While image filtering is limited to two dimensions, the filtering of image sequences can utilize three dimensions; two spatial and one temporal. Unfortunately, simple extensions of common two-dimensional filters into three dimensions yield undesirable motion blurring of the images. This thesis addresses this problem and introduces a novel filtering approach termed the general flow-adaptive filter.
Most often a three-dimensional filter can be visualized as a cubic lattice shifted over the data, and at each point the element corresponding to the central coordinate is replaced with a new value based entirely on the values inside the lattice. The general principle of the flow-adaptive approach is to spatially adapt the entire filter lattice to possibly complex spatial movements in the temporal domain by incorporating local flow-field estimates.
Results using the flow-adaptive technique on five filters the temporal discontinuity filter, a tensor-based adaptive filter, the average, the median and a Gaussianshaped convolution filter are presented. Both ultrasound image sequences and synthetic data sets were filtered. An edge-adaptive normalized mean-squared error is used as performance metric on the filtered synthetic sets, and the error is shown to be substantially reduced using the flow-adaptive technique, as much as halved in many instances. There are even indications that simple Gaussian-shaped convolution filters can outperform larger and more complex adaptive filters by implementing the flow-adaptive procedure. For the ultrasound image sequences, the filters adopting the flow-adaptive principles had outputs with less motion blur and sharper contrast compared to the outputs of the non-flow-adaptive filters.
At the cost of flow estimation, the flow-adaptive approach substantially improves the performance of all the filters included in this study.