# A SIFT-Based DEM Extraction Approach Using GEOEYE-1 Satellite Stereo Pairs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Ground to Image

#### 2.2. Cascading

#### 2.3. SIFT Feature Point Detection and Matching

#### 2.4. Outlier Detection

#### 2.5. Image to Ground

#### 2.6. Evaluation Criteria

## 3. Case Study

^{®}IMAGINE software (Leica Geosystems, Atlanta, GA, USA) using the same Geoeye-1 stereo pair and a 5-m commercial DEM produced from aerial photography stereo pairs were also compared with the ground truth measurements. Prior to comparison, a single GCP within the study site is used to compensate for shift terms and achieve accurate absolute geopositioning (Fraser and Ravanbakhsh, 2009; Fraser and Yamakawa, 2003).

## 4. Results and Discussion

^{−4}, the RANSAC method has little or no effect on the filtering of feature points, assuming all of them are homologous. Nevertheless, the results display several outliers that cause irregular spike-like artefacts in the DEM (Figure 10a). For values of distance threshold between 10

^{−5}and 10

^{−7}, the number of candidate homologous feature points drops fast down to 30% of the unique features originally detected in the stereo pair. As $t$ decreases more, points become irregularly spaced (Figure 10b), and the produced DEM (Figure 10c) becomes less detailed, showing steep surfaces as a result of the linear interpolation used to produce it. At these values of threshold $t$, RANSAC acts as an overtuned high-pass filter eliminating true information. Therefore, a good approximation for the optimum $t$ threshold is 10

^{‒6}, which produces an acceptable average spacing irregularity of 1.55 m (Figure 9b) and a smooth DEM with a high level of detail and no apparent outliers (Figure 10b). For this value, the homologous detected pixels are 37,000, representing 3.7% of the 1-M pixel sample.

## 5. Conclusions

^{®}, which served as a benchmark for this study (Table 1). The results from the statistical analysis (RMSE and error values) undertaken to investigate the accuracy of the 1.5-m DEM by comparing the Total Station elevations at 360 points with on-ground field survey elevations indicate that the 1.5-m satellite stereo pair DEM adequately represents the ground elevations for any detailed environmental modeling application.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Example of cascading of a rectangular image of size $Q\times Q$ pixels broken down in tiles of size $p\times p$ that overlap by $t\times p$.

**Figure 3.**RANdom SAmple Consensus (RANSAC) algorithm for estimating homologous coordinate sets of corresponding points in a stereo image pair.

**Figure 4.**Members of a sample Geoeye-1 stereo pair from Almirida watershed. Images are shown at original positioning, and dashed lines show their respective location after rough georeferencing with their Rational Function Models (RFMs) (

**top pair**). A fast image matching is used to determine homologous features (

**bottom pair**). Axes units in pair (

**a**) in m of the Greek National Grid coordinate system. Axes units in pair (

**b**) in pixels.

**Figure 5.**Resulting iterations and computational processing unit (CPU) time [s] from the cascading of rectangular tiles with side $p$ ranging from 30 to 250 pixels and overlap of 30 to 90%.

**Figure 6.**Number of resulting total, unique, and tentative feature matches (logarithmic scale) from cascading of rectangular tiles with side $p$ ranging from 30 to 250 pixels and an overlap of 30% to 90%.

**Figure 7.**Resulting first, second, and third quartiles and average spacing irregularity of point matches from cascading of rectangular tiles with side $p$ ranging from 30 to 250 pixels and overlap of 30% to 90%.

**Figure 8.**Homologous matches produced by iterative Scale-Invariant Feature Transform (SIFT) on tile sides of (

**a**) 250 pixels, (

**b**) 130 pixels, and (

**c**) −50 pixels at 70% tile overlap and threshold $t$ = 10

^{−6}the red band of stereo pair members (one pear per row). Axes units in m of the Greek National Grid coordinate system.

**Figure 9.**(

**a**) Number of resulting unique and tentative feature matches and (

**b**) homologous feature spacing statistics for different values of RANSAC distance threshold $t$ on a logarithmic scale.

**Figure 10.**DEMs created for RANSAC distance thresholds $t$ equal to (

**a**) 10

^{−2}, (

**b**) 10

^{−6}, and (

**c**) 10

^{−10}.

**Figure 11.**(

**a**) Part of the Geoeye-1 sample used in the study and (

**b**) visual comparison of produced 1.5-m Digital Elevation Models (DEM) with (

**d**) reference 2-m DEM produced from the Geoeye-1 using ERDAS

^{®}and (

**f**) 5-m commercial DEM from aerial photo stereo pair, and difference between the produced 1.5-m DEM and the reference 2-m DEM (

**c**), as well as the 5-m commercial DEM (

**e**). Red arrows denote areas of interest for comparison.

**Table 1.**Statistics and goodness of fit metrics of the two reference DEMs (5-m and 2-m resolution) and the newly produced DEM (1.5-m resolution).

5-m DEM | 2-m DEM | 1.5-m DEM | |
---|---|---|---|

Min value [m] | 19.02 | 26.72 | 22.56 |

Max value [m] | 93.95 | 96.86 | 90.36 |

Mean value [m] | 53.00 | 58.69 | 53.26 |

St. dev. [m] | 19.04 | 17.85 | 17.70 |

Min difference from 1.5 m DEM [m] | −14.05 | −14.50 | - |

Max difference from 1.5 m DEM [m] | 9.03 | 4.89 | - |

Mean difference from 1.5 DEM [m] | −1.57 | −5.42 | - |

St. dev. of difference from 1.5 DEM [m] | 3.24 | 2.53 | |

$\overline{\mathit{e}}$[m] from Total Station field measurements | −1.56 | 0.59 | −0.45 |

St. dev. of$\overline{\mathit{e}}$[m] from Total Station | 1.18 | 1.02 | 1.00 |

$\overline{{\mathit{e}}_{\mathit{r}}}$[%] from the Total Station | −2.65% | 0.83% | −0.86% |

St. dev. of$\overline{{\mathit{e}}_{\mathit{r}}}$[%] from Total Station | 2.02% | 1.65% | 1.64% |

RMSE from the Total Station | 1.96 | 1.18 | 1.10 |

R^{2} from the Total Station | 0.9911 | 0.9948 | 0.9938 |

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**MDPI and ACS Style**

Daliakopoulos, I.N.; Tsanis, I.K.
A SIFT-Based DEM Extraction Approach Using GEOEYE-1 Satellite Stereo Pairs. *Sensors* **2019**, *19*, 1123.
https://doi.org/10.3390/s19051123

**AMA Style**

Daliakopoulos IN, Tsanis IK.
A SIFT-Based DEM Extraction Approach Using GEOEYE-1 Satellite Stereo Pairs. *Sensors*. 2019; 19(5):1123.
https://doi.org/10.3390/s19051123

**Chicago/Turabian Style**

Daliakopoulos, Ioannis N., and Ioannis K. Tsanis.
2019. "A SIFT-Based DEM Extraction Approach Using GEOEYE-1 Satellite Stereo Pairs" *Sensors* 19, no. 5: 1123.
https://doi.org/10.3390/s19051123