The shadow of oil containers can be used to determine their fullness level. This can be done due to the fact that oil containers usually have a floating roof, such that the spatial relationship between the shadow within an oil container and the one on the outside can be utilized appropriately.

Satellite images are especially useful in this matter, as they provide a top down view in which the geometry is conveniently flattened. It therefore is particularly easy to determine the spatial geometry of the said shadows.

The following excerpt consequently provides an overview of a method that can be used in order to determine the intended fullness level.

# 1 - Causa

The setting of this excerpt assumes that a particular oil container has already been located, such that a satellite image can easily be obtained (see figure 1).

One restriction however is the lack of additional information of the said image, such that the time at which it has been recorded is unknown. The direction of the sun and therefore the shadow can therefore not determined analytically.

# 2 - Modus Operandi

With the assumption that oil containers in general have a round shape, hough circles can be utilized to precisely determine the exact location of the container [1]. In doing so, the input image is first being converted into a gray colorspace and preprocessed by applying a sobel filter [1]. The dominant hough circle can subsequently be determined within the filtered image (see figure 2 and figure 3).

After the dominant hough circle has been obtained, the direction of the sun and therefore the direction of the shadows has to be determined. The set of most significant hough circles is being utilized for this task, as they are heavily influenced by the shadows of the round oil container (see figure 4).

The direction in question can accordingly be approximated by fitting a line through the center of each individual hough circle within the previously determined set (see figure 5). This has been done within the prototype for this excerpt via total least squares by minimizing the sum of the squared perpendicular distances [2]. The influence of outliers could additionally be reduced by incorporating a randomly sampled consensus, what has not been necessary yet though [3].

The determined direction can subsequently be used in combination with the center of the dominant hough circle in order to obtain an appropriate scanline consisting of intensity values. In doing so, a filter can be introduced such that occurring noise like the dark pipe within the otherwise bright inner of the oil container is being compensated (see figure 6).

The width of the two distinguishing valleys within the signal can finally be used to calculate the fullness level. In order to identify these valleys, the derivative of the signal is being calculated. While the sign of the derivative can be incorporated for this task, the energy of the derivative alone has already been sufficient within the chosen samples though.

The four most significant peaks are therefore being determined in order to classify the two valleys (see 7). This being said, the described method determined through the width of the valleys that the fullness level of the oil container within the given sample is roughly $$60.4$$ percent (see figure 8).

# 3 - Status Quo

Since the described method has not thoroughly been evaluated, no statement about its applicability can be made. Further work should thus be done in order to gather a bigger sample size that has already been classified manually, such that a ground truth can be used for evaluating the correctness of the described method.

# References

[1]

D. Ballard, “Generalizing the hough transform to detect arbitrary shapes,” *Pattern Recognition*, vol. 13, no. 2, pp. 111–122, 1981.

[2]

S. Van Huffel and J. Vandewalle, *The total least squares problem: Computational aspects and analysis*, 1st ed. Siam, 1991.

[3]

M. Fischler and R. Bolles, “Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,” *ACM Transactions on Communications*, vol. 24, no. 6, pp. 381–395, Jun. 1981.