  We study the generalized Procrustes analysis (GPA), as a minimal formulation
to the simultaneous localization and mapping (SLAM) problem. We propose
KernelGPA, a novel global registration technique to solve SLAM in the
deformable environment. We propose the concept of deformable transformation
which encodes the entangled pose and deformation. We define deformable
transformations using a kernel method, and show that both the deformable
transformations and the environment map can be solved globally in closed-form,
up to global scale ambiguities. We solve the scale ambiguities by an
optimization formulation that maximizes rigidity. We demonstrate KernelGPA
using the Gaussian kernel, and validate the superiority of KernelGPA with
various datasets. Code and data are available at
\url{https://bitbucket.org/FangBai/deformableprocrustes}.
