Feature selection with the image grand tour

The grand tour is a method for visualizing high dimensional data by presenting the user with a set of projections and the projected data. This idea was extended to multispectral images by viewing each pixel as a multidimensional value, and viewing the projections of the grand tour as an image. The user then looks for projections which provide a useful interpretation of the image, for example, separating targets from clutter. We discuss a modification of this which allows the user to select convolution kernels which provide useful discriminant ability, both in an unsupervised manner as in the image grand tour, or in a supervised manner using training data. This approach is extended to other window-based features. For example, one can define a generalization of the median filter as a linear combination of the order statistics within a window. Thus the median filter is that projection containing zeros everywhere except for the middle value, which contains a one. Using the convolution grand tour one can select projections on these order statistics to obtain new nonlinear filters.