Continuum robots and soft robots have shown great potential in industrial and medical applications. Sensing the shapes of continuum robots is a challenging but significant problem for enhancing their performance during various tasks. In this paper, we present a novel method to estimate the shapes of continuum robots by capturing passive tendon displacements with image sensors. This method is reliable but low-cost. To reconstruct the shape of the continuum robot, an intuitive way based on screw theory and the material frame is also presented. The displacements of passive tendons are related to the integral of the geometric parameters of the continuum robot. By using passive tendon displacements, not only bending but also twisting of the robot can be calculated. The experiments show that our method can estimate the shapes of the robot deformed in different conditions. The mean distal position error is 3.01% of the length and the mean shape error is 1.86% of the length. The mean distal direction error is 4.1 degrees. Besides, sensing the shapes of continuum robots in real-time is also achieved.