title: [Geometrical analysis of benign and malignant breast lesions].
abstract: OBJECTIVE
  The aim of this study was to describe a computer-assisted method based on fractal dimension and the coefficient of roundness, two mathematical descriptors of irregularly shaped objects, in order to discriminate benign and malignant mammographic lesions.
  
  
  METHODS
  Twenty-three digitized mammograms were classified as containing benign lesions (n=12) or as containing malignant lesions (n=11) on the basis of readings by two independent radiologists. Morphometrical and fractal analysis of the breast lesions were automatically performed by a computer-assisted image analysis system.
  
  
  RESULTS
  The method shows, for the first time, two parameters that allow the classification of irregularly shaped objects, such as benign and malignant breast lesions. A significant increase was obtained when comparing the fractal dimension and the coefficient of roundness of benign versus malignant mammographic lesions.
  
  
  CONCLUSIONS
  Benign and malignant breast lesions are characterized by complex morphologies. Complexity is the main property of all biological systems, including natural and pathological structures. In this study, we showed that fractal geometry allows quantitative measurement of the complex morphology of benign and malignant mammographic lesions. Furthermore, this mathematical approach may be helpful for the study of the non-linear dynamic processes involved in breast carcinogenesis.
authors.affiliation: Direzione Scientifica, Istituto Clinico Humanitas, Rozzano, Milan, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Grizzi
authors.forename: P C
authors.initials: PC
authors.lastname: Muzzio
authors.forename: A
authors.initials: A
authors.lastname: Di Maggio
authors.forename: N
authors.initials: N
authors.lastname: Dioguardi
mesh_terms: D001941:Breast Diseases / Q000000981:diagnostic imaging* / Q000473:pathology; D001943:Breast Neoplasms / Q000000981:diagnostic imaging* / Q000473:pathology; D006801:Humans; D008327:Mammography; D008433:Mathematics