RI: EAGER: Complex Wave Formulations for Shape Analysis

University Of Florida, Gainesville FL

Investigators

Abstract

Variegated and multifaceted shapes fill our world. Currently, there is no universally accepted vocabulary for shape analysis which inhibits the emergence and deployment of shape comparison technologies. This project draws its inspiration from an old idea usually attributed to Christiaan Huygens: when waves (usually represented as complex exponentials) emanate orthogonally from each point on the shape boundary, they travel in open space until they meet other waves emanating from different shape boundary locations. Each point in space is then "owned" by a wavefront thereby giving rise to the complex wave representation (CWR) of shape. When shape alignment is required (usually as part of a larger shape recognition goal), the CWRs of the two shapes can be more robustly aligned than the original shapes, since in the CWR, every point in space (in a bounded region) now carries an imprint of the shape. Shape analysis often raises the need for performing shape statistics: shape averages (usually referred to as shape atlases) and deviations from the mean are required. Shape statistics carried out in the CWR are arguably simpler since the vocabulary shifts to averages and standard deviations of frequencies (of the waves in the shape representation) which is rather straightforward. The significance of this work lies in the introduction of complex wave representations into the shape analysis lexicon. This research is expected to impact all areas of shape representation and analysis: the matching, registration, indexing and recognition of shapes with open source code dissemination facilitating re-use and vertical integration.