Exploring Optimality of Piecewise Polynomial Interpolation Functions for Lung Field Modeling in 2D Chest X-Ray Images

Abstract

In this paper, a landmark based approach, using five different interpolating polynomials (linear, cubic convolution, cubic spline, PCHIP, and Makima) for modeling of lung field region in 2D chest X-ray images have been presented. Japanese Society of Radiological Technology (JSRT) database which is publicly available has been used for evaluation of the proposed method. Selected radiographs are anatomically landmarked using 17 and 16 anatomical landmark points to represent left and right lung field regions, respectively. Local, piecewise polynomial interpolation is then employed to create additional semilandmark points to form the lung contour. Jaccard similarity coefficients and Dice coefficients have been used to find accuracy of the modeled shape through comparison with the prepared ground truth. With the optimality condition of three intermediate semilandmark points, PCHIP interpolation method with an execution time of 5.04873 s is found to be the most promising candidate for lung field modeling with an average Dice coefficient (DC) of 98.20 and 98.54% (for the left and right lung field, respectively) and with the average Jaccard similarity coefficient (JSC) of 96.47 and 97.13% for these two lung field regions. While performance of Makima and cubic convolution is close to the PCHIP with the same optimality condition, i.e., three intermediate semilandmark points, the optimality condition for the cubic spline method is of at least seven intermediate semilandmark points which, however, does not result in better performance in terms of accuracy or execution time.