λ-Transform: A Mathematical Tool for Accurate Shape Description

Radon transform is a useful mathematical tool for shape analysis. It is a lossless transform and makes the extraction of structural shape features become very easy. However it cannot be directly applied to shape recognition due to its sensitivity to translation, scaling and rotation of the shape. The existing Radon transform based methods have had many attempts to remove the information of size, position and orientation of the shape from the Radon transform. However in these methods, the invariant features are achieved at the expense of useful shape features. To address this issue, a novel mathematical tool termed λ-transform is proposed for shape description. The λ-transform utilizes the relative position information between the parallel lines (encoded in a variable r∊[0, 1]) and their integrals over the shape to construct a 2D function of the variable r and the direction angleθof the line for shape description. This study theoretically proves that λ-transform is invariant to the translation and scaling and a rotation only makes it shift along the θ direction. It also theoretically concludes that λ-transform can effectively preserve the useful information of Radon transform. These desirable characteristic make λ-transform outperform the other Radon based methods for shape recognition. Tests on the proposed λ-transform are carried out on several commonly used shape image datasets, and the experimental results indicate it achieves better performance over other Radon based shape descriptors. © Copyright 2017, Institute of Software, the Chinese Academy of Sciences. All rights reserved.