An efficient method dedicated to detecting and segmenting of the rib and spine was introduced based on convex polygon vertex detection utilizing position and anatomic characteristics of the rib and spine. Firstly, according to the basic characteristics of liver CT perfusion images, the Gaussian blurring technique and maximum correlation criterion was utilized to obtain the binary image, and then the binarified regions of the rib and spine were segmented based on convex polygon vertex detection. Experimental results show that the algorithm can effectively segment the rib and spine in liver CT perfusion images. Due to relatively low computation cost together with adoption of fast implementation to the large time-consuming connected components labeling and analysis, the presented method runs with a most high speed. The method has great reference value in clinical application to further liver segmentation and registration in liver CT computer-aided diagnosis system.