N-D Tensor Voting - Manual
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.