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/* Copyright (c) 2008-2025 the MRtrix3 contributors.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* Covered Software is provided under this License on an "as is"
* basis, without warranty of any kind, either expressed, implied, or
* statutory, including, without limitation, warranties that the
* Covered Software is free of defects, merchantable, fit for a
* particular purpose or non-infringing.
* See the Mozilla Public License v. 2.0 for more details.
*
* For more details, see http://www.mrtrix.org/.
*/
#include "command.h"
#include "progressbar.h"
#include "math/rng.h"
#include "math/SH.h"
#include "dwi/gradient.h"
#include "dwi/directions/file.h"
#include <random>
#include <functional>
using namespace MR;
using namespace App;
void usage ()
{
AUTHOR = "J-Donald Tournier (jdtournier@gmail.com)";
SYNOPSIS = "Reorder a set of directions to ensure near-uniformity upon truncation";
DESCRIPTION
+ "The intent of this command is to reorder a set of gradient directions such that "
"if a scan is terminated prematurely, at any point, the acquired directions will "
"still be close to optimally distributed on the half-sphere.";
ARGUMENTS
+ Argument ("input", "the input directions file").type_file_in()
+ Argument ("output", "the output directions file").type_file_out();
OPTIONS
+ Option ("cartesian", "Output the directions in Cartesian coordinates [x y z] instead of [az el].");
}
using value_type = double;
vector<size_t> optimise (const Eigen::MatrixXd& directions, const size_t first_volume)
{
vector<size_t> indices (1, first_volume);
vector<size_t> remaining;
for (size_t n = 0; n < size_t(directions.rows()); ++n)
if (n != indices[0])
remaining.push_back (n);
while (remaining.size()) {
ssize_t best = 0;
value_type best_E = std::numeric_limits<value_type>::max();
for (size_t n = 0; n < remaining.size(); ++n) {
value_type E = 0.0;
ssize_t a = remaining[n];
for (size_t i = 0; i < indices.size(); ++i) {
ssize_t b = indices[i];
E += 1.0 / (directions.row(a) - directions.row(b)).norm();
E += 1.0 / (directions.row(a) + directions.row(b)).norm();
}
if (E < best_E) {
best_E = E;
best = n;
}
}
indices.push_back (remaining[best]);
remaining.erase (remaining.begin()+best);
}
return indices;
}
value_type calc_cost (const Eigen::MatrixXd& directions, const vector<size_t>& order)
{
const size_t start = Math::SH::NforL (2);
if (size_t(directions.rows()) <= start)
return value_type(0);
Eigen::MatrixXd subset (start, 3);
for (size_t i = 0; i != start; ++i)
subset.row(i) = directions.row(order[i]);
value_type cost = value_type(0);
for (size_t N = start+1; N < size_t(directions.rows()); ++N) {
// Don't include condition numbers where precisely the number of coefficients
// for that spherical harmonic degree are included, as these tend to
// be outliers
const size_t lmax = Math::SH::LforN (N-1);
subset.conservativeResize (N, 3);
subset.row(N-1) = directions.row(order[N-1]);
const value_type cond = DWI::condition_number_for_lmax (subset, lmax);
cost += cond;
}
return cost;
}
void run ()
{
auto directions = DWI::Directions::load_cartesian (argument[0]);
size_t last_candidate_first_volume = directions.rows();
if (size_t(directions.rows()) <= Math::SH::NforL (2)) {
WARN ("Very few directions in input ("
+ str(directions.rows())
+ "); selection of first direction cannot be optimised"
+ " (first direction in input will be first direction in output)");
last_candidate_first_volume = 1;
}
value_type min_cost = std::numeric_limits<value_type>::infinity();
vector<size_t> best_order;
ProgressBar progress ("Determining best reordering", directions.rows());
for (size_t first_volume = 0; first_volume != last_candidate_first_volume; ++first_volume) {
const vector<size_t> order = optimise (directions, first_volume);
const value_type cost = calc_cost (directions, order);
if (cost < min_cost) {
min_cost = cost;
best_order = order;
}
++progress;
}
decltype(directions) output (directions.rows(), 3);
for (ssize_t n = 0; n < directions.rows(); ++n)
output.row(n) = directions.row (best_order[n]);
DWI::Directions::save (output, argument[1], get_options("cartesian").size());
}
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