Comparative study of description algorithms for complex-valued gradient fields of digital images using linear dimensionality reduction methods

The paper presents an analysis of various approaches to constructing descriptions for the gradient fields of digital images. The analyzed approaches are based on the well-known methods for data dimensionality reduction, such as Principal (PCA) and Independent (ICA) Component Analysis, Linear Discriminant Analysis (LDA). We apply these methods not to the original image, represented as a two-dimensional field of brightness (a halftone image), but to its secondary representation in the form of a two-dimensional gradient field, that is, a complex-valued image. In this case, approaches based on using both the entire gradient field and only its phase component are considered. In addition, two independent ways of forming the final description of the original object are considered: using expansion coefficients of the gradient field in a derived basis and using an original authors' design that is called model-oriented descriptors. With the latter, the number of real coefficients used in the description of the original object can be halved. The studies are conducted via solving a face recognition problem. The effectiveness of the analyzed methods is demonstrated by applying them to images from Extended Yale Face Database B. The comparison is made using a nearest neighbor's classifier.