation-
equivariant non-linear filters that is based on the principle of group in-
tergration. These filters become efficiently computable by an iterative
scheme based on repeated differentiation of products and summations of
the intermediate results. Our experiments show that the proposed filter
detects pollen porates with only half as many errors than alternative
approches, when high localization accuracy is required.
1 Introduction
In image processing the term 'filter' is mostly related to the special class of image
transformations that is characterized by the fact that they are equivariant with
respect to the group of translations. If F is an image transformation, then it is
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