remove levenberg-marquardt algorithm

modules/img/alg/src/CMakeLists.txt

@@ -59,7 +59,6 @@ gaussian.hh
 gaussian_laplacian.hh
 highest_peak_search_3d.hh
 histogram.hh
-levenberg_marquardt.h
 line_iterator.hh
 local_sigma_threshold.hh
 mask_image.hh

modules/img/alg/src/levenberg_marquardt.h

-// Copyright (c) 2007, 2008, 2009 libmv authors.
-//
-// Permission is hereby granted, free of charge, to any person obtaining a copy
-// of this software and associated documentation files (the "Software"), to
-// deal in the Software without restriction, including without limitation the
-// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
-// sell copies of the Software, and to permit persons to whom the Software is
-// furnished to do so, subject to the following conditions:
-//
-// The above copyright notice and this permission notice shall be included in
-// all copies or substantial portions of the Software.
-//
-// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
-// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
-// IN THE SOFTWARE.
-//
-// A simple implementation of levenberg marquardt.
-//
-// [1] K. Madsen, H. Nielsen, O. Tingleoff. Methods for Non-linear Least
-// Squares Problems.
-// http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf
-//
-// TODO(keir): Cite the Lourakis' dogleg paper.
-
-#ifndef LIBMV_NUMERIC_LEVENBERG_MARQUARDT_H
-#define LIBMV_NUMERIC_LEVENBERG_MARQUARDT_H
-
-#include <cmath>
-#include <Eigen/Core>
-#include <Eigen/Eigenvalues>
-
-
-namespace ost { namespace img { namespace alg {
-
-template<typename Function,
-         typename Jacobian,
-         typename Solver = Eigen::JacobiSVD<
-                  Eigen::Matrix<typename Function::FMatrixType::RealScalar,
-                  Function::XMatrixType::RowsAtCompileTime,
-                  Function::XMatrixType::RowsAtCompileTime> > >
-class LevenbergMarquardt {
- public:
-  typedef typename Function::XMatrixType::RealScalar Scalar;
-  typedef typename Function::FMatrixType FVec;
-  typedef typename Function::XMatrixType Parameters;
-  typedef Eigen::Matrix<typename Function::FMatrixType::RealScalar,
-                        Function::FMatrixType::RowsAtCompileTime,
-                        Function::XMatrixType::RowsAtCompileTime> JMatrixType;
-  typedef Eigen::Matrix<typename JMatrixType::RealScalar,
-                        JMatrixType::ColsAtCompileTime,
-                        JMatrixType::ColsAtCompileTime> AMatrixType;
-
-  // TODO(keir): Some of these knobs can be derived from each other and
-  // removed, instead of requiring the user to set them.
-  enum Status {
-    RUNNING,
-    GRADIENT_TOO_SMALL,            // eps > max(J'*f(x))
-    RELATIVE_STEP_SIZE_TOO_SMALL,  // eps > ||dx|| / ||x||
-    ERROR_TOO_SMALL,               // eps > ||f(x)||
-    HIT_MAX_ITERATIONS,
-  };
-
-  LevenbergMarquardt(const Function &f)
-      : f_(f), df_(f) {}
-
-  struct SolverParameters {
-   SolverParameters()
-       : gradient_threshold(1e-20),
-         relative_step_threshold(1e-20),
-         error_threshold(1e-16),
-         initial_scale_factor(1e-3),
-         max_iterations(200) {}
-    Scalar gradient_threshold;       // eps > max(J'*f(x))
-    Scalar relative_step_threshold;  // eps > ||dx|| / ||x||
-    Scalar error_threshold;          // eps > ||f(x)||
-    Scalar initial_scale_factor;     // Initial u for solving normal equations.
-    int    max_iterations;           // Maximum number of solver iterations.
-  };
-
-  struct Results {
-    Scalar error_magnitude;     // ||f(x)||
-    Scalar gradient_magnitude;  // ||J'f(x)||
-    int    iterations;
-    Status status;
-  };
-
-  Status Update(const Parameters &x, const SolverParameters &params,
-                JMatrixType *J, AMatrixType *A, FVec *error, Parameters *g) {
-    *J = df_(x);
-    *A = (*J).transpose() * (*J);
-    *error = -f_(x);
-    *g = (*J).transpose() * *error;
-    if (g->array().abs().maxCoeff() < params.gradient_threshold) {
-      return GRADIENT_TOO_SMALL;
-    } else if (error->norm() < params.error_threshold) {
-      return ERROR_TOO_SMALL;
-    }
-    return RUNNING;
-  }
-
-  Results minimize(Parameters *x_and_min) {
-    SolverParameters params;
-    return minimize(params, x_and_min);
-  }
-
-  Results minimize(const SolverParameters &params, Parameters *x_and_min) {
-    Parameters &x = *x_and_min;
-    JMatrixType J;
-    AMatrixType A;
-    FVec error;
-    Parameters g;
-
-    Results results;
-    results.status = Update(x, params, &J, &A, &error, &g);
-
-    Scalar u = Scalar(params.initial_scale_factor*A.diagonal().maxCoeff());
-    Scalar v = 2;
-
-    Parameters dx, x_new;
-    int i;
-    for (i = 0; results.status == RUNNING && i < params.max_iterations; ++i) {
-//      LOG(INFO) << "iteration: " << i;
-//      LOG(INFO) << "||f(x)||: " << f_(x).norm();
-//      LOG(INFO) << "max(g): " << g.array().abs().maxCoeff();
-//      LOG(INFO) << "u: " << u;
-//      LOG(INFO) << "v: " << v;
-      AMatrixType A_augmented = A + u*AMatrixType::Identity(J.cols(), J.cols());
-      Solver solver(A_augmented, Eigen::ComputeThinU | Eigen::ComputeThinV);
-      dx = solver.solve(g);
-      if (dx.norm() <= params.relative_step_threshold * x.norm()) {
-          results.status = RELATIVE_STEP_SIZE_TOO_SMALL;
-          break;
-      }
-
-      x_new = x + dx;
-      // Rho is the ratio of the actual reduction in error to the reduction
-      // in error that would be obtained if the problem was linear.
-      // See [1] for details.
-      Scalar rho((error.squaredNorm() - f_(x_new).squaredNorm())
-                 / dx.dot(u*dx + g));
-      if (rho > 0) {
-        // Accept the Gauss-Newton step because the linear model fits well.
-        x = x_new;
-        results.status = Update(x, params, &J, &A, &error, &g);
-        Scalar tmp = Scalar(2*rho-1);
-        u = u*std::max(Scalar(1/3.), 1 - (tmp*tmp*tmp));
-        v = 2;
-        continue;
-      }
-      
-      // Reject the update because either the normal equations failed to solve
-      // or the local linear model was not good (rho < 0). Instead, increase u
-      // to move closer to gradient descent.
-      u *= v;
-      v *= 2;
-    }
-    if (results.status == RUNNING) {
-      results.status = HIT_MAX_ITERATIONS;
-    }
-    results.error_magnitude = error.norm();
-    results.gradient_magnitude = g.norm();
-    results.iterations = i;
-    return results;
-  }
-
- private:
-  const Function &f_;
-  Jacobian df_;
-};
-
-}}}  // namespace mv
-
-#endif  // LIBMV_NUMERIC_LEVENBERG_MARQUARDT_H