Morphological multiscale representation for boundaries and surfaces

A new shape and object representation method for binary and range images is presented in this paper. It is a multiscale representation of an object based on morphological scale transforms. It is proven that erosions and dilations with multiscale structuring elements are equivalent to distance transforms. Through morphological scale transforms (MSTs), morphological scale functions (MSFs) are constituted as the multiscale representation functions of shapes and objects. Intuitively, MSF´s are weighted boundaries and surfaces of shapes and objects. Their properties are illustrated in this paper. Invariants of MSFs are applicable to shape matching under scaling and rotation. Applications of MSFs such as corner detection and range image segmentation are studied