Fast and accurate kernel density approximation using a divide-and-conquer approach

Density-based nonparametric clustering techniques, such as the mean shift algorithm, are well known for their flexibility and effectiveness in real-world vision-based problems. The underlying kernel density estimation process can be very expensive on large datasets. In this paper, the divide-and-conquer method is proposed to reduce these computational requirements. The dataset is first partitioned into a number of small, compact clusters. Components of the kernel estimator in each local cluster are then fit to a single, representative density function. The key novelty presented here is the efficient derivation of the representative density function using concepts from function approximation, such that the expensive kernel density estimator can be easily summarized by a highly compact model with very few basis functions. The proposed method has a time complexity that is only linear in the sample size and data dimensionality. Moreover, the bandwidth of the resultant density model is adaptive to local data distribution. Experiments on color image filtering/segmentation show that, the proposed method is dramatically faster than both the standard mean shift and fast mean shift implementations based on kd-trees while producing competitive image segmentation results.