# HPT: A High Spatial Resolution Multispectral Sensor for Microsatellite Remote Sensing
## 3 Image Analysis Methods and Results
### Multispectral Images  
Multispectral images selectable from 650-1050 nm are acquired with the NIR band of the HPT. A combination of the selected wavelengths is configured in advance, and multispectral images are captured sequentially at a scheduled time and at a specified time interval.  
Figure 6 shows a series of multispectral images acquired at 665 nm, 690 nm, 700 nm, 720 nm, 750 nm, and 873 nm. The area in these scenes is dominated by forests, whose spectral reflectance is lower at 665 nm and 690 nm (the red region), and higher at 750 nm and 873 nm (the NIR region). Due to attitude fluctuations during the off-nadir pointing of the satellite, these scenes deviate from one another spatially. Hence, band-to-band registration using the feature-based method is also required for the processing of the multispectral images prior to the calculation of indices such as the normalized difference vegetation index (NDVI), which is derived from red and NIR images. The NDVI is calculated from the following expression:  
\[NDVI=\frac{\rho_{\text{NIR}}-\rho_{\text{RED}}}{\rho_{\text{NIR}}+\rho_{\text{ RED}}} \tag{1}\]  
where \(\rho_{\text{RED}}\) and \(\rho_{\text{NIR}}\) are the surface reflectance in the red and NIR regions, respectively. However, the result of feature matching between the red and NIR images is usually poor because of the differences in their spectral reflectance. As seen in Figure 6, the multispectral images at 720 nm, belonging to \"red edge\" between the red and NIR regions, have features common to both regions, and sufficient numbers of matched feature points. Therefore, the feature matching of multispectral images is iterated sequentially, with its neighboring spectral band from the red to the NIR through the red edge, before all of the images are transformed to the coordinate system of the NIR image. This spectrally sequential image registration method is also effective for the analysis of hyperspectral images obtained by a wavelength-scanning imager on an unmanned aerial vehicle [13].  
In order to calculate the NDVI, 10-bit digital numbers for each pixel after the image registration are converted to surface reflectance \(\rho\) using the following steps. (1) The digital number is converted into spectral radiance at the sensor's aperture L\({}_{\text{sat}}\) using the unit conversion coefficient, which is obtained by the preflight calibration test using an integrating sphere as the uniform light source. (2) An image-based atmospheric correction is applied to the path radiance L\({}_{\text{p}}\) calculation using the dark object subtraction (DOS) method [14; 15]. (3) The surface reflectance is calculated as:  
\[\rho\ =\frac{\pi\left(\text{L}_{\text{sat}}-\text{L}_{\text{p}}\right)\ d^{2}}{ E\ \cos\theta} \tag{2}\]  
Figure 6: Multispectral images of Shimonoseki City, Yamaguchi Prefecture, Japan, acquired on 29 May 2015.  
where \(d\) is the Earth-Sun distance, \(E\) is the solar exoatmospheric irradiance, and \(\theta\) is the solar zenith angle. Figure 7a,b shows the NDVI derived from the multispectral images in Figure 6. Images at 665 nm and 873 nm were used for the calculation of spectral reflectance in the red and NIR regions, respectively. A true color image comprising Bands 2, 3, and 4 of the Operational Land Imager (OLI) on the Landsat 8 satellite is also shown in Figure 7a for comparison. Figure 7c shows the NDVI derived from Bands 4 and 5 of the Landsat 8 OLI; this value was acquired eight days before the acquisition of the RISING-2 HPT images, which were corrected similarly using the DOS method. Although the spatial resolution of the RISING-2 HPT in this scene is 7.2 m and approximately four times higher than 30-m spatial resolution of the Landsat 8 OLI, the NDVI values in Figure 7b are in good agreement with those in Figure 7c. This image indicates that the multispectral image analysis was implemented successfully, and that the RISING-2 HPT was calibrated accurately during the preflight tests.