Elimination and simulation of Terrain Effects on Remote Sensing images using DTM

Elimination and simulation of Terrain Effects on Remote Sensing images using DTM

Weiqing Zhang,Runsheng Wang
Center for Remote Sensing in Geology
29 College Road, Beijing, 100083, China

Abstract
The paper presents an approach of using three parameters (slope, aspect and viewfield factor) and a shadow map derived from DTM to produce the apparent reflectance image from the satellite image at visible and reflecting-infrared spectrum, then reconstruct the simulated image at any given sunshine direction based on it. The results of comparative analyses reveal that the influence of incident angle, slope, viewfield factor on the satellite image is decreasing sequently. In this approach to produce the apparent reflectance image, only three suppositions are made in advance: 1. the atmosphere is homogeneous over the entire image. 2. the sunlight is parallel. 3. the intensity of scattered space light is same at all directions and in any places. The only limit to this approach is the data accuracy of DTM.

Introduction
Remotely sensed data, as well as many geodata, are obtained from space about the earth surface, therefore are influenced by the terrain undulation. The original satellite image at visible and reflecting-infrared spectrum contains two kinds of information: the terrain characteristics and the surface reflectance. The terrain effect on the image, for some applications such as target discrimination and classification, is a kind of noise and should be gotten rid of; while for others such as visual interpretation of geological structures, is some useful information which gives the interpreter the perspective view. images usually southeast-illuminated (in the northern hemisphere) make the northeast—southeast structure emphasized and the northwest—southeast structure depressed. It will be very useful for geological structural researchers if we can simulate images at different azimuthes and elevation angles of the sunlight to enhance different directions of structures.

Kiyonari Fukue (1981) introduced a function exp(-nx) in his attempt to remove the shadow on the Landsat image which would be discussed later. Li Xianhua (1986) selected the special pixels, such as the one without the illumination of sunlight and space light, to computer the parameters used to correct the terrain effect one remotely sensed images. As a result the results were influence heavily by the pixels selected or the human factor. Here we theoretically developed two formulations to calculate the apparent reflectance of pixels within and outside the shadow using parameters computed by statistical processing, with little human influence.

Factor Analysis
The radiance a pixels received can be divided into sunlight and space light. The intensity of the sunlight is much higher than the space light. The major terrain factors influencing satellite images are shadow, slope, aspect and viewfield factor, all of which can be derived from Digital Terrain Model (DTM). The shadow map depicts the pixels that the sunlight can not reach. It is obvious that in a satellite image the intensity values of the pixels in shadow which are only due to the space light are much lower than those out of shadow with contributions from both sunlight and space light, and those two pixel sets should be processed separately. The terrain slope determines the real area of a pixel surface, because the areas of the pixel projection on the horizontal plane are the same. The higher is the slope, the more is the real area, as a result, the higher is the pixel value on the image if the amount of radiance a unit receives is the same. The incident sunlight angle of a pixel is the angle between the pixel normal and the sunlight direction. The less is the incident angle, the more sunlight the pixel receives.

While the sunlight direction is the same over the entire image because the sunlight is considered to be parallel, the pixel normal is a function of the slope and aspect of the pixel. The incident angle is irrelevant to the space light. In opposite, the viewfield factor influences only the space light. The viewfield factor is defined as the ratio of the space light a actural pixel receives to that a pixel in horizontal plane receives supposing the intensity of scattered space light is same at all directions and in any spaces, the viewfield factor is the ratio of the solid angle at the pixel over that on the plane. Because the computation of the solid angle is rather complex, it is computed actually in simplication by the product of the included angles of the earth surface in south—north and east—west directions.

Based on the above analysis, an approach is designed to remove the terrain effects on the satellite image to produce the apparent reflectance image. In the inverse process, the terrain effects of different sunlight directions are added to the apparent reflectance image to simulate the real satellite image. The influence of the incident angle, slope and viewfield factor can be analysized individually when we add each of the parameters into the constant reflectance image which is artificially made to produce the simulated images and comparing these outputs.

The real ground objects are neither diffuse reflector nor mirror reflector. The reflectance varies with the observing direction. It can be expressed as: R = F * R . R. is the reflectance measured under certain standard conditions. Function F describes the reflecting property of the object which varies with different qualities, shapes, surface roughness etc. of the object. Kiyonari Fukue [1986] used exp(-nx) to approximate the function F. Where x is the included angle between the observing direction and the reflecting light and n is a parameter. For diffuse reflector, n – 0; for mirror reflector, n = ¥. It is a good approximation for a single object. But for different objects, n varies. It is not reasonable to assume that all the pixels on the satellite image have the same n value. Because the satellite image is recorded under certain sunlight and observation direction, we can only get the reflectance under that sunlight and observation direction from the image. Therefore it is unrealistic and senseless to separate the function F and R. from reflectance R by setting the same reflectance property to all the pixels of the image. in the following discussion, all the reflectances refer are the ones under certain sunlight and observation direction, R.

Method
We know that the pixel value N on the satellite image is quantified from the spectral energy E received by the sensor:

N = a * E + b [1]

a and b are constants.

The spectral energy E can be divided into three parts: 1) energy of the space light scattered directly into the sensor, E_A. 2) energy of the space light reflected from the ground surface and coming into the sensor, E_S 3) energy of the sunlight reflected from the round surface and coming into the sensor, E_D. It can be expressed as:

E = E_A+E_S+E_D [2]

Let us define:
r' : ground reflectance
L_S: energy of space light received by pixels on horizontal plane
L_D: energy of sunlight received by pixels on horizontal plane
T : atmosphere transmissivity
q : ground slope
n : ground aspect
G: ground viewfield factor
a: sun azimuth
b: sun elevation
j: incident angle of sunlight toward the ground pixel

Supposing that the atmosphere is homogenuous and the sunlight is parallel, the values of T, E_A, a, b, L_S, L_D are contents for all pixels in the image extent. Also we have:

if the intensity of scattered space light is same at all directions and in any places, them:

Where D_S is a constant unknown, same for all pixels; N, G, cosq are known parameters, varying with the pixels; r is a variable unknown, varying with the pixel. As a result, Ds can be computed by the minimum square-root criterion using the pixels in the shadow. From equation [6] for the pixels out of the shadow we have;

Where D_s, N, q, j and G are all known. SD is a constant unknown, r is a variable unknown, varying with the pixel. So S_D can be calculated by the minimum square-root criterion using the pixels out of the shadow. Now that parameters D_s and S_D are known, the apparent reflectance map r can be computed:

In order to simulate the images at different sunlight directions, it is necessary to locate the shadow area at that direction at first, then the simulated image can be calculated using equation [10] for the pixels in the shadow and equation [6] for those out of the shadow. If we let r = 1, q = 0, G = 1 for all pixels and set the incident angle as 900 if it is greater than 900, an image can be produced using equation [6], meaning that the single influence of incident angle is added onto the constant reflectance image in which the reflectance of all pixels are the same such as 1. In this way, the influence of other factors and combinations of factors can be added onto the constant reflectance image separately to produce the simulated images corresponding which are the comparative analysis basis of the influence of the single factor and factor combination.

Dicussion of test result
PHOTO 2 is the apparent reflectance map computed out using equations [12] and [13] from PHOTO 1, a LANDSAT MSS image (band 5). The terrain effects have been removed on PHOTO 2. Two reflecting features on PHOTO 1, the higher intensity value in upper part than in lower part and the high reflectance of the river, are represented on PHOTO 2.

PHOTO 3 is the artificially simulated image from PHOTO 2 using equations [6] and [10], the sunlight azimuth and elevation of which are 450 and 300. The southeast northwest structures on PHOTO 3 are obviously enhanced.

PHOTO 4 includes four image produced by adding different kinds of terrain effects onto the constant reflectance image. The upper left represent the influence of a single factor, the incident angle; and the upper right contains the terrain effect of two kinds, the incident angle and the ground slope. The lower left is the result influenced by the incident angle and the ground viewfield factor, while the lower right is produced by adding four factors, the shadow, the incident angle, the ground slope and the ground viewfield factor all together onto the constant reflectance image.

The similarity between the upper left and the lower right demonstrates that the in fluence of the incident angle on the satellite image is the biggest. Because the upper right is more similar to the lower right than the lower left, it is considered that the influence of the ground slope is bigger then that of the ground view field factor. The in fluencies the shadow is virtually included in the incident angle affect, because most pixels in the shadow are shaded by the neighboring pixel, the incident angle of which are no les, then 900 . Only small number of pixels in the shadow are shaded by the distant pixel.

The above results can be explained theoretically. It is clear that the intensity of sunlight is much higher than that of the space light. The ground view field only influences the space light, so its effect is the smallest. Although both the incident angle and the ground slope influence the ground slope influence the sunlight, the sunlight, the dynamic range of cosq is from 0 to 1, much higher that of cosq, because the ground slope is limited. As a result, the effect of the incident angle is the biggest.

Conclusion
The element of the above approach to compute the apparent reflectance is to calculate the light parameters S_D and D_s by using the terrain parameters and intensity value of the satellite image to process statistically the reflectance variations, than to compute the apparent reflectance of each pixel. The whole process is completed automatically by the computer, without the human effect. The three hypotheses about homogeneous atmosphere, parallel sunlight and diffusing space light are rather reasonable. The terrain effects on the satellite image can be eliminated consequently.

Because the apparent reflectance map is the one under certain sunlight direction, all simulated images of different sunlight directions are produced on the hypothesis that the apparent reflectances of different sunlight directions are the same. These images can enhance the corresponding information.

Through the comparative analysis of the influences of individual factors, it is found that the incident angle contributes the most part of the entire effect, Using only the incident angle factor to simulate the whole terrain effect for the generation of artificial relief on some images can get reasonable results and be time- saving.

Due to the DTM accuracy, the test results are far from ideal. DTMs with the grid size similar to or smaller than the pixel size of the satellite image are highly recommended.

Reference
Kiyonari Fukue: 7th International Symposium áá Machine Processing of Remotely Sensed Dateññ , June 23-26, 1981
Li Xianhua: Correction of Terrain Effect on Remotely Sensed information, Journal of Survey and Mapping, Voll5-2, 1986.5