Cartesian differential invariants in scale-space

摘要: We present a formalism for studying local image structure in systematic, coordinate-independent, and robust way, based on scale-space theory, tensor calculus, the theory of invariants. concentrate ondifferential The is general applicability to analysis grey-tone images various modalities, defined aD-dimensional spatial domain. propose “diagrammar” differential invariants tensors, i.e., diagrammatic representation derivatives together with set simple rules representing meaningful properties. All properties given level inner scale can be represented terms such diagrams, and, vice versa, all diagrams represent coordinate-independent combinations derivatives, true presentcomplete andirreducible sets (nonpolynomial) appropriate description up any desired order. Any invariant expressed ofpolynomial invariants, pictorially by closed diagrams. Here we consider complete, irreducible polynomial second order (inclusive). Examples fourth (inclusive), calculated synthetic, noiseperturbed, 2-dimensional test images, are included illustrate main theory.