Abstract 

Shape analysis is a method for measuring, describing and comparing the shape of x-x-objects in geometric space. An important aspect is to obtain Procrustes distance based on least square method. We note that the shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an x-x-object. However, and unfortunately, when we cannot measure some landmarks which are some biologically or geometrically meaningful points of any x-x-object, it is not possible to measure the variation of all shapes of an x-x-object, including that of the incomplete x-x-object. Hence, we need to replace the missing landmarks. In particular, Albers and Gower (2010) studied the missing rows of configurations in Procrustes analysis. They noted that the convergence of their approach can be quite slow. In this study, alternatively, we derive an algorithm for estimating the missing landmarks based on the pre-shapes. The pre-shape is invariant under the location and scaling of the original configuration with the centroid size of the pre-shape being one. Therefore we expect that we can reduce the amount of total computing time for obtaining the estimate of the missing landmarks. 

Keywords: estimate, missing landmark, pre-shape, Procrustes distance, shape analysis