| Abstrakt: |
There has been a growing interest in shape analysis in recent years. We present a novel shape signature for 2D Jordan domains. The proposed signature is based on Sharon's conformal welding signature [E. Sharon and D. Mumford, Internat. J. Comput. Vis., 70 (2006), pp. 55--75], which is one of the main building blocks of our proposed shape signature. The conformal welding signature is a well-known shape signature used to represent 2D shapes. Nevertheless, it is not invariant under rotation. It is also sensitive to the choice of particular feature points and shape perturbations. Motivated by this, we propose in this paper an invariant shape signature under rigid transformations and scaling. The proposed signature does not require the delineation of feature points and is robust under shape perturbations. More specifically, the proposed signature is a Beltrami coefficient of the harmonic extension of the conformal welding. We show that there is a one-to-one correspondence between a quotient space of Beltrami coefficients and the space of 2D Jordan domains up to a translation, rotation, and scaling. With a suitable normalization, each equivalence class in the quotient space is associated with a unique representative named the Harmonic Beltrami Signature (HBS). As such, each shape is associated with a unique HBS. Conversely, the associated shape of an HBS can be reconstructed based on quasiconformal Teichm\"uller theories, which are uniquely determined up to a translation, rotation, and scaling. The HBS is thus an effective fingerprint to represent a 2D shape. The robustness of the HBS is studied both theoretically and experimentally. With the HBS, simple metrics, such as L2, can measure geometric dissimilarity between shapes. Experiments have been carried out to classify shapes into different classes using HBS. Results show good classification performance, which demonstrates the efficacy of our proposed shape signature. [ABSTRACT FROM AUTHOR] |
