Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance Transform Gradient Density Estimation using the Stationary
  Phase Approximation   The complex wave representation (CWR) converts unsigned 2D distance
transforms into their corresponding wave functions. Here, the distance
transform S(X) appears as the phase of the wave function
\phi(X)---specifically, \phi(X)=exp(iS(X)/\tau where \tau is a free parameter.
In this work, we prove a novel result using the higher-order stationary phase
approximation: we show convergence of the normalized power spectrum (squared
magnitude of the Fourier transform) of the wave function to the density
function of the distance transform gradients as the free parameter \tau-->0. In
colloquial terms, spatial frequencies are gradient histogram bins. Since the
distance transform gradients have only orientation information (as their
magnitudes are identically equal to one almost everywhere), as \tau-->0, the 2D
Fourier transform values mainly lie on the unit circle in the spatial frequency
domain. The proof of the result involves standard integration techniques and
requires proper ordering of limits. Our mathematical relation indicates that
the CWR of distance transforms is an intriguing, new representation.

25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs