# A Method to Determine the Maximum Side Perspective of Satellite with the Constraints of Mapping Accuracy

TL;DR: A method to determine the maximum side perspective with map precision constraints, and set up a conversion relationship among satellite side view, DEM error and image point error is put forward.

Abstract: In order to shorten the revisit period, and improve the efficiency of imaging, currently, all the in orbit high resolution remote sensing satellites adopt side-view imaging technology. When satellites imaging with a side perspective, it would inevitably cause the degradation of image quality, like spatial resolution reduction, image deformation incensement, and the reduction of positioning accuracy. In addition, with the increase of the side perspective, the error of DEM data will be amplified in the process of ortho-rectification, which, thus, will bring bigger error for image mapping accuracy. To address this problem, embarked from the impact of side view and DEM precision on image point error, this paper used Quick bird image data of the same area but different side perspectives, and simulate the impacts of different DEM elevation error on different side view image. At last we put forward a method to determine the maximum side perspective with map precision constraints, and set up a conversion relationship among satellite side view, DEM error and image point error. Finally, the paper combines the errors of 1:50000 DEM, ASTERGDEM and the requirement of ortho-image drawing, discusses and gives the values of maximum side perspective in the mountains and plains.

## Summary (2 min read)

### 1 Introduction

- Along with the continuous improvement of remote sensing satellites’ spatial resolution, it also brought adverse effects of the image width and image acquisition efficiency reduction.
- As is well-known, when the satellites side-view imaging, the observation path is increased, the relative geometric relationship between satellite and ground objects is changed, which caused the degeneration of image quality [1] (such as the spatial resolution reduced, image deformation increase, etc.).
- The error of satellite orbit and attitude is decided by the control accuracy of the satellite itself and the in-orbit state, which cannot be changed by the average user.
- It can be seen from the above error analysis of ortho-rectification, in general case, the factors to be considered most by users are side perspective and DEM errors.
- Many scholars have carried out some research work about the effects on image quality degradation and ortho-rectification precision caused by side perspective, and the effects on ortho-rectification precision caused by DEM errors.

### 2.1 Experimental DATA

- The experimental area is the northern part of Beijing, including plain and mountain.
- Experimental data are multispectral image collected by using high-resolution Quickbird satellite in 2002 to 2012.
- With 2.44 m resolution, side perspective spanning from 5.6°to 43.7°ten different angles in total.
- Image side perspective spanned broadly, evenly distributed, specifically details can be seen in the table below.

### 2.2 Experimental Methods

- According to the principle of photogrammetry, the comparation between image point error caused by the side perspective and imaginary horizontal photograph as Figure 1(a) shows.
- After two photograph overlapping along isocon line，the position of (m) in the horizontal photograph is m, obviously mm0 is the tilt error.
- During the process of ortho-rectification, image points error will be affected by side perspective and relief at the same time.
- In the existing research results, different influence factors are often analyzed independently, which ignores the mutual influence and internal relations of different factors and is not real and comprehensive enough to reflect the objective situation of data.
- Input the satellite images and their corresponding parameters, original DEM data into RPC model, when the side perspective is given.

### 3 Results and Discussion

- Figure 3 shows that using experimental data with different side perspectives, the paper calculated the influence law distribution on ortho-rectification accuracy caused by DEM error.
- From the numerical distribution and the fitting results in figure 3, it can be seen that under the same side perspective, pixel positioning errors increase with the increasement of DEM elevation values；the larger the side perspective is, the greater the pixel positioning is.
- From numerical distribution and fitting results in the figure 5, it can be seen that it is also a linear relationship between the side perspective and fitting line slope.
- Therefore, the relationship between fitting line slope of DEM error and ortho-rectification and satellite side perspective can be considered linear.
- 10000 topographic mapping requirements, the error of image calibration is no more than 5m on plains and hilly lands,7.5m on mountainous and alpine areas, also known as Corresponding 1.

### 5 Conclusions

- This paper established the quantitative conversion relationship among satellite side perspective, DEM error，ortho-rectification，and image rectification, proposed a method to determine the maximum imaging side perspective with map precision constraints, and provided guidance on data selection and processing.
- When known DEM data accuracy and the accuracy that ortho-rectification expected to achieve, the maximum side perspective of the satellite can be calculated to meet those conditions.
- On the other hand, when the existing satellite data side perspective is known, the minimum accuracy of DEM data can be calculated to achieve the expected orthorectification precision.
- Because the model in this article is obtained by the analysis of real data, thus, the authenticity of the results is guaranteed, and the conclusion is also in line with the actual situation.
- In addition, the ideas and methods adopted by this paper are also applicable to the analysis and study of other sensors with the same kind.

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##### References

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### "A Method to Determine the Maximum S..." refers background or methods in this paper

...According to the error analysis of satellite imagery ortho-rectification model, the main factors affect the accuracy of ortho-rectification are as follows: orthorectification model error, satellite orbital attitude error, control point accuracy, DEM error, etc[3]....

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...The conclusions indicate that with increment of the side perspective, the image ortho-rectification accuracy will gradually decline, and the decrease amplitude is quite obvious[3]....

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2 citations

### "A Method to Determine the Maximum S..." refers background in this paper

...The results show that the ortho-rectification accuracy is higher with small basic grid and high-precision DEM data[6]....

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2 citations

### "A Method to Determine the Maximum S..." refers background in this paper

...It is also why many scholars assume that the variables are independent in the derivation of the law of ortho-rectification error[10][11]....

[...]

1 citations

### "A Method to Determine the Maximum S..." refers background in this paper

...It is also why many scholars assume that the variables are independent in the derivation of the law of ortho-rectification error[10][11]....

[...]

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### Additional excerpts

...remote sensing image geometry processing model[5]....

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