A compact formula for the derivative of a 3-D rotation in exponential coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.Comment: 6 page

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates

Optimal estimation of perspective camera pose

In this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of camera pose estimation for calibrated cameras. While traditional methods may get trapped in local minima, due to the non-convexity of the problem, we have developed an approach that guarantees global optimality. The scheme is based on ideas from global optimization theory, in particular, convex under-estimators in combination with branch and bound. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data. 1

Optimal estimation of perspective camera pose

In this paper we propose apractical and efficient method for finding the globally optimal solution to the problem of camera pose estimation for calibrated cameras. While traditional methods may get trapped in local minima, due to the non-convexity of the problem, we have developed an approach that guarantees global optimality. The scheme is based on ideas from global optimization theory, in particular, convex under-estimators in combination with branch and bound. We provide aprovably optimal algorithm and demonstrate good performance on both synthetic and real data