Reconstruction of Probability Density Functions from Channel Representations

The channel representation allows the construction of soft histograms, where peaks can be detected with a much higher accuracy than in regular hard-binned histograms. This is critical in e.g. reducing the number of bins of generalized Hough transform methods. When applying the maximum entropy method to the channel representation, a minimum-information reconstruction of the underlying continuous probability distribution is obtained. The maximum entropy reconstruction is compared to simpler linear methods in some simulated situations. Experimental results show that mode estimation of the maximum entropy reconstruction outperforms the linear methods in terms of quantization error and discrimination threshold. Finding the maximum entropy reconstruction is however computationally more expensive.