Probability density function estimation with the frequency polygon transform

• A probability density function estimator is proposed, which is based on frequency polygons.
• Its convergence to the true density is formally proved.
• A mode finding algorithm is also proposed, as an alternative to mean-shift.
• Our approach outperforms histogram and kernel based estimators in synthetic and real datasets.
• Our proposal is shown to be suitable to object tracking in video sequences.

Most current nonparametric approaches to probability density function estimation are based on the kernel density estimator, also known as the Parzen window estimator. A usual alternative is the multivariate histogram, which features a low computational complexity. Multivariate frequency polygons have often been neglected, even though they share many of the advantages of the histograms, while they are continuous unlike the histograms. Here we build on our previous work on histograms in order to propose a new probability density estimator which is based on averaging multivariate frequency polygons. The convergence of the estimator is formally proved. Experiments are carried out with synthetic and real machine learning datasets. Finally, image denoising and object tracking applications are also considered.