Sergiu Deitsch
91773746be
If arguments are passed to a cost function that can be used to construct the functor, the latter will be instantiated by the cost function using std::make_unique to ensure exception safety. This not only avoids static analysis warnings caused by calling new but also spelling the cost functor type name multiple times. Also expand deduction guides for instantiating Dynamic(Auto|Numeric)DiffCostFunction from std::unique_ptr enabled constructor overloads. Finally, make CostFunction default move constructible and assignable but only through derived classes. This in turn allows derived classes to be movable without relying on custom implementations of corresponding operators. Change-Id: Idee8b9871d862bc9f9f8b5a8d0bedc52863e93c0
Sampled Functions
It is common to not have an analytical representation of the optimization problem but rather a table of values at specific inputs. This commonly occurs when working with images or when the functions in the problem are expensive to evaluate. To use this data in an optimization problem we can use interpolation to evaluate the function and derivatives at intermediate input values.
There are many libraries that implement a variety of interpolation schemes, but it is difficult to use them in Ceres' automatic differentiation framework. Instead, Ceres provides the ability to interpolate one and two dimensional data.
The one dimensional interpolation is based on the Cubic Hermite Spline. This
interpolation method requires knowledge of the function derivatives at the
control points, however we only know the function values. Consequently, we will
use the data to estimate derivatives at the control points. The choice of how to
compute the derivatives is not unique and Ceres uses the Catmull-Rom Spline
variant which uses 0.5 * (p_{k+1} - p_{k-1}) as the derivative for control
point p_k. This produces a first order differentiable interpolating
function. The two dimensional interpolation scheme is a generalization of the
one dimensional scheme where the interpolating function is assumed to be
separable in the two dimensions.
This example shows how to use interpolation schemes within the Ceres automatic
differentiation framework. This is a one dimensional example and the objective
function is to minimize 0.5 * f(x)^2 where f(x) = (x - 4.5)^2.
It is also possible to use analytical derivatives with the provided
interpolation schemes by using a SizedCostFunction and defining the
``Evaluate` function. For this example, the evaluate function would be:
bool Evaluate(double const* const* parameters, double* residuals, double** jacobians) const {
if (jacobians == nullptr || jacobians[0] == nullptr)
interpolator_.Evaluate(parameters[0][0], residuals);
else
interpolator_.Evaluate(parameters[0][0], residuals, jacobians[0]);
return true;
}