Extraction of Local Symmetries using Tensor Field Filtering
Carl‐Fredrik Westin, Hans E. Knutsson · 1992
Abstract. Feature extraction from a tensor based local image represen-tation is discussed. This tensor image representation keeps statements of local structure, certainty of statement and energy separate. Further processing for obtaining new features also having these three entities separate is achieved by the use of a new concept, tensor ¯eld ¯ltering. Tensor ¯lters for smoothing and for extraction of circular symmetries are presented and discussed in particular. The main reason for deriving a tensor ¯ltering procedure is to ¯nd a general operator between levels in a feature hierarchy. A tensor representation of features combined with this operator gives some advantages; e.g. when the model on the next higher level do not have support from data this yields \\round " tensors. Thus, events not supporting the model are passed on to the next higher level in the norm of the tensors. It is the shape of the tensor that in-dicates the validity of the statement. Conventional operators in general do not share this property of having a separation between statements of local structure, certainty of statement, and energy. 1 1