Shape matching and classification using height functions

We propose a novel shape descriptor for matching and recognizing 2D object silhouettes. The contour of each object is represented by a fixed number of sample points. For each sample point, a height function is defined based on the distances of the other sample points to its tangent line. One compact and robust shape descriptor is obtained by smoothing the height functions. The proposed descriptor is not only invariant to geometric transformations such as translation, rotation and scaling but also insensitive to nonlinear deformations due to noise and occlusion. In the matching stage, the Dynamic Programming (DP) algorithm is employed to find out the optimal correspondence between sample points of every two shapes. The height function provides an excellent discriminative power, which is demonstrated by excellent retrieval performances on several popular shape benchmarks, including MPEG-7 data set, Kimia’s data set and ETH-80 data set.

► We presented a novel shape descriptor for matching and recognizing 2D shapes.
► For each sample point, a height function is defined as its descriptor.
► The height function provides excellent discriminative power for shape similarity.
► This method achieves the state-of-the-art retrieval performance on three benchmarks.