Spatial Cognition of Geometric Figures in the Context of Proportional Analogies

The cognition of spatial objects differs among people and is highly influenced by the context in which a spatial object is perceived. We investigated experimentally how humans perceive geometric figures in geometric proportional analogies and discovered that subjects perceive structures within the figures which are suitable for solving the analogy. Humans do not perceive the elements within a figure individually or separately, but cognize the figure as a structured whole. Furthermore, the perception of each figure in the series of analogous figures is influenced by the context of the whole analogy. A computational model which shall reflect human cognition of geometric figures must be flexible enough to adapt the representation of a geometric figure and produce a similarly structured representation as humans do while solving the analogy. Furthermore, it must be able to take into account the context, i.e. structures and transformations in other geometric figures in the analogy.