3D Mexican Sign Language Static Alphabet, Normalized about the origin and in scale

This dataset is about Mexican Sign Language (MSL) static alphabet. The 21 sign letters were acquired in 3D using a MS Kinect v1 sensor. Fifteen persons participated to perform each of the signs once. Therefore, 315 files were captured.

The main difference between Version 2 and Version 1 of the Dataset, is that in Version 2 all the point clouds are normalized about the origin. This means that each point cloud is centered on (0,0,0). Also all the point clouds are normalized in scale. Each point cloud is inside a sphere of radious one in 3D space.

Normalization in coordinates. The normalization consists in computing the centroid of the point cloud (X_c,Y_c,Z_c)= 1/N ∑_(X_i,Y_i,Z_i), where N is the number of points in the point cloud, and (X_i,Y_i,Z_i) is the ith point in the point cloud, then new coordinates are computed as (X_i^0,Y_i^0,Z_i^0 )= (X_i,Y_i,Z_i )- (X_c,Y_c,Z_c) . The resulting point cloud is centered at the origin (0,0,0).
Normalization in scale. To obtain invariance to scale for each point cloud the farthest point from the centroid is searched, and the maximum Euclidean distance Distmax is computed. The new coordinates (X_i^s,Y_i^s,Z_i^s )of the point cloud which is centered at the origin an inside a sphere of radious one is computed as (X_i^s,Y_i^s,Z_i^s )= (X_i^0,Y_i^0,Z_i^0 )/ Distmax.
The resulting point clouds preserve the original shape and pose, and are invariant to translation and scaling, although the original scale is lost. The new coordinates are unitless.

All the point clouds in this Dataset are centered at (0,0,0), the origin of the 3D Cartesian coordinate system, and are inside a sphere of radious one in 3D space.

The average Distmax of the point clouds in Version 1 is 0.09106 meters, with a standard deviation of 0.01208 meters.

The average centroid of the point clouds in Version 1 is (0.056, -0.1283, 0.7698), in meters units. The standard deviation of the centroid coordinates is (0.017, 0.004, 0.0808) meters.

These values can be used to recover approximately the original position and scale of the point clouds in Version 1, from the point clouds in Version 2.