Inferring shape transformations in a drawing task

Abstract

Many objects and materials in our environment are subject to transformations that alter their shape. For example, branches bend in the wind, ice melts, and paper crumples. Still, we recognize objects and materials across these changes, suggesting we can distinguish an object’s original features from those caused by the transformations (“shape scission”). Yet, if we truly understand transformations, we should not only be able to identify their signatures but also actively apply the transformations to new objects (i.e., through imagination or mental simulation). Here, we investigated this ability using a drawing task. On a tablet computer, participants viewed a sample contour and its transformed version, and were asked to apply the same transformation to a test contour by drawing what the transformed test shape should look like. Thus, they had to (i) infer the transformation from the shape differences, (ii) envisage its application to the test shape, and (iii) draw the result. Our findings show that drawings were more similar to the ground truth transformed test shape than to the original test shape—demonstrating the inference and reproduction of transformations from observation. However, this was only observed for relatively simple shapes. The ability was also modulated by transformation type and magnitude but not by the similarity between sample and test shapes. Together, our findings suggest that we can distinguish between representations of original object shapes and their transformations, and can use visual imagery to mentally apply nonrigid transformations to observed objects, showing how we not only perceive but also ‘understand’ shape.