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Area and perimeter calculation using super resolution algorithms

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## Area and perimeter calculation using super resolution algorithms

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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**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.**PREVIOUS CONSIDERATIONS**-The original image is of B-band type. -Resolution is measured in L meters per pixel. Band 1 Band 2 Band 3 Band 4 Band 5 Band 7 Images Landsat 7 ® Resolution 30 meters per pixel**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.**PREVIOUS CONSIDERATIONS**Mask 1: Threshold =127 Grey scale image Mask 2: Threshold =160 Histogram A threshold chosen from the luminance histogram is used to compute a (binary) black and white mask from the grey scale original picture.**SEGMENTATION**- An auxiliary image is constructed in levels of grey. Distance Image -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.**SEGMENTATION**Distance Image Mask Image Clear mask Image**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.**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.**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.**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.**TRADITIONAL METHODS FOR AREA AND PERIMETER CALCULATION**Chain code**TRADITIONAL METHODS FOR AREA AND PERIMETER CALCULATION**Chain code**TRADITIONAL METHODS FOR AREA AND PERIMETER CALCULATION**Chain code • 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.**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.**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.**SUPER RESOLUTION METHOD**Description The area is calculated as the sum of the areas of the polygons that compose the object.**SUPER RESOLUTION METHOD**Results – Analysis for the object size**SUPER RESOLUTION METHOD**Results – Analysis for the object size**SUPER RESOLUTION METHOD**Results – Analysis for the object size**SUPER RESOLUTION METHOD**Results – Analysis for the object rotation**SUPER RESOLUTION METHOD**Results – Analysis for the object rotation – 0 degrees**SUPER RESOLUTION METHOD**Results – Analysis for the object rotation – 1 degree**SUPER RESOLUTION METHOD**Results – Analysis for the object rotation – 25 degrees**SUPER RESOLUTION METHOD**Results – Analysis for the object rotation – 45 degrees**SUPER RESOLUTION METHOD**Results – Measurement of a field**SUPER RESOLUTION METHOD**Results – Measurement of a field**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.-Minimizes errors caused by orientation, shape and size • of the object.**END**Thank you!