Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For analyzing shapes of planar, closed curves,  propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces.  use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database,  demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images.
['Eric Klassen', 'Anuj Srivastava', 'Mitsunobu Mio', 'Shantanu H. Joshi']
I am writing a research paper on a idea Analysis of planar shapes using geodesic paths on shape spaces
[{"from": "human", "value": "I am writing a research paper on a idea Analysis of planar shapes using geodesic paths on shape spaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For analyzing shapes of planar, closed curves,  propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces.  use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database,  demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images."}]