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The executable reads an input file, performs tensor
voting with the user-defined value for sigma2 and writes
the resulting tensors to the output file. The syntax
is:
VotingND infile outfile sigma2
The input file is a text file that begins with an
unsigned integer that specifies the dimensionality of
the space, followed by a list of un-oriented points or
tensors, or a mixture of both. An un-oriented point is
represented by its coordinates followed by a 0, such
that a file containing un-oriented points would look
like this:
N
x1_1 x1_2 … x1_N 0
x2_1 x2_2 … x2_N 0
…
xM_1 xM_2 … xM_N 0
Where xi are the M points and xi_j, j=1..N are the
coordinates of each point. The number of points does not
need to be specified. The points are encoded as unit
ball tensors with all eigenvalues equal to one and an
orthonormal set of eigenvectors.
Alternatively, one can input points with orientation
information in the form of tensors. In this case, the
coordinates are followed by a 1 to indicate that the
point is associated with a tensor. Following the 1, the
input file contains the eigenvalues of the tensor in
decreasing order and then the eigenvectors starting from
the one corresponding to the maximum eigenvalue. The
input file should be in the following form:
N
x1_1 x1_2 … x1_N 1
lambda1_1 lambda1_2… lambda1_N
e1_11 e1_12 … e1_1N
…
e1_N1 e1_N2 … e1_NN
…
…
xM_1 xM_2 … xM_N 1
lambdaM_1 lambdaM_2… lambdaM_N
eM_11 eM_12 … eM_1N
…
eM_N1 eM_N2 … eM_NN
Line feeds are actually ignored. They are included
here for clarity. Also, the code can read the 0 or 1
index in integer or floating form. If one wishes to
compute saliency values at locations that do not
participate in the computation, these should be
associated with zero ball tensors. Such tensors have to
be provided in the second format as tensors with all
eigenvalues equal to zero.
The output file is also a text file that contains the
tensors accumulated after voting at the input positions.
It is always in the second format. It can be used
directly as input for a second pass of tensor voting, if
so desired.
The final parameter is the square of the scale of the
voting field which effectively determines the size of
the voting neighborhood and the degree of smoothness.
The scale should be set according to the dimensions of
the input space. A scale below 1.0 would probably result
in no information propagation in a space where the
average distance between points is more than 10 units of
length.
Since Euclidean distances are used when computing the
magnitude of the votes that are cast from point to
point, the input coordinates may need to be scaled in a
way that ensures that the Euclidean distances between
points are meaningful. This functionality is not
provided since it is problem-dependent.
Note: Our software contains the Approximate Nearest
Neighbor (ANN) k-d tree library (release 0.1) of the
University of Maryland and Sunil Arya and David Mount.
We are grateful to the authors for making their software
publicly available. The license agreement of the ANN
library is the following:
Copyright (c) 1997-1998 University of Maryland and
Sunil Arya and David Mount. All Rights Reserved.
This software and related documentation is part of
the Approximate Nearest Neighbor Library (ANN).
Permission to use, copy, and distribute this software
and its documentation is hereby granted free of charge,
provided that:
(1) it is not a component of a commercial product, and
(2) this notice appears in all copies of the software
and related documentation.
The University of Maryland (U.M.) and the authors
make no representations about the suitability or fitness
of this software for any purpose. It is provided "as is"
without express or implied warranty.
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