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The movement parallax field due to the translation of an observer relative to a plane surface is studied in an infinitesimal neighborhood of a visual direction. The parallax field is decomposed into elementary transformations: a translation, a rigid rotation, a similarity, and a deformation. A topologically invariant classification based on critical-point analysis is also obtained. It is shown that the field is either that of a node or that of a saddle point. Numerical results for a general case are offered as illustration. We discuss the relevance of the local, as opposed to the global structure of the parallax field for visual perception and the visual space sense.