GUIBAS L.: Functional maps: A flexible representation of maps between shapes

Figure 1: Horse algebra: the functional representation and map inference algorithm allow us to go beyond point-to-point maps. The source shape (top left corner) was mapped to the target shape (left) by posing descriptor-based functional constraints which do not disambiguate symmetries (i.e. without landmark constraints). By further adding correspondence constraints, we obtain a near isometric map which reverses orientation, mapping left to right (center). The representation allows for algebraic operations on shape maps, so we can subtract this map from the ambivalent map, to retrieve the orientation preserving near-isometry (right). Each column shows the first 20x20 block of the functional map representation (bottom), and the action of the map by transferring colors from the source shape to the target shape (top). We present a novel representation of maps between pairs of shapes that allows for efficient inference and manipulation. Key to our approach is a generalization of the notion of map that puts in corre-spondence real-valued functions rather than points on the shapes. By choosing a multi-scale basis for the function space on each shape, such as the eigenfunctions of its Laplace-Beltrami opera-tor, we obtain a representation of a map that is very compact, yet fully suitable for global inference. Perhaps more remarkably, mos