How to use the p(y|X) to obtain the y*?

[jichaofeng]

Thank you for sharing your code. During inference, when we obtain the pose distribution p(y|X) by the probabilistic PnP layer, how to use the p(y|X) to obtain the y*? We can not understand the Section 3.4.

[Lakonik]

Hi! By definition, y* = argmax p(y|X), which is equivalent to solving the optimization problem in Eq. (1). We use Levenberg-Marquardt or Gauss-Newton algorithm to solve the optimization.

[jichaofeng]

Thank you for your answer. y* = argmax p(y|X), which is equivalent to solving the optimization problem in Eq. (1). Are these two optimization function is equivalent? Please excuse my poor math.

[Lakonik]

Yes they are equivalent. y* = argmax p(y|X) = argmin -log p(y|X) = argmin -log p(X|y) + const

[jichaofeng]

I probably understand the process. EPro-PnP is a differentiable loss function to supervise the correspondences X. During inference, the learned X is used to obtain the y*, and EPro-PnP is no longer used. Is this understanding right?

[Lakonik]

Yes that's right