Classification of image data in conjugate representation spaces

Over the past few years, automatic multivariate statistical classification techniques have successfully been used for analyzing large and noisy electron-microscopic data sets. After the raw data are compressed with eigenvector–eigenvalue procedures, classes of images are formed, using unsupervised clustering procedures. The classes elucidate even subtle differences existing within the data set. Here we extend these methods to find classes of pixels or features in the images (or other n-dimensional signals) that exhibit a homogeneous statistical behavior throughout the data set. This feature extraction—itself a form of data compression—is mathematically entirely symmetric to the determination of the image classes and also serves the purpose of revealing the information present in the set of input images. The properties of simultaneous representations of the image-space and feature-space data onto the same two-dimensional map are discussed in relation to the metrics used in both spaces. Model data are used to illustrate the basic ideas.