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Area and perimeter calculation using super resolution algorithms M. P. Cipolletti – C. A. Delrieux – M. C. Piccolo – G. M. E. Perillo IADO – UNS – CONICET & Comparison of results with pre-existing methods

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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 Band 1Band 2 Band 3Band 4Band 5Band 7 -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 m 2 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. Grey scale image Mask 1: Threshold =127 Mask 2: Threshold =160 Histogram

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SEGMENTATION -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. - An auxiliary image is constructed in levels of grey. Distance Image

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SEGMENTATION Distance Image Mask Image Clear mask Image

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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 -The total area is taken as the sum of the square L 2 areas corresponding to the pixels inside the object. Outside borders of pixels

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TRADITIONAL METHODS FOR AREA AND PERIMETER CALCULATION Outside borders of pixels -Advantage: Implementation 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, L 2 is added if the pixel is completely inside the object, and L 2 /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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-Advantage: Results are more precise. -Disadvantages: The 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. TRADITIONAL METHODS FOR AREA AND PERIMETER CALCULATION

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Description SUPER RESOLUTION METHOD - Given two neighboring pixels, p 0 belonging to the object and p 1 outside of it, the coordinates of the frontier point P A are determined by a coefficient alpha. - Alpha relates the values of luminance between p0 and p1 with the threshold value used for segmentation. - P A will be located over the line segment that connects the center of both pixels.

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Description SUPER RESOLUTION METHOD 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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Description SUPER RESOLUTION METHOD The area is calculated as the sum of the areas of the polygons that compose the object.

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Results – Analysis for the object size SUPER RESOLUTION METHOD

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Results – Analysis for the object size SUPER RESOLUTION METHOD

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Results – Analysis for the object size SUPER RESOLUTION METHOD

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Results – Analysis for the object rotation SUPER RESOLUTION METHOD

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Results – Analysis for the object rotation – 0 degrees SUPER RESOLUTION METHOD

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Results – Analysis for the object rotation – 1 degree SUPER RESOLUTION METHOD

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Results – Analysis for the object rotation – 25 degrees SUPER RESOLUTION METHOD

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Results – Analysis for the object rotation – 45 degrees SUPER RESOLUTION METHOD

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Results – Measurement of a field SUPER RESOLUTION METHOD

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Results – Measurement of a field SUPER RESOLUTION METHOD

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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. -Minimizes errors caused by orientation, shape and size of the object. SUPER RESOLUTION METHOD

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END Thank you!

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