Robust Diffusion Kernels for Optical Flowsmoothing

This paper provides a comparison study among a set of novel algorithms that implement robust diffusion on optical flows. The proposed algorithms combine the anisotropic smoothing ability of the heat kernel and the outlier rejection mechanism of robust statistics algorithms. The diffusion kernel is considered Gaussian, where the covariance matrix is the local Hessian. This enables the kernel to detect significant transitions in the signal. In this study we show that diffusion does not eliminate outliers but rather spreads them around. We calculate the resulting bias induced by diffusing the outliers in their neighbourhood. On the other hand robust statistics operators reject the outliers from the diffusion process. Alpha-trimmed mean and median statistics are considered in combination with the diffusion processing. The proposed algorithms are applied for smoothing optical flow.