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Shape inference for sheet of paper with text via characteristic strips

Shape inference for sheet of paper with text via characteristic strips. Project by Arie Kozak. Introduction and goals. Given photograph with sheet of paper with text only, infer shape of the surface and plot it in 3d.

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Shape inference for sheet of paper with text via characteristic strips

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  1. Shape inference for sheet of paper with text via characteristic strips Project by ArieKozak

  2. Introduction and goals • Given photograph with sheet of paper with text only, infer shape of the surface and plot it in 3d. • Single (infinite) light source from above, using reflectance map (paper is nearly Lambertian surface): • The surface is assumed to be constant in one direction.

  3. Step 1Locate the sheet in the image • Mark it using personal biological visual system.

  4. Step 1Locate the sheet in the image • Divide the image into two connected sub-images divided by red border.

  5. Step 2Locate text • Use thresholding twice: after high pass and original image. Text found in the intersection.

  6. Step 3Remove text • Constant albido assumption for ink, doesn’t work, use (cubic) interpolation. • Smooth image with Gaussian kernel before to reduce “sharpening effect” (lateral inhibition), and also after.

  7. Step 4Starting points for characteristic strips • Maximum intensity point in image => p = q = 0. Use parabolic approximation according to B.K.P. Horn's chapter 11:

  8. Step 4Starting points for characteristic strips • Solution • Only solutions with a<0,c<0 are relevant.

  9. Step 4Starting points for characteristic strips • Identify “clusters” – areas of local maxima/minima. All points within certain % of highest intensity values.

  10. Step 5Apply characteristic strips • Start with H = 0, perform for each cluster separately.

  11. Step 6Merge clusters • Find closest clusters A and B; B with known height. • For points in A close to B, calculate expected height according to B. • Find closest points using Voronoi diagram.

  12. Step 6Merge clusters • Find relative height between A and B. If is current and expected height of point i accordingly, find relative height x, such that error will be minimal:

  13. Step 7Rebuild the surface of the sheet • Find direction v, in which H is constant => derivative is 0. • Find least square line, its directions is perpendicular to v.

  14. Step 8Rebuild the surface of the sheet • If v is new x-axis, calculate projection of all points to YZ plane.

  15. Step 8Rebuild the surface of the sheet • Use polyline approximation. Given number of desired points = number of clusters + 2, the desired error can be approximated using binary search. • Example – 5 points:

  16. Step 8Rebuild the surface of the sheet • Finally, use spline, on polyline edge points.

  17. Results • Not perfect, usually works sufficiently.

  18. Results

  19. Future work • Detect sheet of paper automatically. • Relax assumptions (light direction, H is constant in one direction). • Improve clusters search. • Replace/improve polyline approximation. • Use this for text recognition.

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