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Reconstruction of Locally Disturbed Pictures With Non-Linear Filtering In Fourier Space

IP.com Disclosure Number: IPCOM000119884D
Original Publication Date: 1991-Mar-01
Included in the Prior Art Database: 2005-Apr-02
Document File: 3 page(s) / 94K

Publishing Venue

IBM

Related People

Stoll, EP: AUTHOR

Abstract

Local perturbations or distortions can badly deface a picture and confuse the beholder by drawing the eye to the damaged spot. This can greatly hamper the further processing of such a picture. Therefore, such pictures must be restored without falsifying the information they contain. This is not too difficult as long as there are only small changes in brightness or color in the distorted regions. Otherwise, and if the images are very busy, it is possible to develop a procedure for restoring the pictures by transferring periodic, as well as quasiperiodic, redundant picture information into the distorted parts from their environment. Periodic or quasiperiodic structures occur in pictures obtained with most scanning microscopes.

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Reconstruction of Locally Disturbed Pictures With Non-Linear Filtering
In Fourier Space

      Local perturbations or distortions can badly deface a
picture and confuse the beholder by drawing the eye to the damaged
spot.  This can greatly hamper the further processing of such a
picture.  Therefore, such pictures must be restored without
falsifying the information they contain. This is not too difficult as
long as there are only small changes in brightness or color in the
distorted regions. Otherwise, and if the images are very busy, it is
possible to develop a procedure for restoring the pictures by
transferring periodic, as well as quasiperiodic, redundant picture
information into the distorted parts from their environment.
Periodic or quasiperiodic structures occur in pictures obtained with
most scanning microscopes.  These pictures are often correlated by
the fact that, to prevent aliasing effects, the spacing between
neighboring picture elements is made much smaller than the
instrumental resolution.

      Provided the locations of the perturbances are known, by means
of Fourier transformation and nonlinear filtering in Fourier space,
locally disturbed pictures having redundant information in the
environment of the damaged areas and periodic or quasiperiodic
structures can be restored.  With a sequence of iterations in which
the damaged areas are replaced by improvements in the preceding
steps, they are then transformed together with the unperturbed parts
into Fourier space.  After reduction of the nonlinearity filter
parameters, information flows into the damaged areas reconstructing
the lost data.

      Mathematically, local disturbances of picture elements (pixels)
are described as a multiplication of the picture information f(x, y)
with the perturbation function h(x, y). Here, we assume that the
locations of the perturbed pixels are known, e.g., from visual
inspection.  For further processing, we no longer need the perturbed
pixels, so that the perturbance function h(x, y) is zero at the
unperturbed pixels and one at the perturbed pixels.  The remaining
picture g(x, y) satisfies the relation

                            (Image Omitted)

 (1)

      Transformed into Fourier space, Eq. (1) corresponds to the
convolution

                            (Image Omit...