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Shapes from Pixels

Fatemi, M ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. DOI: 10.1109/TIP.2016.2514507
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2016
  4. Abstract:
  5. Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (e.g., bandlimitedness). In this paper, we study the problem of recovering shape images with smooth boundaries from a set of samples. Thus, the reconstructed image is constrained to regenerate the same samples (consistency), as well as forming a shape (bilevel) image. We initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes. Next, we relax the non-convex shape constraint to transform the problem into minimizing the total variation over consistent non-negative-valued images. We also introduce a requirement (called reducibility) that guarantees equivalence between the two problems. We illustrate that the reducibility property effectively sets a requirement on the minimum sampling density. We also evaluate the performance of the relaxed alternative in various numerical experiments. © 1992-2012 IEEE
  6. Keywords:
  7. Binary images ; Cheeger sets ; Measurementconsistency ; Shapes ; Total variation ; Binary images ; Bins ; Image reconstruction ; Cheeger sets ; Measurementconsistency ; Numerical experiments ; Reconstructed image ; Reconstruction techniques ; Sampling densities ; Shapes ; Total variation ; Image processing
  8. Source: IEEE Transactions on Image Processing ; Volume 25, Issue 3 , 2016 , Pages 1193-1206 ; 10577149 (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/7372449