第五讲
Two Paths for Open-Loop Grasping
- For known objects, pose estimation would be useful.
- For unknown objects and general objects, directly predict grasping pose.
Singularities
a singularity is a point at which a given mathematical object is not defined or not well-behaved (ambiguity, non-differentiation, etc.)
Discontinuity and Singularities in Rotation Representation
Euler Angles
the limit of identity rotation is undefined: 0 or .
Axis-angle
- at , each axis represents identity rotation
- at , each axis and its negation represent the same rotation (discontinuous)
Quaternions
double coverage: and represent the same rotation .
6D Representation
Rotation Matrix is a continuous representation in , but has excessive number of parameters.
simply eliminates the last column of rotation matrix → 6D representation.
6D representation applies Gram-Schmidt orthogonalization to map the Euclidean output of neural networks to .
9D Representation
Suppose is the output matrix of a model.
Conduct SVD
本来可以直接 ，但是这样可能使得 。
所以修正一下
Orthogonal Procrustes Problem
given 3D-3D dense correspondence, use Orthogonal Procrustes to solve .
For and , solve
such that .
solution:
If we have the SVD
then
If we only allow to be a rotation matrix, then
Object Pose Estimation
Instance-Level 6D Pose Estimation
need CAD Model
Category-Level 6D Pose Estimation
input:
- RGB
- Depth
output:
- 6D Pose
- 3D Size
Normalized Object Coordinate Space (NOCS)
Category Level.