# Normalization in Unsupervised Segmentation Parameter Optimization: A Solution Based on Local Regression Trend Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study and Software

#### 2.2. Fixed Range Normalization

_{i}= x

_{i}− $\overline{x}$, $\overline{x}$ is the mean value of x, M = $\sum}_{i=1}^{n}{\displaystyle \sum}_{j=1}^{n}{w}_{ij$ and w

_{ij}is the element of the matrix of spatial proximity M, which depicts the degree of spatial association between the points i and j [36]. In the above description x refers to the value of the variable we are testing for spatial autocorrelation—in this case a spectral band. The matrix of spatial proximity was constructed by using the common borders approach. In detail, w

_{ij}= 1 when j shares a boundary with i and w

_{ij}= 0 elsewhere [37]. The normalization of these two measures (0–1 range) follows the implementation of Espindola et al. [19]:

_{n}is the normalized WV (or MI), X

_{max}is the maximum WV (or MI) value of all candidate segmentations, ${X}_{min}$ is the minimum WV (or MI) value of all candidate segmentations and X is the WV (or MI) value of the current segmentation. The GS is the sum of these normalized values:

_{n}+ MI

_{n}

#### 2.3. Selection of Relevant Ranges Based on Local Regression (LOESS) Trend Analysis

- Selection of a segmentation to act as minima (fine scale) and a step value as user-based inputs. A very low scale parameter, which produces very oversegmented results, is appropriate for this task. The results of LOESS are sensitive to the step between each segmentation as the algorithm is more efficient when a lot of data points are given and as such, a very small step parameter is required in order for the trends to manifest. In our case, we used a segmentation produced from a scale parameter of 0.001 as minimum range with the same value as a step. Tests with a step parameter higher than 0.003 failed to provide reasonable results.
- Consider an initial amount of segmentations and compute MI and WV values for each one. For the LOESS curve to produce meaningful results, at least a few segmentations (n~10) should be produced, as it is a local fitting method that operates in subsets of the input data.
- Computing the difference of MI (MI
_{D}) and WV (WV_{D}) between a segmentation and the next coarser one:MI_{D}= MI_{i}− MI_{i}_{+1}WV_{D}= WV_{i}_{+1}− WV_{i}_{i}is the MI value of the current segmentation and MI_{i+}_{1}the value of the next coarser one, and WV_{i}is the WV value of the current segmentation and WV_{i+}_{1}the value of the next coarser one. - Standardizing the differences of each metric (standard deviation of 1 and mean of 0) as shown in Equation (7):$$XDS=({X}_{D}-{\overline{X}}_{D})/SD$$
_{D}(or WV_{D}), ${\overline{X}}_{D}$ is the mean value of the MI_{D}(or WV_{D}) for considered segmentations and SD their standard deviation. - Fit a LOESS curve to the standardized differences with a second-degree polynomial. The results of the fit are sensitive to the span parameter, which controls the degree of smoothing. The default value (0.75) of the loess package in R statistical software was used.
- Examine the residuals between the LOESS predictions and the raw values. Since the data are standardized, the residuals correspond to standard deviations. Residuals that are sufficiently high for both MI
_{DS}and WV_{DS}are indicators of a break in the trends. As a rule of thumb, we can assume that a significant shift in the trends manifests when the residuals are higher than 0.4 (larger than 0.4 times a standard deviation) for both MI and WV at the same time while the sum of their absolute residuals is larger than 1. This rule assures both individual and combined evaluation of the trends. - Selecting the segmentation that satisfies the previous rule as the maximum range. If the criteria are not satisfied, compute an additional coarser segmentation by incrementing the scale parameter, and repeat from step 3.

#### 2.4. Validation Scheme

^{®}Xeon

^{®}CPU E5-2690 (2.90 GHz, 2 processors, 16 cores, 32 processing threads) and 96 GB of RAM. The average time for the “i.segment” module of GRASS to produce a segmentation for a single scale parameter is 34 and 28 s for each ROI, respectively. For performing the USPO procedure as proposed by the authors, roughly 15 (ROI 1) and 11 (ROI 2) minutes are required. This includes the computation of the actual segmentation layer proposed by the USPO as well as descriptive files regarding the MI, WV and GS values for each considered scale parameter. The processing time requirements reported above refer to non-parallelized, single thread versions. If parallelized using the specifications of our hardware, the whole process for both ROIs at the same time would require approximately 4 min.

## 3. Results

#### 3.1. Segmentation Goodness Metrics

#### 3.2. Classification Results

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{i}is the reference object, y

_{imax}is the segment intersecting x

_{i}that has the largest area, y

_{i}is the segment intersecting x

_{i}and area (x

_{i}∩ y

_{i}) is the area of their intersection.

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**Figure 1.**(

**a**) Pleiades image of Dakar (RGB composite), (

**b**) location map of Dakar within the African continent, (

**c**) ROI 1 (1.05 km

^{2}), representing a low-density large size built-up zone and (

**d**) ROI 2 (0.82 km

^{2}), representing a high-density medium sized built-up zone.

**Figure 3.**Normalized MI and WV values for each computed segmentation for (

**a**) ROI 1 and (

**b**) ROI 2 using the FT approach.

**Figure 5.**Differences in MI and WV between each computed segmentation and the next for (

**a**) ROI 1 and (

**b**) ROI 2.

**Figure 6.**LOESS curve results for the two ROIs. The breakpoint signifies the point where the absolute residuals are larger than 0.4 standard deviations for both Variance and Moran’s I and their sum greater than 1. In ROI 1 (

**a**) the breakpoint was found with a scale parameter of 0.028 while in ROI 2 (

**b**) a parameter of 0.023 was identified as suitable.

**Figure 8.**Examples of digitized buildings and trees for the computation of segmentation goodness metrics in (

**a**) ROI 1 and (

**b**) ROI 2.

**Figure 9.**Example of segmentation results for the two ROI. (

**a**,

**c**) FT approach, (

**b**,

**d**) LOESS approach. Highlighted objects in color other than yellow display undersegmented areas where several LULC classes are mixed for the FT approach, while colored objects in the LOESS case showcase some of the clear improvements as the objects now represent discrete LULC classes (e.g., asphalt, vegetation, building).

**Figure 10.**Classification results for the two approaches at two levels from ROI 1. (

**a**) Segmentation and highlighted objects from the FT method, (

**b**) classification results for Classification Level 2 and (

**c**) Classification Level 1 for FT, (

**d**) Segmentation and highlighted objects from the LOESS method, (

**e**) classification results for Classification Level 2 and (

**f**) Classification level 1 for LOESS.

**Figure 11.**Classification results for the two approaches at two levels from ROI 1. (

**a**) Segmentation and highlighted objects from the FT method, (

**b**) classification results for Classification Level 2 and (

**c**) Classification Level 1 for FT, (

**d**) Segmentation and highlighted objects from the LOESS method, (

**e**) classification results for Classification Level 2 and (

**f**) Classification level 1 for LOESS.

Fixed Thresholds | Region 1 | Region 2 |
---|---|---|

WV_{max} | 128,314 | 112,811 |

WV_{min} | 0 | 0 |

MI_{max} | 1 | 1 |

MI_{max} | −1 | −1 |

Level 1 | Level 2 | Training Samples |
---|---|---|

Artificial Surface (AS) | Buildings (BU) | 91 |

Light concrete (CS) | 42 | |

Asphalt (AS) | 57 | |

Bare Soil (BS) | Bare Soil (BS) | 48 |

Vegetation (VG) | Trees (TR) | 70 |

Low Vegetation (LV) | 60 | |

Shadow (SH) | Shadow (SH) | 71 |

**Table 3.**Descriptive statistics for the Area Fit Index (AFI) and MergeSum (MS) metrics for the buildings category based on 20 reference objects.

Descriptive Statistics | Built-Up | ||||
---|---|---|---|---|---|

Area Fit Index (AFI) | MergeSum (MS) | ||||

FT | LOESS | FT | LOESS | ||

Mean | −1.64 | 0.59 | 1.14 | 0.96 | |

SD | 3.60 | 0.20 | 1.24 | 0.09 | |

1st Quartile | −2.73 | 0.48 | 1.24 | 0.97 | |

3rd Quartile | 0.54 | 0.72 | 1.00 | 0.99 |

**Table 4.**Descriptive statistics for the Area Fit Index (AFI) and MergeSum (MS) metrics for the trees category based on 20 reference objects.

Descriptive Statistics | Trees | ||||
---|---|---|---|---|---|

Area Fit Index (AFI) | MergeSum (MS) | ||||

FT | LOESS | FT | LOESS | ||

Mean | −50.81 | 0.53 | 24.69 | 0.91 | |

SD | 113.74 | 0.23 | 79.97 | 0.14 | |

1st Quartile | −26.42 | 0.37 | 0.82 | 0.89 | |

3rd Quartile | 0.19 | 0.69 | 2.05 | 0.99 |

Classification Scheme | Level 1 | Level 2 | ||
---|---|---|---|---|

Optimization Method | FT | LOESS | FT | LOESS |

Overall Accuracy (%) | 88.08 | 94.34 | 77.24 | 88.68 |

Kappa Index | 0.83 | 0.92 | 0.72 | 0.87 |

Class | Level 1 | Class | Level 2 | ||
---|---|---|---|---|---|

FT | LOESS | FT | LOESS | ||

Artificial Surface | 0.91 | 0.95 | Asphalt | 0.69 | 0.84 |

Vegetation | 0.92 | 0.97 | Buildings | 0.85 | 0.90 |

Bare Soil | 0.71 | 0.86 | Light concrete | 0.43 | 0.70 |

Shadow | 0.90 | 0.96 | Bare Soil | 0.75 | 0.82 |

Trees | 0.83 | 0.90 | |||

Low Vegetation | 0.75 | 0.88 | |||

Shadow | 0.91 | 0.96 |

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## Share and Cite

**MDPI and ACS Style**

Georganos, S.; Lennert, M.; Grippa, T.; Vanhuysse, S.; Johnson, B.; Wolff, E.
Normalization in Unsupervised Segmentation Parameter Optimization: A Solution Based on Local Regression Trend Analysis. *Remote Sens.* **2018**, *10*, 222.
https://doi.org/10.3390/rs10020222

**AMA Style**

Georganos S, Lennert M, Grippa T, Vanhuysse S, Johnson B, Wolff E.
Normalization in Unsupervised Segmentation Parameter Optimization: A Solution Based on Local Regression Trend Analysis. *Remote Sensing*. 2018; 10(2):222.
https://doi.org/10.3390/rs10020222

**Chicago/Turabian Style**

Georganos, Stefanos, Moritz Lennert, Tais Grippa, Sabine Vanhuysse, Brian Johnson, and Eléonore Wolff.
2018. "Normalization in Unsupervised Segmentation Parameter Optimization: A Solution Based on Local Regression Trend Analysis" *Remote Sensing* 10, no. 2: 222.
https://doi.org/10.3390/rs10020222