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The basic idea is that expressions can be treated by inspecting their effect on the surface of a flattened face. Each expression can then be treated using isometries, which are an area explored by others too [21]. The surface of the face is deformed to a Canonical Form using Multi-Dimensional Scaling (MDS) such that geodesic distances between the points are preserved. This helps remove the impact of expressions on the surface in a different way than the one adopted with PCA. There is an extension to this work, which is known as Generalised Multi-dimensional Scaling (GMDS). Bronstein et al. used variants of such a non-rigid method to tackle the face recognition problem, whereas many others stick to rigid methods which preserve the geometry of the faces as they approach the recognition problem. GMDS can also be used in a wide range of other problems, including deformation-invariant comparisons, similarity of deformable shapes with partial similarity, and correspondence of deformable shapes. This will be discussed in a later section which deals with implementational considerations.