Diapositiva 1

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Area and perimeter calculation using super
resolution algorithms
Comparison of results with pre-existing methods
M. P. Cipolletti C. A. Delrieux M. C. Piccolo
G. M. E. PerilloIADO UNS CONICET
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PURPOSE OF THIS WORK

• Data acquisition by non invasive methods
• -Development of a robust algorithm for area and
  perimeter calculation from digital images.
• -Utilization of standard low resolution
  satellite images.
• -Application of the new methods to study
  geographic features.

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PREVIOUS CONSIDERATIONS
-The original image is of B-band type.
-Resolution is measured in L meters per pixel.
Images Landsat 7 Resolution 30 meters per pixel
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PREVIOUS CONSIDERATIONS
- Utilization of a rectangular grid of i rows by
j columns.-Each pixel has a square surface of
LxL m2 and its luminance value is Y.
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PREVIOUS CONSIDERATIONS
A threshold chosen from the luminance histogram
is used to compute a (binary) black and white
mask from the grey scale original picture.
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SEGMENTATION
- An auxiliary image is constructed in levels of
grey.
-The calculation of a scalar function d(i,j) is
then carried out for each pixel, evaluating the
distance between that pixel and a reference (or
prototype) value. -The value of d(i,j) is
associated to a level of grey in the picture.
-The ground-truth is chosen in such a way that
it provides the luminance data of each band
characterizing the object to be segmented.
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SEGMENTATION
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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Outside borders of pixels
The most simple method for perimeter calculation
uses the mask image, computing it as the sum of
the outside pixels borders.

• All pixels are tested and for each one that
  belongs to the object (white pixel), the 4
  neighboring pixels are also analyzed.
• -Each neighboring pixel outside the figure
  adds L to the calculation, giving as a result
  the total perimeter at the end of the loop.

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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Outside borders of pixels
-The total area is taken as the sum of the
square L2 areas corresponding to the pixels
inside the object.
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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Outside borders of pixels

• AdvantageImplementation is fast and
  simple.Disadvantages-Strongly affected by the
  image resolution.-Error increases if shape,
  orientation and/or size of the object
  changes.-In general, results for the values of
  perimeter and area are both over-dimensioned, but
  the error in the perimeter is much bigger.

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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Chain code
Uses the mask considering the perimeter as a
chain that surrounds the object through the
center of the inside pixels next to the border.

• Analyzes each pixel and its neighbors and,
  depending on the configuration, it determines
  the contour of the object moving in right angles
  or in 45 degrees.
• - For the area calculation, L2 is added if
  the pixel is completely inside the object, and
  L2/2 if the pixel corresponds to a turn in 45
  degrees.

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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Chain code
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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Chain code
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TRADITIONAL METHODS FOR AREA AND PERIMETER
CALCULATION
Chain code

• AdvantageResults are more precise.
  -DisadvantagesThe main source of error is
  due to objects of small size, although
  resolution, shape and orientation also alter the
  result.Solutions usually provide perimeter
  and area results
• smaller than real measures.

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SUPER RESOLUTION METHOD
Description
- Given two neighboring pixels, p0 belonging to
the object and p1 outside of it, the coordinates
of the frontier point PA are determined by a
coefficient alpha.
- Alpha relates the values of luminance between
p0 and p1 with the threshold value used for
segmentation. - PA will be located over the
line segment that connects the center of both
pixels.
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SUPER RESOLUTION METHOD
Description
There are 4 possible configurations and their
rotations.
Once the contour points have been determined,
the frontier segments are computed as the
Euclidean distance between them.
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SUPER RESOLUTION METHOD
Description
The area is calculated as the sum of the
areas of the polygons that compose the object.
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SUPER RESOLUTION METHOD
Results Analysis for the object size
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SUPER RESOLUTION METHOD
Results Analysis for the object size
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SUPER RESOLUTION METHOD
Results Analysis for the object size
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SUPER RESOLUTION METHOD
Results Analysis for the object rotation
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SUPER RESOLUTION METHOD
Results Analysis for the object rotation 0
degrees
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SUPER RESOLUTION METHOD
Results Analysis for the object rotation 1
degree
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SUPER RESOLUTION METHOD
Results Analysis for the object rotation 25
degrees
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SUPER RESOLUTION METHOD
Results Analysis for the object rotation 45
degrees
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SUPER RESOLUTION METHOD
Results Measurement of a field
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SUPER RESOLUTION METHOD
Results Measurement of a field
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SUPER RESOLUTION METHOD
Conclusions

• Developed to overcome the disadvantages found in
  the traditional methods described before. -Uses
  additional information provided by the luminance
  which is lost after the threshold is applied to
  the image
• for computing the mask.-The resulting method is
  robust and the results obtained
• are more precise than those achievable by
  the other
• methods for images of the same resolution.-Minimi
  zes errors caused by orientation, shape and
  size
• of the object.

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END
Thank you!