The grand tour is a method for visualizing high dimensional data by presenting the user with a sequence of projections of the data. This idea was extended by Wegman and Poston to multispectral images by viewing each pixel as a multidimensional observation, and viewing the projections of the grand tour as mapping these observations into a grayscale image. The user then looks for projections which provide a useful interpretation of the image, for example, separating targets from clutter.

I will discuss a modification of this to single band images, 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 an window. Thus the median filter is that projection containing zero's 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. Other possible modifications will be discussed.