We study the generalized Procrustes analysis (GPA), as a minimal formulation to the simultaneous localization and mapping (SLAM) problem. We propose Kernel-GPA, 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 Kernel-GPA using the Gaussian kernel and validate the superiority of Kernel-GPA with various datasets. Code and data are available at https://bitbucket.org/FangBai/deformableprocrustes.
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