Robust Shape Retrieval Using Maximum Likelihood Theory

The most commonly used shape similarity metrics are the sum of squared differences (SSD) and the sum of absolute differences (SAD). However, Maximum Likelihood (ML) theory allows us to relate the noise (differences between feature vectors) distribution more generally to a metric. In this paper, a shape is partitioned into tokens based on its concave regions, invariant moments are computed for each token, and token similarity is measured by a metric. Finally, a non-metric measure that employs heuristics is used to measure the shape similarity. The desirable property of this scheme is to mimic the human perception of shapes. We show that the ML metric outperforms the SSD and SAD metrics for token matching. Instead of the ML metric based on histograms for PDF approximation, which suffer from being sensitive to choices of bin width, we propose a Parzen windows method that is continuous and more robust.