Pyramid symmetry transforms: From local to global symmetry

Pyramid computation is a natural paradigm of computation in planning strategies and multi-resolution image analysis. This paper introduces a new paradigm that is based on the concept of soft-hierarchical operators implemented in pyramid architecture to retrieve global versus local symmetries. The concept of symmetry is mathematically well defined in geometry whenever patterns are crisp images (two levels). Necessity for a soft approach occurs with multi-levels images and whenever the separation between object and background is subjective or not well defined. The paper describes two new pyramid operators to detect symmetries based on previously introduced conventional operators. For sake of applications, experiments in the detection of point of interest are shown to support the hierarchical scheme.