Four dual-energy projective decomposition algorithms that may be applied to the X-ray bone densitometry, including surface fitting method, lookup table method, contour fitting method, and neural network method, are studied and compared. The photon counting detector has high energy resolution and low noise. The projection data acquired by the multi energy bin photon counting detector on a bench-top imaging setup helps to improve the decomposition precision. Aluminum (Al) and polymethyl methacrylate (PMMA) are selected as the base materials to represent bone and soft tissue respectively. Combinations with different base material thicknesses are used for calibration experiments to build lookup tables for high energy and low energy projections. The four projective decomposition algorithms mentioned above are used to establish the inverse lookup table, nine test points are selected in table and are decomposed by the four decomposition algorithms, and the decomposition deviation and running time of various algorithms are calculated and compared. The results show that Al thicknesses with a bias of 0.11%-3.68%, 0-2.86%, 0.07%-3.23% and 0.41%-4.18%, PMMA thicknesses with a bias of 0.11%-3.42%, 0.44%-5.33%, 0.02%-2.83% and 0.09%-4.89% are estimated by the surface fitting method, the lookup table method, the contour fitting method and the neural networks method, respectively. Compared to the lookup table method and the neural network method, the surface fitting method and the contour fitting method are faster by about an order of magnitude. The results suggest that the contour fitting method is superior in terms of decomposition accuracy and rate.