Geometric Corrections

CHAPTER 2 LITERATURE REVIEW

2.7 Remote Sensing and Its Roles in Landslide Hazard Assessment

2.7.5 Image Pre-processing

2.7.5.1 Geometric Corrections

Images produced from remote sensing satellite contain distortions or geometric errors. They need to be freed from such errors to allow extraction any measurements from corrected images. According to Lillesand, et al. [166], the distortions may come from orbit perturbation (e.g. variation of satellite altitude, altitude and velocity due to inhomogeneous land mass and solar pressure), earth curvature, and relief displacement. Image distortions can be either systematic or random/non-systematic.

The sources of both distortions are many. An example of systematic distortion is the distortion due to earth‘s rotation. While Landsat scanning the earth from first to last line at approximately 28 seconds, the target beneath the satellite has move eastward due to earth‘s rotation. This causes 185 km x 185 km Landsat footprint on the ground become a rhombus shape not square. Such error is usually fixed before the data delivered to users. Random distortions are usually related to orbit perturbation causing the platform unstable so that the altitude (height) and attitude (stability from movement/rotation in x, y, and z directions known as pitching, rolling and yawing) of the platform are disturbed.

The detail procedure of removing random geometric distortion can be found in most of remote sensing image processing literatures such as in Lillesand, et al. [166], Gao [165], Gibson and Power [94], and Unger Holtz [167]. Geometric distortions can be removed by means of rectification process. In doing so, a set of ground control points (GCPs) is required. GCPs can be a georeferenced/corrected map or a set of ground control points whose coordinates are known in a desired (usually local)

reference system. A GCP is required to be easy to find/recognize on both uncorrected image and corrected image. Illustration of rectification process is shown in Fig. 2.9.

Rectification process requires collection of the same number and position of GCPs from both images to tie down uncorrected image. It results in a list of coordinates known points extracted from georeferenced image and screen (pixel) coordinates of uncorrected image. Using a polynomial equation, each pixel on uncorrected image is transformed to a position in a real world coordinate system (such as Latitude/Longitude or Easting/Northing) resulting in a new georeferenced image.

A polynomial function is a mathematical equation that can be used to transform uncorrected image to georeferenced image coordinate system. During transformation, uncorrected image undergoes translation, rotation, and scaling. Some image processing softwares provide first order (linear), second order (quadratic), and third order (cubic) polynomial function for rectification process. The higher the polynomial orders the more complex the equation relating both parameters. The following equation is a first order polynomial equation relating coordinates on uncorrected image (xu, yu) and those on georeferenced/corrected images (x, y) as explained in Gibson and Power [94]:

Fig. 2.9 Geometric correction procedures

Corrected image Uncorrected image

P1(x1, y1) P2(x₂, y₂)

…

… P6(x₆, y₆) P‘1(xu1, y_u1)

P‘2(xu2, y_u2)

…

… P‘6(xu6, y_u6)

Polynomial function

Source:

Gibson and Power [94]

y a x a a

x_u  ₀  ₁  ₂ y b x b b

y_u  ₀  ₁  ₂

(2.10) First order polynomial only performs translation of uncorrected image to a desired reference system. Second order polynomial links both images using quadratic form, a more complicated polynomial equation, as follows:

2 5 2 4 3 2 1

0 c x c y c xy c x c y

c

x_u      

2 5 2 4 3

2 1

0 d x d y d xy d x d y

d

y_u      

(2.11) To solve Equation 2.10, 3 GCPs are required since it contains 6 parameters (unknown). Meanwhile, 6 GCPs are required to solve Equation 2.11 since it contains 12 parameters.

The quality of rectification result is expressed in RMSE (root mean square error) as explained by Gao [165]. The error is the different between the coordinates of georeferenced image and those resulted from the transformation process. For a given point, it has RMSE values in both directions, Northing and Easting. The magnitude of RMSE of both directions is not necessarily the same. The overall accuracy of transformation equals to the total of RMSE of both directions. Equation 2.12, 2.13, and 2.14 in the following are RMSE of Northing, Easting, and the final accuracy.

 

²

1 1

2 1 ˆ

1

 









 ⁿ

i

i i n

i Ei

E E E

n

RMSE n 

(2.12)

 

²

1 1

2 1 ˆ

1

 









 ⁿ

i

i i n

i Ni

N N N

n

RMSE n 

(2.13)

 







 ⁿ

i

Ei Ni

EN n

RMSE

1

2

1 2 

(2.14) In general, the first two equations indicate the different between the known coordinates from corrected image and the predicted coordinates on uncorrected image

using polynomial transformation. The last equation indicates the total error in both directions. Gao [165] reported that there is no exact standard regarding the acceptable value of overall RMSE. People usually use rule of thumb or conventional wisdom stating that the overall RMSE should not be greater than one pixel size in value.

Therefore, for Landsat satellite image with 30 m resolution or SPOT 5 with 10 meter resolution, the overall RMSE should be below 30 m and 10 m accordingly.

There are factors affecting the accuracy of rectification/geometric correction.

Gibson and Power [94] identified two factors. The first is the selection of GCPs.

GCPs should be easy to identify on both images and do not have possibility to move such as coastal line and river bends, otherwise it may result in a large RMSE. In addition, a sufficient number of GCPs which are well/evenly distributed over the image are required. Having GCPs clustered on a particular part of an image, e.g. east part or west part, will lead to an inaccurate rectification result since the remaining parts of an image are not well tied down.

Illustration of the effect of the number and the distribution of GCPs involved in rectification process on the accuracy of rectification is shown in Fig. 2.10 which is expressed in the changing grid pattern. The grid pattern shows how the rectified image will be distorted. Fig. 2.9a shows rectification result using only 4 GCPs concentrated on upper left corner of the image (shown circled). Grid boxes seem tilted to the east. Adding 4 more GCPs on the upper part of the image, as shown in Fig. 2.9b, causes the lower part extremely distorted westward. Since GCPs on left corner is denser than those on right, the remaining part of the image is dragged to the lower left, showing the expected rectified image. Addition of 2 more GCPs on lower left of the image, shown in Fig. 2.9c, appears to repair the distortion at lower left part left by previous experiment. The lower right part of the image is still distorted. Three more GCPs are added forming a stretch of GCPs from lower left to lower right (Fig.

2.9d). This addition repairs the distortion on the lower right. More GCPs are defined on middle left and right (Fig. 2.9e). The total GCPs are 24. Grid lines seem to have properly aligned. However, center part of the images still experience distortion even though it cannot be seen by human eyes. Finally, addition of 33 more GCPs located mostly on the center part and its surroundings refines the rectification result. These

rectification sequences show visually how the number of GCPs and its distribution affect the result. The actual accuracy is indicated by RMSE.

(a) 4 GCPs (b) 8 GCPs (c) 10 GCPs

(d) 13 GCPs (e) 24 GCPs (f) 57 GCPs

Fig. 2.10 Pattern of distortion due to the number and distribution of GCPs Gao [165] added other factors affecting the accuracy of rectification. The accuracy of the corrected map, hence the picked GCPs, is an important issue. One has to make sure about the accuracy of the map before using. A set of control points gained from GPS (Global Positioning System) survey would provide more accurate GCPs than those picked ups from the georeferenced topographic map. The last factor is the order of polynomial transformation. It is said that by applying high order of polynomial transformation will result in more accurate rectification result.