We define new measures of convexity for binary images. The convexity considered here is the so called Q-convexity, that is, convexity by quadrants. This kind of convexity has been mostly studied in Discrete Tomography for its good properties, and permits to generalize h-convexity to any two or more directions. Moreover convex binary images are also Q-convex, and for these two classes similar properties hold. Here we present two measures based on the geometrical properties of “Q-convex shape” which have the following features: (1) their values range from 0 to 1; (2) their values equal 1 if and only if the binary image is Q-convex; (3) their efficient computation can be easily implemented.