Image presents the basic physical features of an object. Geometry, on the other hand, provides us a powerful way to quantify the information reflected by images or their shapes. Traditional geometry however finds limitation in describing the differences between highly irregular objects, which requires us to find new approaches to measure an object and quantify its difference from another. In this paper, we define some scalars in two dimensions to meet this demand. These approaches, grounded on circularity, convexity and cavity, describe the geometry of shapes in statistic sense, and they can also be applied to qualify the differences of shapes.