Journal of Digital Imaging

, Volume 20, Issue 3, pp 223-237

First online:

Fractal Analysis of Contours of Breast Masses in Mammograms

  • Rangaraj M. RangayyanAffiliated withDepartment of Electrical and Computer Engineering, Schulich School of Engineering, University of CalgaryDepartment of Radiology, University of Calgary Email author 
  • , Thanh M. NguyenAffiliated withDepartment of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Fractal analysis has been shown to be useful in image processing for characterizing shape and gray-scale complexity. Breast masses present shape and gray-scale characteristics that vary between benign masses and malignant tumors in mammograms. Limited studies have been conducted on the application of fractal analysis specifically for classifying breast masses based on shape. The fractal dimension of the contour of a mass may be computed either directly from the 2-dimensional (2D) contour or from a 1-dimensional (1D) signature derived from the contour. We present a study of four methods to compute the fractal dimension of the contours of breast masses, including the ruler method and the box counting method applied to 1D and 2D representations of the contours. The methods were applied to a data set of 111 contours of breast masses. Receiver operating characteristics (ROC) analysis was performed to assess and compare the performance of fractal dimension and four previously developed shape factors in the classification of breast masses as benign or malignant. Fractal dimension was observed to complement the other shape factors, in particular fractional concavity, in the representation of the complexity of the contours. The combination of fractal dimension with fractional concavity yielded the highest area (A z ) under the ROC curve of 0.93; the two measures, on their own, resulted in A z values of 0.89 and 0.88, respectively.

Key Words

Box counting method breast cancer breast masses breast tumors contour analysis fractal analysis fractal dimension ruler method shape analysis signatures of contours