Multi-scale embedded descriptor for shape classification

We present a new shape descriptor that are robust to deformation and capture part details. In our framework, the shape descriptor is generated by 1) using running angle to transforming a shape into a 2-D description image in the position and scale space. 2) performing circular wavelet-like sub-band decomposition of this 2-D description image based on its periodic convolution with orthogonal kernel functions. Each sub-band is described by the histogram of its decomposition coefficients. To capture unique and discriminative part, we compare the decomposition coefficients across sub-band to detect singularity in the position and scale space. The singularity information is encoded with a tree of binary bits. The coded feature vectors of all sub-bands and singularity trees are pooled together to form the descriptor of the shape. The shapes are classified with linear SVM. Our performance evaluations on several public datasets, demonstrating that the proposed method significantly outperforms state-of-the-art methods.