PROPOSAL : EFFICIENT KERNEL DENSITY ESTIMATION AND ROBUST REAL - TIME OBJECT TRACKING by

Evaluating sums of multivariate Gaussians is a common computational task in computer vision and pattern recognition, including in the general and powerful kernel density estimation technique. The quadratic computational complexity of the summation is a significant barrier to the scalability of this algorithm to practical applications. The fast Gauss transform (FGT) has successfully accelerated the kernel density estimation to linear running time for low-dimensional problems. Unfortunately, the cost of a direct extension of the FGT to higher-dimensional problems grows exponentially with dimension, making it impractical for dimensions above 3. We develop an improved fast Gauss transform to efficiently estimate sums of Gaussians in higher dimensions, where a new multivariate expansion scheme and an adaptive space subdivision technique dramatically improve the performance. The improved FGT has been applied to the mean shift algorithm achieving linear computational complexity. We also proposed an object tracking algorithm using a novel simple symmetric similarity function between spatially-smoothed kernel-density estimates of the model ii and target distributions. The similarity measure is based on the expectation of the density estimates over the model or target images. The density is estimated using radial-basis kernel functions which measure the affinity between points and provide a better outlier rejection property. The mean-shift algorithm is used to track objects by iteratively maximizing this similarity function. To alleviate the quadratic complexity of the density estimation, we employ Gaussian kernels and the improved fast Gauss transform to reduce the computations to linear order. This leads to very efficient and robust nonparametric tracking algorithms. The proposed algorithms are tested with several image sequences and shown to achieve robust and reliable real-time tracking performance.