apefile. Next, the raster extraction tool from the ESRI ArcGIS toolbox was used to extract matching pairs of aerial and ground measurements. Another shapefile with on-campus buildings was prepared by digitizing a high- resolution raster image in ArcMap. This shapefile was used to analyze raster data separately for every building. Finally, a shapefile with the structure of the UNI steam pipeline network was provided by the facility services department. This shapefile was used to locate the segments of the steam network that were in any way obscured on the thermal image.
3.1 Georeferencing and Mosaicing
As was mentioned before, aerial data was provided in the form of SAF files, which is an archive that stores a time series of images in the single-file form. In order to access individual raster images, another format had to be used. Portable Network Graphics format was chosen because it supports 16- bit grayscale data as well as lossless compression. An open-source software library, libpng
, developed by Schalnat et al.
] was used to create PNG rasters. Raw data was extracted from the SAF files with a small application written by the author of this paper in compliance with SAF specifications.
Before georeferencing and mosaicing, a histogram of the pixel values distribution was created (Figure 3
From the histogram, it is clear that the majority of pixels belong to the range of values between 1,300 and 2,100, which corresponds to less than 5% of the 16-bit range used by the camera. In order to improve visual contrast, the image histogram was stretched accordingly, using 850 and 2,835 as boundaries. Figure 4
is an example of an image before and after the histogram stretch. These boundary values were selected according to the Chebyshev's Inequality, which guarantees that 99% of the dataset are within the range specified.
After stretching the histogram, raster images were mosaiced manually in the ERDAS Imagine software using existing high-resolution airborne imageries of the UNI Campus as a reference. RMSE for the resulting model were normally distributed with mean of 1.94 pixels and standard deviation of 0.69.
3.2 Pixel to Radiance Conversion
There are two common ways to convert pixel values to temperature. The first approach, utilized by MacKay [2
], Kulacki, Mintzer and Winget [3
] and Tanis and Sampson [10
] is to convert pixel values into temperature directly. The second approach is to convert pixel values to radiance, then use the radiance values as an input to the Planck's formula, as was done by Schott and Wilkinson [8
] and Schott et al.
]. In this study, the second approach was used, because it provides additional control over the level of emissivity of the objects of interest.
It was initially planned to convert pixel values into radiance by using conversion polynomials of the form
are calibration coefficients and p is the pixel value. Calibration data for the sensor was gathered on board the plane using a black body as a reference, as was done by MacKay [2
], Tanis et al.
] and Brown et al.
]. However, the resulting polynomials produced erroneous temperatures that did not correspond to the ground truth. Instead, the dataset that was supposed to act as ground truth was used to create the regression model for the pixel to radiance conversion.
The regression model was built in two steps. First, using Planck's Law:
, h is the Planck constant, k is the Boltzmann constant and c is the speed of light, the radiance of the ground samples was calculated as a function of their temperature. Only samples with well-known emissivity levels (concrete pavements) were used in this process. In the second step, ESRI ArcGIS was used to extract pixel values from the mosaiced thermal image at the locations of the ground samples. Then a linear regression model was built with the pixel values and radiance as variables.
The resulting model has a coefficient of determination (R2
) of approximately 0.78. However, the model is only reliably defined for the range of pixel values between the coldest and the hottest object sampled (approximately -1