AutoDifferentiation of a Sampled function

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Manohar Kuse

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Aug 5, 2016, 1:19:08 AM8/5/16
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I have a cost function which is a sampled function. The function is R^2 --> R (stored as a 2d matrix). However as I look up the values
in operator() it gives the following compiler error: The relevant part of the error is as follows:

/home/mpkusex/ros_workspaces/robotic_vision/src/edge_alignment/src/SolveEA.cpp:349:1:   required from here
/home/mpkusex/ros_workspaces/robotic_vision/src/edge_alignment/include/EAResidue.h:151:60: error: no match for call to ‘(const MatrixXd {aka const Eigen::Matrix<double, -1, -1>}) (ceres::Jet<double, 7>&, ceres::Jet<double, 7>&)’
             double readVal = now_dist_transform_eig( _v, _u);


I am aware that ceres version 1.11 
  1. has CubicInterpolator and BiCubicInterpolator to allow smooth interpolation of sampled functions and integration with automatic differentiation.
    I cannot quite figure out how to get it working.
Looking for your reply..!

My class :
class EAResidue {
public:
    /// Set the constants of the problem
    /// @param list_edge_ref : a list of 3d points in reference image 3xN
    /// @param now_dist_transform_eig : distance transform of now frame as an image (row x cols)
    EAResidue( MatrixXd& __list_edge_ref, MatrixXd& __now_dist_transform_eig, Matrix3d& K )
    {
        list_edge_ref = __list_edge_ref;
        now_dist_transform_eig = __now_dist_transform_eig;

        fx = ( K(0,0) );
        fy = ( K(1,1) );
        cx = ( K(0,2) );
        cy = ( K(1,2) );
    }


    template <typename T>
    bool operator()(const T* const Q, const T* const t, T* residual) const
    {
        T R[9];
        ceres::QuaternionToRotation(Q, R); //use `ceres::QuaternionRotatePoint`

        for( int i =0 ; i<list_edge_ref.cols() ; i++ )
        {
            T _x = T(list_edge_ref(0,i));
            T _y = T(list_edge_ref(1,i));
            T _z = T(list_edge_ref(2,i));

            // xd = R*x + t
            T _xd = t[0] + R[0] * _x + R[3] * _y + R[6] * _z;
            T _yd = t[1] + R[1] * _x + R[4] * _y + R[7] * _z;
            T _zd = t[2] + R[2] * _x + R[5] * _y + R[8] * _z;

            // de-homegenous and project
            T _u = T(fx) * _xd / _zd + T(cx);
            T _v = T(fy) * _yd / _zd + T(cy);

            double readVal = now_dist_transform_eig( _v, _u); 
//            residual[i] = T( now_dist_transform_eig( (int)_v, (int)_u) ); // <<<<<< This line is the trouble. 

        }

        return true;
    }

private:
    MatrixXd list_edge_ref;
    MatrixXd now_dist_transform_eig;
    double fx, fy, cx, cy;
};

Sameer Agarwal

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Aug 5, 2016, 1:22:48 AM8/5/16
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The problem is the line 

double readVal = now_dist_transform_eig( _v, _u);

you are using values of type T (which in this case are Jets) to index into a matrix.

is now_dist_transform_eig the matrix you want to interpolate ?

Sameer

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Manohar Kuse

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Aug 5, 2016, 1:24:44 AM8/5/16
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Yes. I need to interpolate that matrix. 
I should be using Grid2D I think, but cannot figure out how.

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Sameer Agarwal

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Aug 5, 2016, 1:25:22 AM8/5/16
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have you looked at the example code or the tests?

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Manohar Kuse

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Aug 5, 2016, 1:30:31 AM8/5/16
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Sameer Agarwal

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Aug 5, 2016, 1:37:40 AM8/5/16
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MatrixXd a;
// Fill a somehow.

Grid2D<double, 1> grid(a.data(), a.rows(), a.cols());
BiCubicInterpolator<Grid2D<double, 1> > interpolated_a(grid);

now your cost function should use the interpolated_a instead of a.

class EAResidue {
public:
     EAResidue( MatrixXd& list_edge_ref, BiCubicInterpolator<Grid2D<double, 1> >& interpolated_a) 
: list_edge_ref(list_edge_ref), interpolated_a(interpolated_a) {}
    template <typename T>
    bool operator()(const T* const Q, const T* const t, T* residual) const
    {
/// some calculation
               T _u = T(fx) * _xd / _zd + T(cx);
         T _v = T(fy) * _yd / _zd + T(cy);
       interpolated_a.Evaluate(_u, _v, residuals + i);
        return true;
    }

private:
    MatrixXd list_edge_ref;
    const BiCubicInterpolator<Grid2D<double, 1> >& interpolated_a;
    double fx, fy, cx, cy;
};

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Manohar Kuse

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Aug 5, 2016, 2:52:47 AM8/5/16
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Perfect...! Exactly what I was looking for..

Thanks :)

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Manohar Kuse

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Jul 26, 2018, 5:54:08 AM7/26/18
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 I am trying to create a 2D grid. 

e_disTrans is a MatrixXd of size 500x500. 
I am trying to create a Grid2D as you had suggested (long ago :P). 

```
ceres::Grid2D::Grid2D<double,1> grid( e_disTrans.data(), e_disTrans.rows(), e_disTrans.cols() );
```
I get a compilation issue, 
```
/home/mpkuse/Downloads/edge_alignment/standalone/standalone_edge_align.cpp: In function ‘int main()’:
/home/mpkuse/Downloads/edge_alignment/standalone/standalone_edge_align.cpp:103:12: error: ‘template<class T, int kDataDimension, bool kRowMajor, bool kInterleaved> struct ceres::Grid2D’ used without template parameters
     ceres::Grid2D::Grid2D<double,1> grid( e_disTrans.data(), e_disTrans.rows(), e_disTrans.cols() );
            ^
/home/mpkuse/Downloads/edge_alignment/standalone/standalone_edge_align.cpp:103:27: error: expected primary-expression before ‘double’
     ceres::Grid2D::Grid2D<double,1> grid( e_disTrans.data(), e_disTrans.rows(), e_disTrans.cols() );
                           ^
CMakeFiles/edge_align.dir/build.make:62: recipe for target 'CMakeFiles/edge_align.dir/standalone_edge_align.cpp.o' failed
```

Has the usage changed? How can I fix this? 

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I

Manohar Kuse

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Jul 26, 2018, 6:01:40 AM7/26/18
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I tried this from one of the examples: 

const double data[] = {1.0, 3.0, -1.0, 4.0,
                        3.6, 2.1,  4.2, 2.0,
                       2.0, 1.0,  3.1, 5.2};
    ceres::Grid2D<double, 1>  grid(data, 3, 4);


I realized ceres::Grid2D is not a namespace. 

Still get the following compilation error: 

/home/mpkuse/Downloads/edge_alignment/standalone/standalone_edge_align.cpp: In function ‘int main()’:
/home/mpkuse/Downloads/edge_alignment/standalone/standalone_edge_align.cpp:111:46: error: no matching function for call to ‘ceres::Grid2D<double, 1>::Grid2D(const double [12], int, int)’
     ceres::Grid2D<double, 1>  grid(data, 3, 4);
                                              ^
In file included from /home/mpkuse/Downloads/edge_alignment/standalone/standalone_edge_align.cpp:16:0:
/usr/local/include/ceres/cubic_interpolation.h:390:3: note: candidate: ceres::Grid2D<T, kDataDimension, kRowMajor, kInterleaved>::Grid2D(const T*, int, int, int, int) [with T = double; int kDataDimension = 1; bool kRowMajor = true; bool kInterleaved = true]
   Grid2D(const T* data,
   ^
/usr/local/include/ceres/cubic_interpolation.h:390:3: note:   candidate expects 5 arguments, 3 provided
/usr/local/include/ceres/cubic_interpolation.h:386:8: note: candidate: constexpr ceres::Grid2D<double, 1>::Grid2D(const ceres::Grid2D<double, 1>&)
 struct Grid2D {
        ^
/usr/local/include/ceres/cubic_interpolation.h:386:8: note:   candidate expects 1 argument, 3 provided
/usr/local/include/ceres/cubic_interpolation.h:386:8: note: candidate: constexpr ceres::Grid2D<double, 1>::Grid2D(ceres::Grid2D<double, 1>&&)
/usr/local/include/ceres/cubic_interpolation.h:386:8: note:   candidate expects 1 argument, 3 provided
CMakeFiles/edge_align.dir/build.make:62: recipe for target 'CMakeFiles/edge_align.dir/standalone_edge_align.cpp.o'
failed
make[2]: *** [CMakeFiles/edge_align.dir/standalone_edge_align.cpp.o] Error 1
CMakeFiles/Makefile2:67: recipe for target 'CMakeFiles/edge_align.dir/all' failed
make[1]: *** [CMakeFiles/edge_align.dir/all] Error 2
Makefile:83: recipe for target 'all' failed
make: *** [all] Error 2



Manohar Kuse

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Jul 26, 2018, 6:04:50 AM7/26/18
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I managed to get it working!
Sorry to bother though. 

The solution was :


 const double data[] = {1.0, 3.0, -1.0, 4.0,
                     3.6, 2.1,  4.2, 2.0,
                    2.0, 1.0,  3.1, 5.2};

 ceres::Grid2D<double, 1>  grid(data, 0,3, 0,4); //< Interface changed.

The interface for Grid2D has changed I guess, need to specify the start and ends of rows and cols. 
Please correct me If i interpret it wrongly. 

Thanks

Sameer Agarwal

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Jul 26, 2018, 9:18:30 AM7/26/18
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