pypose.module.GeodesicLoss

class pypose.module.GeodesicLoss(reduction='mean')

Creates a criterion that measures the Geodesic Error between the rotation part of the input LieTensor \(x\) and target LieTensor \(y\).

\[\operatorname{norm}(\operatorname{Log}(\mathbf{x}\times\mathbf{y}^{-1})). \]

Warning

The above equation holds only if \(x\) and \(y\) are quaternions. When \(x\) and \(y\) are rotation matrices, the geodesic error is

\[\arccos \left(\frac{\operatorname{trace}( \mathbf{x}\times\mathbf{y}^{-1})-1}{2}\right). \]

This class accepts all forms of input LieTensors, including SO3, SE3, RxSO3, Sim3, so3, se3, rxso3, sim3, where their rotation part will be extracted.

Parameters:

reduction (str, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction is applied, 'mean': the sum of the output is divided by the number of elements in the output, 'sum': the output is summed. Default: 'mean'

Examples

>>> input, target = pp.randn_SO3(2), pp.randn_SO3(2)
>>> criterion = pp.module.GeodesicLoss(reduction='mean')
>>> loss = criterion(input, target)
tensor(1.0112)

forward(input, target)

Parameters:

• input (pp.LieTensor) – input LieTensor.

• target (pp.LieTensor) – target LieTensor.