# Landform Monitoring and Warning Framework Based on Time Series Modeling of Topographic Databases

## Abstract

**:**

## 1. Introduction

**Figure 1.**Direct datum-transformation of two different Digital Terrain Model (DTM) databases showing topographic and morphologic inconsistencies, depicted by arrows, which can be resolved only by rigorous local adjustment.

## 2. Problem Definition

**Figure 2.**An area near Kashmir, Pakistan, experienced local landslides in the year 2005: images are made from near-infrared, red, and green light, so vegetation is depicted in red, water in blue, and the effect of the landslide in white or light gray (source: NASA images by Robert Simmon, based on ASTER data).

## 3. Methodology

- Global pre-modeling, i.e., registration: relying solely on the databases’ coordinate system might lead to an erroneous comparison quantification. While no implicit information on the spatial correspondence among the topographic databases is present, choosing a common schema (spatial framework) is crucial for non-biased modeling. Registration provides a rough quantification of the modeling discrepancy artifacts. A preliminary registration, or approximate geographic correspondence, of the databases is therefore vital. It is achieved by relying on sets of unique homologous features or objects (geomorphologies) that are identified in the modeled databases. For such a purpose, novel morphologic maxima point identification is developed. The approximate correspondence, which can be expressed by spatial translation, is extracted by constraining a rigid affine spatial transformation-model to selected unique homologous geomorphologic-features, which represent the same real-world object present in the modeled databases. This is a crucial stage when such modeling takes place, more distinctively, when spatial geometric matching process is at hand (e.g., [22,23]). The rigid affine spatial transformation-model is achieved by introducing a constrained ranking of the forward Hausdorff distance mechanism ([24,25]); originally used mainly for image registration, this algorithm was found to facilitate the discrete data representation and was modified to introduce specific constraints to ensure correct solution convergence.
- Local matching: after registration is achieved, a more precise and localized matching of databases can take place, which aspires to locally fine-tune the global registration quantification extracted. Matching of spatially continuous entities is usually based on geometric or conflation schema specifications analyses, while algorithms implemented are mainly dependent on the geometric types of the objects needed to be matched, their topological relations, their data volume and the semantics of attributes [26]. A robust and qualitative matching process suitable for the data characteristics present is the Iterative Closest Point (ICP) algorithm [27]. The ICP algorithm is designed for matching 2D/3D curves and rigid surfaces using nearest neighbor criteria. The implementation carried out here utilizes an iterative Least Squares Matching (LSM) process [28], with specific geometric constraints and optimizations tailored for this task [29]; these are intended to achieve a faster convergence, but mainly to overcome constraints and characteristics the non-rigid data impose (landform representation). The a priori corresponding registration value extracted on the global, i.e., higher, working-level is used for initialization of this process. By dividing the entire mutual coverage area into homologous separate frames and implementing the ICP matching process on each of these frames separately, better localized modeling—and hence monitoring—is feasible. This enables more accurate categorization of local phenomena instead of an ambiguous global one, such as the outcome of the footprint effect related to GPS monitoring network.
- Analysis and comparison of time-series databases: the outcome of the local ICP matching process leads to the establishment of a mutual-modeling structure, similar to a 2D matrix. Each cell in this matrix stores the accurate local spatial matching rigid-model quantification (i.e., parameters) that corresponds to each of the local mutual frames matched. By inspecting these quantifications—statistically and with respect to their surroundings—one can identify the deformations and distortions the local landform had experienced. Since the artifact discrepancies are known and modeled, the actual geomorphologic changes that occurred can be precisely and more easily modeled and understood.

#### 3.1. Global Pre-Modeling

#### 3.1.1. Identification of Unique Geomorphologic Entities

- The computation of four best curve-fitting (2D space) orthogonal second-degree polynomials, one for each principal orientation, from all DTM points that exist in the data. Since resolution affect the topographic representation, a sensitivity analysis was done, which showed that the number of points required for defining the polynomial has to be at least 200 m for each principal orientation; for example, in a 50 m grid, 4 points are needed. The assumption is that such coverage area ascertains the identification of local maxima in the topography (see Figure 5);
- The calculation of the integral (area) of the four best-fitting polynomials in the z direction relative to the height of the farthest point in the polynomial with respect to the examined DTM point;
- Statistical thresholds tests of polynomials’ coefficients and integral values to examine the polynomials’ topological behavior (e.g., ascending or descending, magnitude with respect to surroundings);
- Local clustering via distance-measure on all previous identified maxima points (depicted as red points in Figure 5) aimed at finding an area-of-interest; distance value used for clustering equals to the grid interval value;
- Local bi-directional interpolation within each cluster (depicted in Figure 5) to ensure the precise calculation of the highest topographic location (depicted as blue point), thus achieving planimetric sub-resolution accuracy.

**Figure 5.**Clustering (dashed polygon) and local interpolation (depicted with dx and dy) around cluster-maxima for the identification of the precise position of interest point (blue point).

#### 3.1.2. Registration

^{th}ranked point of B, rather than the largest ranked one, as suggested in Equation (2).

^{th}denotes the ranked value in the set of existing distances, while ranking is achieved by the perspective values of this distance. Thus, the “best matching” is chosen by identifying the subset of the model that minimizes the direct Hausdorff distance (h

_{s}).

#### 3.2. Local Matching

**Figure 6.**Schematic explanation of least squares target function minimization via perpendicularity constraints in grid-domain, ensuring closest point.

**Figure 7.**Schematic explanation of least squares target function minimization via perpendicularity constraints in TIN triangular-domain, ensuring closest point.

#### 3.3. Analysis and Comparison

**Figure 8.**Topographic databases with times i and i + 1 (front and background). Each matrix-cell {j} in i stores a set of corresponding transformation parameter that best describe the relative spatial geometry of the mutual homologous topographic frames i + 1 that were matched in the Iterative Closest Point (ICP) process.

## 4. Experimental Results

#### 4.1. Validation

#### 4.1.1. Interest Point Identification

**Figure 9.**3D (

**up**) and 2D (

**bottom**) visualization of interest point identification superimposed on the topography.

**Figure 10.**Height contour representation of the topography superimposed with the interest points identified for each database; corresponding interest points are shown.

#### 4.1.2. Registration

_{x}, t

_{y}, t

_{z}} = {125, −50, 30} m. Vertical arbitrary noise shifts were also added to the cropped DTM z-values, with values of −30–+30 m, with a mean value of 0 m. The cropped area covered approximately 25 km

^{2}, having 32 interest points, while the original DTM covered 100 km

^{2}, having 170 interest points. It is important to note that not all interest points in the cropped area were also identified in the larger area original DTM, proving that the displacement and noise had an effect on the interest point identification algorithm.

**Table 1.**Statistical numerical values of the proposed registration algorithm carried out on synthetic data (values in meters).

Parameter | Used Value | Value Calculated | Value Difference | Value Standard Deviation (SD) |
---|---|---|---|---|

t_{x} (m) | 125 | 124.6 | −0.4 | ±3.2 |

t_{y} (m) | −50 | −50.4 | −0.4 | ±2.8 |

#### 4.1.3. Matching

_{x}, t

_{y}, t

_{z}} = {1.2, 1.0, 2.5} m and {φ, κ, ω} = {2.0, 1.0, 0.0} decimal degrees. First, the entire area was matched in a single process, resulting in the 6-parameter transformation values depicted in Table 2. These values verify that the entire constrained ICP process is correct, while producing accurate and reliable results. The number of registered points for the entire area was more than 90% out of all available.

**Table 2.**Statistical numerical values of the Iterative Closest Point (ICP) process on point clouds (covering approximately 100 m

^{2}).

Parameter | Value Used | Value Calculated | Value Difference |
---|---|---|---|

t_{x} (m) | 1.200 | 1.207 | 0.007 |

t_{y} (m) | 1.000 | 0.998 | 0.002 |

t_{z} (m) | 2.500 | 2.497 | 0.003 |

φ (decimal degrees) | 2.000 | 1.925 | 0.075 |

κ (decimal degrees) | 1.000 | 0.988 | 0.012 |

ω (decimal degrees) | 0.000 | 0.031 | 0.031 |

#### 4.2. Morphological Analysis

#### 4.2.1. Landslide Analysis

^{2}with 25 m resolution was chosen as a reference representing the area of Mount Carmel ridge in the north of Israel. The ridge itself is situated on relatively active faults. A LiDAR scan with a density of approximately 0.2 points per 1 m

^{2}was used as subject for the evaluation of landform changes. The LiDAR scan covers an area of approximately 4 km

^{2}on the southeast side of the reference DTM with approximately 800,000 points (representing a density of more than 120 times the reference within the mutual coverage area). The DTM production time is 20 years earlier than that of the LiDAR.

_{x},t

_{y},t

_{z}) should be relatively close to the initial registration vector used in each independent ICP process, i.e., being continuous in value over the entire area, except for the landslide region. Figure 13 depicts the landslide data (LiDAR topography) superimposed on the DTM data, clearly showing the morphologic changes occurred within the landslide-affected area (while the depletion zone is not visible), with some minor changes in the vicinity, which can be considered natural morphologic changes over time.

**Figure 12.**Shaded relief representation (view from the ridge) of the landslide simulation on subject Light Detection and Ranging (LiDAR) data: before (

**left**) and after (

**right**).

^{2}) matched in the ICP. It is evident that when using the registration quantification calculated in the ICP (left-hand side) the results are more uniform and have the same trend, depicted as arrows; the only area that shows some irregular values is the area suspected to experience the landslide. When no preliminary value is used for matching (right-hand side), the displacement vectors change with no apparent trends, evidently showing noise with no clear matching correspondence or evident trend. Bottom row depicts the 3D displacement vectors for each small area matched in the ICP. Again, left image shows small displacement values—except for the area suspected with landslide, where vectors point to directions that encountered massive morphologic changes. The right image depicts noise with no clear matching, which makes the identification of the landslide and its magnitude very hard.

**Figure 14.**Landslide detection: results received by using the proposed mechanism of hierarchical registration and matching (

**left**), and results received via the straightforward coordinate-based comparison (

**right**).

_{z}values for each matched area, depicted in Figure 15. Again, it is clear that via the proposed hierarchical modeling (left) the area encountered with landslide is easily visible, together with values of vertical displacement; the rest of the area shows a vertical displacement of close to zero (meters), suggesting good correspondence between local surfaces, with minor value changes that can be explained by local minor morphological changes (such as new roads, structures or hydrologic streams created during time). On the right image it is quite hard—almost impossible—to identify the area suspected to have encountered the landslide, which is a result of no preliminary modeling pre-processing, namely spatial registration. These figures illustrate the significance of prior registration to the ICP processes and that both these processes have an essential role in ensuring a correct and accurate modeling for landslide modeling processes or any other natural phenomena. This is in contrast to a direct superimposition process that does not use the geometric inter-relations of the two models. Thus, the extraction of a mutual geospatial framework is mandatory. Without preliminary registration, extracting the spatial artifacts from the real displacements is almost impossible to accomplish—mainly within the horizontal domain.

**Figure 15.**d

_{z}displacement values for matched frames—proposed hierarchical mechanism (

**left**), and straightforward coordinate-based superposition (

**right**). Values are in meters.

#### 4.2.2. Change Detection

^{2}, depicted in Figure 16. Within the mutual coverage area, the DTM had less than 3800 points, with the LiDAR representing more than 630,000, which translates to a ratio of 1:165. The ICP matching process was carried out separately and independently on frame areas covering 100 m

^{2}. Since the DTM database (left) is a representation of the bare earth—and the LiDAR is not (it is a Digital Surface Model (DSM))—it is clear that buildings exist on the western parts of the LiDAR database, together with road infrastructure, which do not exist on the DTM. This is a result of a new neighborhood that was built during the production times of both databases (20 years apart). Again, the assumption is that all mutual frames should be matched accurately, except for the frames experienced with time-dependent morphologic and artificial changes, i.e., no “spatial correspondence” exists between the matched zones.

_{z}displacement values for each matched area. The left image shows that there is a high correlation between areas, where high d

_{z}values represents spatial irregularities in the displacement vectors, which point to areas with less spatial correspondences. The right image, on the other hand, shows a much bigger value range: −15–25 m, as opposed to the correct solution with −8–7 m.

**Figure 16.**DTM (

**left**) and LiDAR Digital Surface Model (DSM) (

**right**) databases showing the same area—20 years apart.

**Figure 17.**Change detection analysis: results received by using the proposed mechanism of hierarchical registration and matching (

**left**), and results received via the straightforward coordinate-based comparison (

**right**). Values are in meters.

**Figure 18.**Change detection analysis: statistical estimators reflecting on ICP process reliability; number of point-coupling (

**top**), Standard Deviation (SD) of height value difference (

**middle**) and average height value difference (

**bottom**). Last two values are in meters.

## 5. Discussion and Conclusions

## Acknowledgments

## Conflict of Interest

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Dalyot, S.
Landform Monitoring and Warning Framework Based on Time Series Modeling of Topographic Databases. *Geosciences* **2015**, *5*, 177-202.
https://doi.org/10.3390/geosciences5020177

**AMA Style**

Dalyot S.
Landform Monitoring and Warning Framework Based on Time Series Modeling of Topographic Databases. *Geosciences*. 2015; 5(2):177-202.
https://doi.org/10.3390/geosciences5020177

**Chicago/Turabian Style**

Dalyot, Sagi.
2015. "Landform Monitoring and Warning Framework Based on Time Series Modeling of Topographic Databases" *Geosciences* 5, no. 2: 177-202.
https://doi.org/10.3390/geosciences5020177