Image Processing – Correction

Radiometric Correction

As any image involves radiometric errors as well as geometric errors, these errors should be corrected. Radiometric correction is to avoid radiometric errors or distortions, while geometric correction is to remove geometric distortion.

When the emitted or reflected electro-magnetic energy is observed by a sensor on board an aircraft or spacecraft, the observed energy does not coincide with the energy emitted or reflected from the same object observed from a short distance. This is due to the sun’s azimuth and elevation, atmospheric conditions such as fog or aerosols, sensor’s response etc. which influence the observed energy. Therefore, in order to obtain the real irradiance or reflectance, those radiometric distortions must be corrected.

Radiometric correction is classified into the following three types

1. Radiometric correction of effects due to sensor sensitivity


In the case of optical sensors, with the use of a lens, a fringe area in the corners will be darker as compared with the central area. This is called vignetting. Vignetting can be expressed by cosn θ where θ is the angle of a ray with respect to the optical axis. n is dependent on the lens characteristics, though n is usually taken as 4. In the case of electro-optical sensors, measured calibration data between irradiance and the sensor output signal can be used for radiometric correction.

2. Radiometric correction for sun angle and topography


A). Sun spot


The solar radiation will be reflected diffusely onto the ground surface, which results in lighter areas in an image. It is called a sunspot. The sunspot together with vignetting effects can be corrected by estimating a shading curve which is determined by Fourier analysis to extract a low-frequency component.

B).Shading

The shading effect due to topographic relief can be corrected using the angle between the solar radiation direction and the normal vector to the ground surface.

3. Atmospheric correction


The solar radiation is absorbed or scattered by the atmosphere during transmission to the ground surface, while the reflected or emitted radiation from the target is also absorbed or scattered by the atmosphere before it reaches a sensor. The ground surface receives not only direct solar radiation but also skylight, or scattered radiation from the atmosphere. A sensor will receive not only the direct reflected or emitted radiation from a target but also the scattered radiation from a target and the scattered radiation from the atmosphere, which is called path radiance. Atmospheric correction is used to remove these effects(see Figure)

The atmospheric correction method is classified into the method using the radiative transfer equation, the method using ground truth data, and other methods.

a). The method using the radiative transfer equation


An approximate solution is usually determined for the radiative transfer equation. For atmospheric correction, aerosol density in the visible and near-infrared region and water vapor density in the thermal infrared region should be estimated. Because these values cannot be determined from image data, a rigorous solution cannot be used.

b). The method with ground truth data


At the time of data acquisition, those targets with known or measured reflectance will be identified in the image. Atmospheric correction can be made by a comparison between the known value of the target and the image data (output signal). However, the method can only be applied to the specific site with targets or a specific season.

c). Other method


A special sensor to measure aerosol density or water vapor density is utilized together with an imaging sensor for atmospheric correction. For example, the NOAA satellite has not only an imaging sensor of AVHRR (Advanced Very high-Resolution Radiometer) but also HIRS (High-Resolution Infrared Radiometer Sounder) for atmospheric correction.

Geometric Distortions of the Image

Geometric distortion is an error on an image, between the actual image coordinates and the ideal image coordinates which would be projected theoretically with an ideal sensor and under ideal conditions.

Geometric distortions are classified into internal distortion resulting from the geometry of the sensor, and external distortions resulting from the attitude of the sensor or the shape of the object.

Figure 9.3.1  schematically shows examples of internal distortions,

while Figure 9.3.2 shows examples of external distortions.

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