root_mean_square_bb_normalised_error

menpofit.error.root_mean_square_bb_normalised_error(shape, gt_shape, norm_shape=None, norm_type='avg_edge_length')

Computes the root mean square error between two shapes normalised by a measure based on the ground truth shape’s bounding box, i.e.

\[\frac{\mathcal{F}(s,s^*)}{\mathcal{N}(s^*)}\]

where

\[\mathcal{F}(s,s^*) = \sqrt{\frac{1}{N}\sum_{i=1}^N(s_i-s^*_i)^2}\]

where \(s\) and \(s^*\) are the final and ground truth shapes, respectively. \(s_i\) and \(s^*_i\) are the coordinates of the \(i\)’th point of the final and ground truth shapes, and \(N\) is the total number of points. Finally, \(\mathcal{N}(s^*)\) is a normalising function that returns a measure based on the ground truth shape’s bounding box.

Parameters

• shape (menpo.shape.PointCloud) – The input shape (e.g. the final shape of a fitting procedure).

• gt_shape (menpo.shape.PointCloud) – The ground truth shape.

• norm_shape (menpo.shape.PointCloud or None, optional) – The shape to be used to compute the normaliser. If None, then the ground truth shape is used.

• norm_type ({'area', 'perimeter', 'avg_edge_length', 'diagonal'}, optional) –

  The type of the normaliser. Possible options are:

  Method	Description
  bb_area	Area of norm_shape’s bounding box
  bb_perimeter	Perimeter of norm_shape’s bounding box
  bb_avg_edge_length	Average edge length of norm_shape’s bbox
  bb_diagonal	Diagonal of norm_shape’s bounding box

Returns

error (float) – The computed root mean square normalised error.