A new multi-scale fuzzy model for Histogram-Based Descriptors

In this paper, we first propose a general Multi-Scale Fuzzy Model (MSFM) which handles distortions at different scales in Histogram-Based Descriptors (HBDs). This model can be applied both on one-dimensional HBDs and multi-dimensional HBDs. We then focus on applying MSFM on the widely used Shape Context for a Simplified Multi-scale Fuzzy Shape Context (SMFSC) descriptor. Fuzzy models are barely used in multi-dimensional HBDs due to the significant increase of computational complexity. We show that by introducing an intra-bin point location approximation and an approximate iterative fuzzification approach, the algorithm can be simplified and thus SMFSC hardly increases computational complexity. Experiments on standard shape dataset show that SMFSC improves upon the Inner Distance Shape Context. We also applied SMFSC on Content-Based Product Image Retrieval and the experimental results further validate the effectiveness of our model.