Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: From an image  construct an invertible orientation score, which provides an overview of local orientations in an image. This orientation score is a function on the group  SE  (2) of both positions and orientations. It allows us to diffuse along multiple local line segments in an image. The transformation from image to orientation score amounts to convolutions with an oriented kernel rotated at multiple angles. Under conditions on the oriented kernel the transform beten image and orientation score is unitary. This allows us to relate operators on images to operators on orientation scores in a robust way such that  can deal with crossing lines and orientation uncertainty. To obtain reasonable Euclidean invariant image processing the operator on the orientation score must be both left invariant and non-linear. Therefore  consider non-linear operators on orientation scores which amount to direct products of  linear  left-invariant scale spaces on  SE  (2). These linear left-invariant scale spaces correspond to ll-known stochastic processes on  SE  (2) for line completion and line enhancement and are given by group convolution with the corresponding Green's functions.  provide the  exact  Green's functions and approximations, which  use together with invertible orientation scores for automatic line enhancement and completion.
['Remco Duits', 'Em Erik Franken']
I am writing a research paper on a idea Line Enhancement and Completion via Linear Left Invariant Scale Spaces on SE(2)
[{"from": "human", "value": "I am writing a research paper on a idea Line Enhancement and Completion via Linear Left Invariant Scale Spaces on SE(2)"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: From an image  construct an invertible orientation score, which provides an overview of local orientations in an image. This orientation score is a function on the group  SE  (2) of both positions and orientations. It allows us to diffuse along multiple local line segments in an image. The transformation from image to orientation score amounts to convolutions with an oriented kernel rotated at multiple angles. Under conditions on the oriented kernel the transform beten image and orientation score is unitary. This allows us to relate operators on images to operators on orientation scores in a robust way such that  can deal with crossing lines and orientation uncertainty. To obtain reasonable Euclidean invariant image processing the operator on the orientation score must be both left invariant and non-linear. Therefore  consider non-linear operators on orientation scores which amount to direct products of  linear  left-invariant scale spaces on  SE  (2). These linear left-invariant scale spaces correspond to ll-known stochastic processes on  SE  (2) for line completion and line enhancement and are given by group convolution with the corresponding Green's functions.  provide the  exact  Green's functions and approximations, which  use together with invertible orientation scores for automatic line enhancement and completion."}]