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EMMCVPR
2011
Springer

The Complex Wave Representation of Distance Transforms

7 years 6 months ago
The Complex Wave Representation of Distance Transforms
The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. The underlying motivation for performing this maneuver is as follows: the normalized power spectrum of the wave function is an excellent approximation (at small values of Planck’s constant—here a free parameter τ) to the density function of the distance transform gradients. Or in colloquial terms, spatial frequencies are gradient histogram bins. Since the distance transform gradients have only orientation information, the Fourier transform values mainly lie on the unit circle in the spatial frequency domain. We use the higher-order stationary phase approximation to prove this result and then provide empirical confirmation at low values of τ. The result indicates that the CWR of distance transforms is an intriguing and novel shape representation. Key words: distance transforms, Voronoi, Hamilton-Jacobi equation, Schrödinger wave function, complex wave represent...
Karthik S. Gurumoorthy, Anand Rangarajan, Arunava
Added 20 Dec 2011
Updated 20 Dec 2011
Type Journal
Year 2011
Where EMMCVPR
Authors Karthik S. Gurumoorthy, Anand Rangarajan, Arunava Banerjee
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