Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Similarity Equivariant Linear Transformation of Joint Orientation-Scale
  Space Representations   Convolution is conventionally defined as a linear operation on functions of
one or more variables which commutes with shifts. Group convolution generalizes
the concept to linear operations on functions of group elements representing
more general geometric transformations and which commute with those
transformations. Since similarity transformation is the most general geometric
transformation on images that preserves shape, the group convolution that is
equivariant to similarity transformation is the most general shape preserving
linear operator. Because similarity transformations have four free parameters,
group convolutions are defined on four-dimensional, joint orientation-scale
spaces. Although prior work on equivariant linear operators has been limited to
discrete groups, the similarity group is continuous. In this paper, we describe
linear operators on discrete representations that are equivariant to continuous
similarity transformation. This is achieved by using a basis of functions that
is it joint shiftable-twistable-scalable. These pinwheel functions use Fourier
series in the orientation dimension and Laplace transform in the log-scale
dimension to form a basis of spatially localized functions that can be
continuously interpolated in position, orientation and scale. Although this
result is potentially significant with respect to visual computation generally,
we present an initial demonstration of its utility by using it to compute a
shape equivariant distribution of closed contours traced by particles
undergoing Brownian motion in velocity. The contours are constrained by sets of
points and line endings representing well known bistable illusory contour
inducing patterns.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg