Prediction error filters to enhance differences

Introduction

Developing and debugging a new approach to an old problem involves constantly comparing your `improved' result to the `old' approach. For 2-D volumes a movie flipping between the `old' and `improved' images is an effective mechanism for the well trained eye. When the dimensionality of your volume increases and/or the training of the observer decreases the human eye approach becomes less useful.

Prediction Error Filters (PEFs) (Claerbout, 1999) provide an estimate of a volume's inverse covariance, with stationary statistics. By using non-stationary Prediction Error Filters (Crawley et al., 1998) or by breaking the problem into patches (Claerbout, 1992) we can characterize some level of non-stationary statistics. Schwab (1998) showed that by estimating a PEF within small patches and then applying the filter on the patch, event's subtle features such as faults become more visible.

In this paper I use a variation on the same technique to highlight differences between volumes (`a' and `b'). I estimates PEFs within small patches on one volume `a' then apply the PEF to both `a' and `b'. I then apply a simple algebraic combination of the volumes resulting from applying the PEF to form a measure of image difference. I compare this technique to a more standard histogram matching approach and apply it on both 2-D and 3-D volumes.

Prediction error filters to enhance differences