Applications of eigenanalysis in digital imaging microscopy

Eigenanalysis is a powerful mathematical technique for analyzing matrices of data. With a data matrix constructed from a digitized image, this technique can be used to extract the features of the image. As a data processing methodology in image processing, the eigenanalysis is principally used in two ways. The first is to treat a single image as a data matrix. The second is to construct a data matrix from multiple images. In both cases, the input information is separated into mutually orthogonal eigenvectors obtained from the correlation or covariance matrix. Since the resulting eigenvectors are orthogonal, the information in each vector is excluded from all other vectors. Alternatively, the singular value decomposition method can be used to represent the data matrix as sum of its outer products, thus avoiding the construction of a correlation/covariance matrix. Both procedures allow sorting of information according to its significance, because the most significant information is associated with highest eigenvalues and corresponding eigenvectors. Consequently, the original data can be reconstituted and clustered using only the significant information. The advantage of this processing is that the preparatory artifacts of the sample and noise in the image are removed from the data. For applications in biological microscopy, the ultimate objective is to relate various structural patterns in the cell, enhanced by eigenanalysis, to their biological function.