Dimensionality reduction and how it helps reduce the search space by leveraging known information

Removing dimensions or making invariant features is a technique used to reduce the search space in a problem by eliminating certain variables or making them irrelevant. This can be especially useful in LiDAR slam, which has a 6Dof search space (x, y, z, roll, pitch, yaw). By reducing the dimensions, the number of permutations in the search space iterations can be significantly reduced, enabling real time applications.

One way to reduce the search space in LiDAR slam is to utilize the gravity vector to predict the roll and pitch. By using an IMU (inertial measurement unit), the gravity vector can be measured and used to determine the orientation of the LiDAR. This eliminates the need to search for the roll and pitch in the search space, reducing it from 6Dof to 4Dof (x, y, z, yaw).

Another way to reduce the search space is to detect the ground plane and eliminate the roll, pitch, and z offsets from the grid space projection. By detecting the ground plane, the LiDAR can align itself with the ground, eliminating the need to search for the roll, pitch, and z in the search space. This reduces the search space from 6Dof to 3Dof (x, y, yaw).

In addition to these techniques, making rotational invariant feature descriptors can also help reduce the search space. By omitting the yaw from the matching process, the LiDAR can focus on matching the x and y coordinates without worrying about the orientation. This reduces the search space from 6Dof to 2Dof (x, y), enabling real time applications.

Overall, removing dimensions or making invariant features is a powerful technique for reducing the search space in LiDAR slam. By utilizing the gravity vector to predict the roll and pitch, detecting the ground plane, and making rotational invariant feature descriptors, the search space can be reduced from 6Dof to 2Dof, enabling real time applications.