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

KernelGPA: A Globally Optimal Solution to Deformable SLAM in Closed-form