Fractal Analysis of Contours of Breast Masses in Mammograms

Abstract

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.

A computer-aided system for malignancy risk assessment of nodules in thyroid US images based on boundary features

“…Other boundary features applied in medical image analysis include the normalized radial length (NRG) [19], the area ratio [20], the fractal dimension (FD) [21], [31], the roughness index, the spiculation index, and the fractional concavity [23]. In addition, the extraction of boundary features by analyzing spectral domain, as it is the case with Fourier descriptor or wavelet descriptor, has been proved to provide noise-robust boundary representation in various applications [31].…”

“…This indicates that boundary features, although not sufficient, could be useful within the context of a nodule classification scheme. Based on the results of previous research which support the utilization of CMP and FD as boundary features [18], [21], [22] this paper investigates their discriminative capability. The utilization of CMP aims to encode large-scale irregularity information as it is the existence of lobes, whereas FD is utilized so as to quantify small-scale irregularity.…”

“…Microlobulated or highly spiculated contours of malignant tumors are expected to demonstrate fractal behavior, which should be absent in the case of benign masses [21], [22]. Rangayyan and Nguyen [21] computed FD from the one-dimensional signature of a given mass, defined as the Euclidean distance of each contour point from the centroid of the contour. …”

Toward Understanding the Size Dependence of Shape Features for Predicting Spiculation in Lung Nodules for Computer-Aided Diagnosis

“…In the field of CAD for breast cancer, it was shown that shape features that were designed to measure the spiculation of breast masses were important to predicting breast mass malignancy [17][18][19]. Given that mammograms for breast cancer assessment have high resolution compared with the CT scans used for lung nodule assessment, it is important to specifically tackle the issue for the low-resolution case of lung nodules.…”

Mass Description for Breast Cancer Recognition

“…The most used descriptors are: circularity, rectangularity [2], compactness(C), spiculation index (SI), fractional concavity (F cc ) [3], fractal dimension [4], Fourier descriptors [5] and statistics based on the distribution of the Normalized Radial Length [6]. One important feature in automated malignity recognition is spiculation level characterization.…”