## PCA in Lower Dimension (Dimension Reduction)

By using PCA and DTW above.

To map the low dimension to 2-dimension. :

The motions to be blended must be aligned temporally. In the low dimensional space, the axis parallel to a motion stream corresponds to poses changing over time, while the axes perpendicular to the curve correspond to a change within a parameterized space of motions at a fixed time instance.

Given a point on the image, two surrounding samples from the original motion streams such that the point on the curve is represented as a weighted sum of two samples. In two-dimensional space, two nearest surrounding samples among the intersections between the line perpendicular to the tangent at the point and the motion curves. The blending weights for the samples are inversely proportional to distance in two-dimensional space.

If only one similarly directed stream intersects the line, the corresponding pose to the intersection is selected without blending since there is no similar motion to blend. If no surrounding streams along the parametrization axes exist within a user-specified range, the point on the sketched curve is invalid.

Pose Blending :

The motion obtained through pose blending above may have unwanted high frequency components due to jitter of the curve or sudden changes of surrounding streams. Instead of blending each pair of poses separately, we create a short motion clip at each frame on the curve by blending consecutive frames selected from two matching streams. This generates a sequence of motion clips overlapping front and back.

Video :

**Source On GitHub (Coming Soon)**