Results of experiments made under the scheme of the Luneburg's model in the author's laboratory were reviewed and were also discussed two fundamental postulates : Frameless binocular perceptual space as a Riemannian space of constant curvature K and the simple and rigid mapping functions between the physical space and the Euclidean map of the perceptual space. Then, experimental results to embed perceptual configurations into a Euclidean space with the aid of the metric multidimensional scaling method were reviewed. In the last part, possibilities of testing the two fundamental postulates independently with each other and of incorporating into the model perturbation as to K And/or to the mapping functions were discussed.