MathWorks' Factor Graph Toolbox is a proprietary software package, and the implementation details of its optimize function are not publicly disclosed. Therefore, it is not possible to say for certain whether Google's Ceres Solver is used as a backbone for this function.
However, it is worth noting that both the Factor Graph Toolbox and Ceres Solver are tools for solving optimization problems, particularly those involving graphical models. Graphical models are a way to represent complex probabilistic relationships between variables, and they often arise in machine learning, computer vision, and other fields.
Therefore, it is possible that the Factor Graph Toolbox and Ceres Solver share some underlying algorithms or techniques for solving optimization problems on graphical models, which could explain why their output appears similar. However, without access to the implementation details of the optimize function, it is difficult to say for sure.
