euclidean_distance_normalised_error

menpofit.error.euclidean_distance_normalised_error(shape, gt_shape, distance_norm_f)

Computes the Euclidean error between two shapes normalised by a distance measure between two shapes, i.e.

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

where

\[\mathcal{F}(s,s^*) = \frac{1}{N}\sum_{i=1}^N\sqrt{(s_{i,x}-s^*_{i,x})^2 + (s_{i,y}-s^*_{i,y})^2}\]

where \(s\) and \(s^*\) are the final and ground truth shapes, respectively. \((s_{i,x}, s_{i,y})\) are the x and y coordinates of the \(i\)’th point of the final shape, \((s^*_{i,x}, s^*_{i,y})\) are the x and y coordinates of the \(i\)’th point of the ground truth shape and \(N\) is the total number of points. Finally, \(\mathcal{N}(s,s^*)\) is a normalising function based on a distance metric between the two shapes.

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.

• distance_norm_f (callable) – The function to be used for computing the normalisation distance metric.

Returns

error (float) – The computed Euclidean normalised error.