Rotational invariant visual object extraction and understanding

In this paper, we discuss a novel method, based on singularity representation, for integrating a rotational invariant visual object extraction and understanding technique,. This new compression method applies Arnold's Differential Mapping Singularities Theory in the context of three-dimensional (3D) object projection onto the 2D image plane. It takes advantage of the fact that object edges can be interpreted in terms of singularities, which can be described by simple polynomials. We discuss the relationship between traditional approaches, including wavelet transform and Differential Mapping Singularities Theory or Catastrophe Theory (CT) in the context of image understanding and rotational invariant object extraction and compression. CT maps 3D surfaces with exact results to construct an image-compression algorithm based on an expanded set of operations. This set includes shift, scaling rotation, and homogeneous nonlinear transformations. This approach permits the mathematical description of a full set of singularities that describes 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 are suitable for image compression and Automatic Target Recognition.