The present invention relates to a method and apparatus for the construction and/or use of multidimensional fields that can be used for high-resolution detection and characterization of features within objects. The multidimensional field is constructed from data that is collected by an array of radiation detectors that substantially surround the object under study. The detected radiation is produced by an array of radiation sources and is subsequently scattered, reflected, transmitted, or diffracted by the object under study and any features within the object under study. In particular embodiments of the invention, the radiation that is used is ultrasonic radiation and the object under study is human or animal tissue or an organ. In this case, the invention permits the detection and identification of cancer by an intelligently trained evaluation system.