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我需要优化由点的二维网格表示的表面,以生成与提供的目标法 vector 对齐的表面法 vector 。网格大小可能在 201x201 和 1001x1001 之间。这意味着变量的数量将为 40,000 到 1,000,000,因为我只修改网格点的 z 坐标。
我正在使用 Ceres 框架,因为它应该擅长处理大规模非线性优化问题。我已经尝试过 MATLAB 的 fmincon,但它使用了难以置信的内存量。我写了一个适用于小网格的目标函数(在 3x3 和 31x31 上成功)。但是,当我尝试编译具有较大网格尺寸 (157x200) 的代码时,我看到以下错误。我读到这是 Eigen 的限制。但是,当我告诉 Ceres 使用 LAPACK 而不是 Eigen 时,对于大矩阵我会得到同样的错误。我试过这些行:
options.dense_linear_algebra_library_type = ceres::LAPACK;
options.linear_solver_type = ceres::DENSE_QR;
这些告诉求解器使用 LAPACK 和 DENSE_QR,如使用 3x3 网格的输出所示:
Minimizer TRUST_REGION
Dense linear algebra library LAPACK
Trust region strategy LEVENBERG_MARQUARDT
Given Used
Linear solver DENSE_QR DENSE_QR
Threads 1 1
Linear solver threads 1 1
但是,当我使用大参数时,我仍然会遇到 Eigen 的错误。
无论如何,我真的需要一些帮助。如何让 Ceres 优化大量变量(> 30,000)?提前致谢
Ceres 链接:http://ceres-solver.org
Eigen 链接:http://eigen.tuxfamily.org/dox/
错误:
In file included from /usr/include/eigen3/Eigen/Core:254:0,
from /usr/local/include/ceres/jet.h:165,
from /usr/local/include/ceres/internal/autodiff.h:145,
from /usr/local/include/ceres/autodiff_cost_function.h:132,
from /usr/local/include/ceres/ceres.h:37,
from /home/ubuntu/code/surfaceopt/surfaceopt.cc:10:
/usr/include/eigen3/Eigen/src/Core/DenseStorage.h: In instantiation of ‘Eigen::internal::plain_array<T, Size, MatrixOrArrayOptions, Alignment>::plain_array() [with T = double; int Size = 31400; int MatrixOrArrayOptions = 2; int Alignment = 0]’:
/usr/include/eigen3/Eigen/src/Core/DenseStorage.h:117:27: required from ‘Eigen::DenseStorage<T, Size, _Rows, _Cols, _Options>::DenseStorage() [with T = double; int Size = 31400; int _Rows = 31400; int _Cols = 1; int _Options = 2]’
/usr/include/eigen3/Eigen/src/Core/PlainObjectBase.h:421:55: required from ‘Eigen::PlainObjectBase<Derived>::PlainObjectBase() [with Derived = Eigen::Matrix<double, 31400, 1, 2, 31400, 1>]’
/usr/include/eigen3/Eigen/src/Core/Matrix.h:203:41: required from ‘Eigen::Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::Matrix() [with _Scalar = double; int _Rows = 31400; int _Cols = 1; int _Options = 2; int _MaxRows = 31400; int _MaxCols = 1]’
/usr/local/include/ceres/jet.h:179:13: required from ‘ceres::Jet<T, N>::Jet() [with T = double; int N = 31400]’
/usr/local/include/ceres/internal/fixed_array.h:138:10: required from ‘ceres::internal::FixedArray<T, inline_elements>::FixedArray(ceres::internal::FixedArray<T, inline_elements>::size_type) [with T = ceres::Jet<double, 31400>; long int inline_elements = 0l; ceres::internal::FixedArray<T, inline_elements>::size_type = long unsigned int]’
/usr/local/include/ceres/internal/autodiff.h:233:70: required from ‘static bool ceres::internal::AutoDiff<Functor, T, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Differentiate(const Functor&, const T* const*, int, T*, T**) [with Functor = ComputeEint; T = double; int N0 = 31400; int N1 = 0; int N2 = 0; int N3 = 0; int N4 = 0; int N5 = 0; int N6 = 0; int N7 = 0; int N8 = 0; int N9 = 0]’
/usr/local/include/ceres/autodiff_cost_function.h:218:25: required from ‘bool ceres::AutoDiffCostFunction<CostFunctor, kNumResiduals, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Evaluate(const double* const*, double*, double**) const [with CostFunctor = ComputeEint; int kNumResiduals = 1; int N0 = 31400; int N1 = 0; int N2 = 0; int N3 = 0; int N4 = 0; int N5 = 0; int N6 = 0; int N7 = 0; int N8 = 0; int N9 = 0]’
/home/ubuntu/code/surfaceopt/surfaceopt.cc:367:1: required from here
/usr/include/eigen3/Eigen/src/Core/DenseStorage.h:41:5: error: ‘OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG’ is not a member of ‘Eigen::internal::static_assertion<false>’
EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
^
/usr/include/eigen3/Eigen/src/Core/DenseStorage.h: In instantiation of ‘Eigen::internal::plain_array<T, Size, MatrixOrArrayOptions, 16>::plain_array() [with T = double; int Size = 31400; int MatrixOrArrayOptions = 1]’:
/usr/include/eigen3/Eigen/src/Core/DenseStorage.h:120:59: required from ‘Eigen::DenseStorage<T, Size, _Rows, _Cols, _Options>::DenseStorage(Eigen::DenseIndex, Eigen::DenseIndex, Eigen::DenseIndex) [with T = double; int Size = 31400; int _Rows = 1; int _Cols = 31400; int _Options = 1; Eigen::DenseIndex = long int]’
/usr/include/eigen3/Eigen/src/Core/PlainObjectBase.h:438:41: required from ‘Eigen::PlainObjectBase<Derived>::PlainObjectBase(Eigen::PlainObjectBase<Derived>::Index, Eigen::PlainObjectBase<Derived>::Index, Eigen::PlainObjectBase<Derived>::Index) [with Derived = Eigen::Matrix<double, 1, 31400, 1, 1, 31400>; Eigen::PlainObjectBase<Derived>::Index = long int]’
/usr/include/eigen3/Eigen/src/Core/Matrix.h:273:76: required from ‘Eigen::Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::Matrix(const Eigen::MatrixBase<OtherDerived>&) [with OtherDerived = Eigen::Transpose<const Eigen::Matrix<double, 31400, 1, 2, 31400, 1> >; _Scalar = double; int _Rows = 1; int _Cols = 31400; int _Options = 1; int _MaxRows = 1; int _MaxCols = 31400]’
/usr/include/eigen3/Eigen/src/Core/DenseBase.h:367:62: required from ‘Eigen::DenseBase<Derived>::EvalReturnType Eigen::DenseBase<Derived>::eval() const [with Derived = Eigen::Transpose<const Eigen::Matrix<double, 31400, 1, 2, 31400, 1> >; Eigen::DenseBase<Derived>::EvalReturnType = const Eigen::Matrix<double, 1, 31400, 1, 1, 31400>]’
/usr/include/eigen3/Eigen/src/Core/IO.h:244:69: required from ‘std::ostream& Eigen::operator<<(std::ostream&, const Eigen::DenseBase<Derived>&) [with Derived = Eigen::Transpose<const Eigen::Matrix<double, 31400, 1, 2, 31400, 1> >; std::ostream = std::basic_ostream<char>]’
/usr/local/include/ceres/jet.h:632:35: required from ‘std::ostream& ceres::operator<<(std::ostream&, const ceres::Jet<T, N>&) [with T = double; int N = 31400; std::ostream = std::basic_ostream<char>]’
/home/ubuntu/code/surfaceopt/surfaceopt.cc:103:50: required from ‘bool ComputeEint::operator()(const T*, T*) const [with T = ceres::Jet<double, 31400>]’
/usr/local/include/ceres/internal/variadic_evaluate.h:175:26: required from ‘static bool ceres::internal::VariadicEvaluate<Functor, T, N0, 0, 0, 0, 0, 0, 0, 0, 0, 0>::Call(const Functor&, const T* const*, T*) [with Functor = ComputeEint; T = ceres::Jet<double, 31400>; int N0 = 31400]’
/usr/local/include/ceres/internal/autodiff.h:283:45: required from ‘static bool ceres::internal::AutoDiff<Functor, T, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Differentiate(const Functor&, const T* const*, int, T*, T**) [with Functor = ComputeEint; T = double; int N0 = 31400; int N1 = 0; int N2 = 0; int N3 = 0; int N4 = 0; int N5 = 0; int N6 = 0; int N7 = 0; int N8 = 0; int N9 = 0]’
/usr/local/include/ceres/autodiff_cost_function.h:218:25: required from ‘bool ceres::AutoDiffCostFunction<CostFunctor, kNumResiduals, N0, N1, N2, N3, N4, N5, N6, N7, N8, N9>::Evaluate(const double* const*, double*, double**) const [with CostFunctor = ComputeEint; int kNumResiduals = 1; int N0 = 31400; int N1 = 0; int N2 = 0; int N3 = 0; int N4 = 0; int N5 = 0; int N6 = 0; int N7 = 0; int N8 = 0; int N9 = 0]’
/home/ubuntu/code/surfaceopt/surfaceopt.cc:367:1: required from here
/usr/include/eigen3/Eigen/src/Core/DenseStorage.h:79:5: error: ‘OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG’ is not a member of ‘Eigen::internal::static_assertion<false>’
EIGEN_STATIC_ASSERT(Size * sizeof(T) <= 128 * 128 * 8, OBJECT_ALLOCATED_ON_STACK_IS_TOO_BIG);
^
make[2]: *** [CMakeFiles/surfaceopt.dir/surfaceopt.cc.o] Error 1
make[1]: *** [CMakeFiles/surfaceopt.dir/all] Error 2
make: *** [all] Error 2
我的代码看起来像这样(为了去掉不相关的 Material 而简化):
#define TEXT true
#define VERBOSE false
#define NV 31400
#define NF 62088
#define NX 157
#define NY 200
#define MAXNB 6
#include <math.h>
#include <ceres/ceres.h>
#include <ceres/rotation.h>
#include "glog/logging.h"
#include <iostream>
#include <fstream>
#include <iterator>
#include <algorithm>
#include <string>
using ceres::AutoDiffCostFunction;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;
using ceres::CrossProduct;
...
class ComputeEint {
private:
double XY_ [NV][2]; // X and Y coords
int C_ [NF][3]; // Connectivity list
int AF_ [NV][MAXNB]; // List of adjacent faces to each vertex
double Ntgt_ [NV][3]; // Target normal vectors
int num_AF_ [NV]; // Number of adjacent faces to each vertex
public:
//Constructor
ComputeEint(double XY[][2], int C[][3], int AF[][MAXNB], double Ntgt[][3], int num_AF[NV]) {
std::copy(&XY[0][0], &XY[0][0]+NV*2,&XY_[0][0]);
...
template <typename T>
bool operator()(const T* const z, T* e) const {
e[0] = T(0);
...
//Computes vertex normals for triangulated surface by averaging adjacent face normals
...
e[0] = e[0]/T(NV);
return true;
}
};
int main(int argc, char** argv) {
google::InitGoogleLogging(argv[0]);
double Tp [NV][3]; //Points in mesh
int Tc [NF][3]; //Mesh connectivity list
double Ntgt [NV][3]; //Target normals
int AF [NV][MAXNB]; //List of adjacent faces of each vertex
int num_AF [NV]; //Number of adjacent faces for each vertex
int nx = NX;
int ny = NY;
//Read Tp, Tc, Ntgt, AF, num_AF from file
...
// Set up XY for cost functor
double XY [NV][2];
double z [NV];
//Copy first two columns of Tp into XY
Problem problem;
// Set up the only cost function (also known as residual). This uses
// auto-differentiation to obtain the derivative (jacobian).
CostFunction* cost_function =
new AutoDiffCostFunction<ComputeEint, 1, NV>(new ComputeEint(XY, Tc, AF, Ntgt, num_AF));
std::cout << "Created cost function" << "\n";
problem.AddResidualBlock(cost_function, NULL, &z[0]);
std::cout << "Added residual block" << "\n";
// Run the solver!
Solver::Options options;
options.minimizer_progress_to_stdout = true;
options.max_num_iterations = 50;
options.function_tolerance = 1e-4;
options.dense_linear_algebra_library_type = ceres::LAPACK;
Solver::Summary summary;
Solve(options, &problem, &summary);
std::cout << summary.FullReport() << "\n";
//Write output of optimization to file
...
return 0;
}
最佳答案
两件事
如果您使用的是 1.9 或更早版本,您将需要 SuiteSpare/CXSparse。如果您使用最新的候选版本或 git 版本,您应该也可以使用 Eigen 来执行稀疏线性代数。
查看 ceres 附带的示例代码,例如 denoising.cc,它对整个图像进行去噪,并具有类似的网格状结构。
更一般地说,为问题中的每个顶点创建一个残差 block 。
关于c++ - 如何用Ceres解决大规模非线性优化问题?,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/26336036/
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