Sharif University of Technology A modified algorithm to obtain Translation, Rotation

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Sharif University of TechnologyA modified
algorithm to obtain Translation, Rotation
Scaleinvariant Zernike Moment shape Descriptors

• G.R. Amayeh
• Dr. S. Kasaei
• A.R. Tavakkoli

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Introduction

• Shape is one of the most important features to
  human for visual distinguishing system.
• Shape Descriptors
• Contour-Base
• Using contour information
• Neglect image details
• Region-Base
• Using region information

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Shape Descriptors
Fig.1 Same regions.
Fig.2 Same contours.
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Zernike Pseudo-Zernike Moments

• Zernike Moments of Order n, with m-repetition
• Zernike Moments Basis Function

(1)
(2)
(3)
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Zernike Pseudo-Zernike Moments

• Zernike Moment Radial Polynomials
• Pseudo-Zernike Radial Polynomials

(4)
(5)
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A Cross Section ofRadial Polynomials of ZM PsZM
Fig.3 ZM (blue) Ps. ZM (red) of 4-order with
repetition 0.
Fig.4 ZM (blue) Ps. ZM (red) of 6-order with
repetition 4.
Fig.5 ZM (blue) Ps. ZM (red) of 5-order with
repetition 1.
Fig.6 ZM (blue) Ps. ZM (red) of 7-order with
repetition 3.
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3-D Illustration of Radial Polynomials of ZM
Ps.ZM
Fig.7 Radial polynomial of ZM of 7-order with
repetition 1.
Fig.8 Radial polynomial of Ps. ZM of 7-order
with repetition 1.
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Zernike Moments Properties

• Invariance Properties
• Zernike Moments are Rotation Invariant
• Rotation changes only moments phase.
• Variance Properties
• Zernike Moments are Sensitive to Translation
  Scaling.

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Achieving Invariant Properties

• What is needed in segmentation problem?
• Moments need to be invariant to rotation, scale
  and translation.
• Solution to achieve invariant properties
• Normalization method.
• Improved Zernike Moments without Normalization
  (IZM).
• Proposed Method.

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Normalization Method

• Algorithm
• Translate images center of mass to origin.
• Scale image

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Normalization Method
Fig.9 From left to right, Original, Translated,
Scaled images (b1800).
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Normalization Method
Fig.10 From left to right, original image
normalized images with different b s.
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Normalization Method Drawbacks

• Interpolation Errors
• Down sampling image leads to loss of data.
• Up sampling image adds wrong information to
  image.

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Improved Zernike Moments without Normalization

• Algorithm
• Translate images center of mass to origin.
• Finding the smallest surrounding circle and
  computing ZMs for this circle.
• Normalize moments

Fig.11 Images fitted circles.
(8)
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Drawbacks

• Increased Quantization Error.
• Since the SSC of images have a small number of
  pixels, images resolution is low and this causes
  more QE.

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Proposed Method

• Algorithm
• Computing a Grid Map.
• Performing translation and scale on the map
  indexes.

Fig.12 Mapping.
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Proposed Method

• Translate origin of coordination system to the
  center of mass

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Fig(13). Translation of Coordination Origin.
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Proposed Method

• Scale coordination system

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Proposed Method

• Computing Zernike Moment in new coordinate
  for where
  .
• We can show that the moments of in the
  new coordinate system are equal to the moments of
  in the old coordinate system.

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Proposed Method
b800
b1200 b1800
b2500
Fig.15 From left to right, original image
normalized images with different b s.
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Proposed Method

• Special case

Fig.17 Zernike moments by proposed method
(b2550) IZM (Improved ZM with out
normalization ).
Fig.16 Original image.
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Experimental Results
Fig.16 Original image 70 scaled image.
Fig.17 Error of Zernike moments between
original image scaled image.
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Experimental Results
Fig.18 Original image 55 degree rotated image.
Fig.19 Error of Zernike moments between
original image rotated image.
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Experimental Results
Fig.21 Error of Zernike moments between
original scaled images.
Fig.20 Original image 120 scaled image.
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Experimental Results
Fig.23 Error of Zernike moments between
original image rotated image.
Fig.21 Original image 40 degree rotated image.
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Conclusions

• Principle of our method is same as the
  Normalization method.
• Does not resize the original image.
• No Interpolation Error.
• Reduces the quantization error. (using beta
  parameter)
• Trade off Between QE and power of distinguishing.
• Has all the benefits of both pervious methods.

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• The End