GradientCorrelation¶
-
class
menpofit.lk.
GradientCorrelation
[source]¶ Bases:
Residual
Class for Gradient Correlation residual.
References
- 1
G. Tzimiropoulos, S. Zafeiriou, and M. Pantic. “Robust and Efficient Parametric Face Alignment”, IEEE Proceedings of International Conference on Computer Vision (ICCV), pp. 1847-1854, November 2011.
-
cost_closure
()[source]¶ Method to compute the optimization cost.
- Returns
cost (float) – The cost value.
-
classmethod
gradient
(image, forward=None)¶ Calculates the gradients of the given method.
If forward is provided, then the gradients are warped (as required in the forward additive algorithm)
- Parameters
image (menpo.image.Image) – The image to calculate the gradients for
forward (tuple or
None
, optional) – A tuple containing the extra weights required for the function warp (which should be passed as a function handle), i.e.(`menpo.image.Image`, `menpo.transform.AlignableTransform>`)
. IfNone
, then the optimization algorithm is assumed to be inverse.
-
hessian
(sdi, sdi2=None)[source]¶ Calculates the Gauss-Newton approximation to the Hessian.
This is abstracted because some residuals expect the Hessian to be pre-processed. The Gauss-Newton approximation to the Hessian is defined as:
\[\mathbf{J J^T}\]- Parameters
sdi (
(N, n_params)
ndarray) – The steepest descent images.sdi2 (
(N, n_params)
ndarray orNone
, optional) – The steepest descent images.
- Returns
H (
(n_params, n_params)
ndarray) – The approximation to the Hessian
-
steepest_descent_images
(image, dW_dp, forward=None)[source]¶ Calculates the standard steepest descent images.
Within the forward additive framework this is defined as
\[\nabla I \frac{\partial W}{\partial p}\]The input image is vectorised (N-pixels) so that masked images can be handled.
- Parameters
image (menpo.image.Image) – The image to calculate the steepest descent images from, could be either the template or input image depending on which framework is used.
dW_dp (ndarray) – The Jacobian of the warp.
forward (tuple or
None
, optional) – A tuple containing the extra weights required for the function warp (which should be passed as a function handle), i.e.(`menpo.image.Image`, `menpo.transform.AlignableTransform>`)
. IfNone
, then the optimization algorithm is assumed to be inverse.
- Returns
VT_dW_dp (
(N, n_params)
ndarray) – The steepest descent images
-
steepest_descent_update
(sdi, image, template)[source]¶ Calculates the steepest descent parameter updates.
These are defined, for the forward additive algorithm, as:
\[\sum_x [ \nabla I \frac{\partial W}{\partial p} ]^T [ T(x) - I(W(x;p)) ]\]- Parameters
sdi (
(N, n_params)
ndarray) – The steepest descent images.image (menpo.image.Image) – Either the warped image or the template (depending on the framework)
template (menpo.image.Image) – Either the warped image or the template (depending on the framework)
- Returns
sd_delta_p (
(n_params,)
ndarray) – The steepest descent parameter updates.