In this paper, we discuss a novel method, for multispectral and hyperspectral imagery data reduction. This method is based on singularity representation and integrates a rotational invariant visual object extraction and understanding technique based on the application of differential mapping to image processing. This new compression method applies Arnold's Differential Mapping Singularities Theory in the context of three-dimensional (3D) terrain and objects projection onto the two-dimensional (2D) image plane. It takes advantage of the fact that terrain features (particularly edges and singular points) and can be interpreted in terms of mapping singularities, which can be described by simple polynomials. We discuss the relationship between traditional approaches, including spatial and spectral decorrelation, and differential mapping singularities theory, or Catastrophe Theory (CT), in the context of multispectral image understanding and data reduction. CT maps 3D surfaces with exact results to construct a multispectral image-compression algorithm based on a finite set of singularities. This approach permits the rigorous mathematical description of a full set of singularities that describes the edges and other specific points of objects. The edges and specific points (degenerate critical points) are the products of mapping smooth 3D surfaces, which can be described by a simple set of polynomials that is suitable for image compression and automatic target recognition. The spectral signature for each extracted object was refined, and its dynamic diapason was compared with traditional methods.