Statistics of Lines in Natural Images

Natural images can be segmented into oriented lines:

We examined a digital library of natural images:

1. Use standard filters to convert images to an orientation field  S(x,y) (in a half-plane).
2. Average over 4 different half-plane representations ([0,pi], [pi/2, 3 pi,2], [pi, 2 pi], [3 pi/2, pi/2])
3. Rotate images to remove vertical/horizontal bias
4. Fourier transform, and extract the power spectrum, along the
   • Longitudinal component  |k . S(k) k . S(k)*|
   • Transverse component  |k x S(k) k x S(k)*|

A proponderance of circles:  M. Sigman et al, PNAS 98, 1935 (2001).

• Circle-land, and its power spectra

Selected Images from Modern Art

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