Generates multigrid length estimations of paramteric shapes using DGtal library.

It will output length estimations (and timings) using several algorithms for decreasing grid steps.

Usage: LengthEstimators [options] –shape <shapeName>

Allowed options are :

-h,--help                             Print this help message and exit
-l,--list                             List all available shapes
-s,--shape TEXT                       Shape name
-R,--radius FLOAT                     Radius of the shape
-A,--axis1 FLOAT                      Half big axis of the shape (ellipse)
-a,--axis2 FLOAT                      Half small axis of the shape (ellipse)
-r,--smallradius FLOAT=5              Small radius of the shape (default 5)
-v,--varsmallradius FLOAT=5           Variable small radius of the shape (default 5)
-k UINT=3                             Number of branches or corners the shape (default 3)
--phi FLOAT=0                         Phase of the shape (in radian, default 0.0)
-w,--width FLOAT=10                   Width of the shape (default 10.0)
-p,--power FLOAT=2                    Power of the metric (default 2.0)
--hMin FLOAT=0.0001                   Minimum value for the grid step h (double, default 0.0001)
--steps INT=32                        Number of multigrid steps between 1 and hMin (integer, default 32)

The list of 2D shape are : -ball Ball for the Euclidean metric. Required parameter(s): –radius [-R]

square square (no signature). Required parameter(s): –width [-w]
lpball Ball for the l_power metric (no signature). Required parameter(s): –radius [-R], –power [-p]
flower Flower with k petals. Required parameter(s): –radius [-R], –varsmallradius [-v], –k [-k], –phi
ngon Regular k-gon. Required parameter(s): –radius [-R], –k [-k], –phi
accflower Accelerated Flower with k petals. Required parameter(s): –radius [-R], –varsmallradius [-v], –k [-k], –phi
ellipse Ellipse. Required parameter(s): –axis1 [-A], –axis2 [-a], –phi

Example:

Application of the multigrid length estimation on a flower shape with 5 petals and maximal radius 20 and min 5:

$ lengthEstimators -s flower -k 5 -R 20 -r 5 --steps 256 > length.dat

You can display using gnuplot:

$ gnuplot

gnuplot> plot [0:][-0.5: 90] 'length.dat' using 1:(($7-$3)*($7-$3)) w l title "squared error length estimation using DSS", 'length.dat' using 1:(($8-$3)*($8-$3)) w l title "squared error length estimation using MLP", 'length.dat' using 1:(($9-$3)*($9-$3)) w l title "squared error length estimation using FP" linewidth 2

You should obtain such a result:

Resulting visualization.

See also: lengthEstimators.cpp