Algorithms For Deformation-Driven 3D Shape Correspondence

Recent advances in graphics technology have led to the creation of many digital objects in different databases,and such objects sometimes are subject to analysis,transfer,or/and comparison.In many cases,before any pair or group of such objects can undergo these tasks,there is a need to first relate them by computing a meaningful correspondence between them.Shape correspondence methods primarily seek to address this by taking two or more shapes as input with the aim to find a meaningful mapping that matches similar or semantically equivalent surface points of the shapes.The focus of this literature is chiefly about computing full or partial correspondence between selected featured or all points of the 3D isometric shapes i.e.of shapes that are semantically similar up to some deformation,bending,or/and scaling.In other words,our correspondence algorithm aims to find the mapping between both rigid and non-rigid classes of shapes putting into consideration their similarities,the resolution of the desired mapping,etc.The problem of non-rigid 3D correspondence has remained an underlying and commonly discussed problem in the digital world as many existing methods including those that establish satisfactory correspondences between given isometric shapes arrive at their results at a prohibitive computational cost and in some cases completely intractable.We explore 3D shape correspondence problem by using the biharmonic distance on the spectral form of multidimensional scaling which effectively reduces the dimensionality of the shapes into Euclidean space making similarities and dissimilarities of isometric shapes more efficiently computed.The result of such embedding is called canonical form,and the motivation is to represent the intrinsic property of the shape as an extrinsic property of it's embedded image.The relevant of our approach is based on the unique property of the biharmonic distance in that it reflects the overall image of the surface points in distance areas from the origin.Utilizing the farthest-point sampling strategy to select a subset of sampled points,we combine the potency of the spectral multidimensional scaling with global awareness of the biharmonic distance operator to propose an approach which embeds 3D shapes into canonical forms that show further “resemblance” between isometric shapes.The experimental result shows effective and efficient approximations with distinctive local features and yet a robust global property of both the model and probe shapes.In comparison to a recent state-of-the-art method,the proposed approach can achieve comparable or even better results and have practical computational efficiency as well.