Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Canonical shape analysis is a popular method in deformable shape matching, trying to bring the shape into a canonical form that undoes its non-rigid deformations, thus reducing the problem of non-rigid matching into a rigid one. The canonization can be performed by measuring geodesic distances beten all pairs of points on the shape and embedding them into a Euclidean space by means of multidimensional scaling (MDS), which reduces the intrinsic isometries of the shape into the extrinsic (Euclidean) isometries of the embedding space. A notable drawback of MDS-based canonical forms is their sensitivity to topological noise: different shape connectivity can affect dramatically the geodesic distances, resulting in a global distortion of the canonical form. ,  propose a different shape canonization approach based on a physical model of electrostatic repulsion.  minimize the Coulomb energy subject to the local distance constraints beten adjacent shape vertices. Our model naturally handles topological noise, allowing to 'tear' the shape at points of strong repulsion. Furthermore, the problem is computationally efficient, as it lends itself to fast multipole methods.  show experimental results in which our method compares favorably to MDS-based canonical forms.
['Davide Boscaini', 'Ramūunas Girdziušas', 'Michael M. Bronstein']
I am writing a research paper on a idea Coulomb shapes: using electrostatic forces for deformation-invariant shape representation
[{"from": "human", "value": "I am writing a research paper on a idea Coulomb shapes: using electrostatic forces for deformation-invariant shape representation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Canonical shape analysis is a popular method in deformable shape matching, trying to bring the shape into a canonical form that undoes its non-rigid deformations, thus reducing the problem of non-rigid matching into a rigid one. The canonization can be performed by measuring geodesic distances beten all pairs of points on the shape and embedding them into a Euclidean space by means of multidimensional scaling (MDS), which reduces the intrinsic isometries of the shape into the extrinsic (Euclidean) isometries of the embedding space. A notable drawback of MDS-based canonical forms is their sensitivity to topological noise: different shape connectivity can affect dramatically the geodesic distances, resulting in a global distortion of the canonical form. ,  propose a different shape canonization approach based on a physical model of electrostatic repulsion.  minimize the Coulomb energy subject to the local distance constraints beten adjacent shape vertices. Our model naturally handles topological noise, allowing to 'tear' the shape at points of strong repulsion. Furthermore, the problem is computationally efficient, as it lends itself to fast multipole methods.  show experimental results in which our method compares favorably to MDS-based canonical forms."}]