# Application of In-Segment Multiple Sampling in Object-Based Classification

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## Abstract

**:**

## 1. Introduction

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- To describe in-segment pixel heterogeneity by exploiting the potential of multiple small set sampling,
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- To study the effect of multiple small set sampling on normality violation with the parametric Student’s t-test,
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- To compare the effectiveness of the Kolmogorov-Smirnov and Student’s t-test based classifiers, and
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- To analyze the impact spectral resolution has on the classification results.

## 2. Data and Methodology

#### 2.1. Case Study Area and Data

^{2}(Figure 2) was selected for the experimental purposes of this research.

**Figure 2.**The highly residential study area measuring 0.16 km

^{2}is located west of the Ljubljana center (Slovenia). It is marked with a black rectangular.

#### 2.2. Segmentation

#### 2.3. The Selection of Training and Testing Samples

**Table 1.**Types of attributes computed per segment for the k-NN and SVM classification methods, as implemented in the ENVI 5.0 processing software.

Attribute | Type | Description |
---|---|---|

Spectral | Minimum | Minimum value of pixels comprising the region in band x. |

Maximum | Maximum value of pixels comprising the region in band x. | |

Mean | Mean value of pixels comprising the region in band x. | |

Standard deviation | Standard deviation value of pixels comprising the region in band x. | |

Texture | Range | Average data range of pixels comprising the region within the kernel. |

Mean | Average value of pixels comprising the region within the kernel. | |

Variance | Average variance of pixels comprising the region within the kernel. | |

Entropy | Average entropy value of pixels comprising the region within the kernel. | |

Spatial | Area | Total area of the polygon, minus the area of the holes. |

Length | The combined length of all polygon boundaries, including the boundaries of the holes. | |

Compactness | A shape measurement that indicates the compactness of the polygon. A circle is the most compact shape with a value of 1/π. | |

Convexity | This attribute measures the convexity of the polygon. The convexity value for a convex polygon with no holes is 1.0, while the value for a concave polygon is below 1.0. | |

Solidity | A shape measurement that compares the area of the polygon to the area of a convex hull that surrounds the polygon. The solidity value for a convex polygon with no holes is 1.0, while the value for a concave polygon is below 1.0. | |

Roundness | A shape measurement that compares the area of the polygon to the square of the maximum diameter of the polygon. The roundness value of a circle is 1, while the value for a square is 4/π. | |

Form factor | A shape measurement that compares the area of the polygon to the square of the total perimeter. The form factor value of a circle is 1, while the value of a square is π/4. | |

Elongation | A shape measurement that indicates the ratio of the major axis of the polygon to the minor axis of the polygon. The elongation value for a square is 1.0, while the value for a rectangle is greater than 1.0. | |

Rectangular fit | A shape measurement that indicates how well the shape is described by a rectangle. The rectangular fit value for a rectangle is 1.0, while the value for a non-rectangular shape is below 1.0. | |

Main direction | The angle subtended by the major axis of the polygon and the x-axis in degrees. The main direction value ranges between 0 and 180°. 90° is North/South, while 0 to 180° is East/West. | |

Major length | The length of the major axis of an oriented bounding box that encloses the polygon. | |

Minor length | The length of the minor axis of an oriented bounding box that encloses the polygon. | |

Number of holes | The number of holes in the polygon. | |

Hole area | The ratio of the total area of the polygon towards the area of the outer contour of the polygon. The hole-solid ratio value for a polygon with no holes is 1.0. |

Class | Number of Selected Segments for Training Samples | Number of Selected Segments for Testing Samples |
---|---|---|

Roads | 6 | 67 |

Buildings | 11 | 257 |

Trees | 7 | 176 |

Grass | 5 | |

Total | 29 | 500 |

#### 2.4. Supervised Classification Process

#### 2.4.1. The Two-Sample Kolmogorov-Smirnov Test Statistics Based Classification Algorithm

#### 2.4.2. Student’s t-Test Statistics Based Classification Algorithm

#### 2.4.3. Random Sampling Approach

**Figure 3.**Random sampling approach. Empirical cumulative distribution functions and mean values are computed for each set of sampled pixel values for segments with a known and unknown class. A p-value between segments with an unknown and known class is computed after each sampling and averaged (mean p-value) in order to obtain a single value for the specific combination of the two segments. ECDF stands for empirical cumulative distribution function, KS for two-sample Kolmogorov-Smirnov test statistics and T for Student’s t-test statistics.

**Figure 4.**Segments from the segmentation layer selected for the sampling analysis: (

**a**) a black roof; (

**b**) a black roof; (

**c**) a grass patch. Each segment contains more than 1000 pixels.

## 3. Results and Discussion

#### 3.1. Sampling Analysis

**Figure 5.**The per-band p-value computation between segments with similar land covers (two black roofs) when different sizes of sampled pixel sets were applied and when: (

**a**) the two-sample Kolmogorov-Smirnov statistics; (

**b**) the Student’s t-test statistics was used.

**Figure 6.**The per-band p-value computation between segments with different land covers (a black roof and a grass patch) when different sizes of sampled pixel sets were applied and when: (

**a**) the two-sample Kolmogorov-Smirnov statistics; (

**b**) the Student’s t-test statistics was used.

**Figure 8.**The per-band p-value computation between segments with similar land covers (two black roofs) when different numbers of 10 pixel samples were applied and when: (

**a**) the two-sample Kolmogorov-Smirnov statistics; (

**b**) the Student’s t-test statistics was used.

**Figure 9.**The per-band p-value computation between segments with different land covers (a black roof and a grass patch) when different numbers of 10 pixel samples were applied and when: (

**a**) the two-sample Kolmogorov-Smirnov statistics; (

**b**) the Student’s t-test statistics was used.

#### 3.2. Classification Results and Accuracy Assessment

**Table 3.**A confusion matrix for all four classifiers for the 4- and 8-band input image in the event when k-NN and SVM classification methods were conducted with four spectral attributes. The user and producer accuracy values in bold represent the mean overall user and producer accuracy.

k-Nearest Neighbor | ||||||||||

4-Band Image | 8-Band Image | |||||||||

Reference | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) |

Roads | 43 | 20 | 4 | 67 | 59.7 | 48 | 18 | 1 | 67 | 57.8 |

Building | 29 | 190 | 38 | 257 | 87.6 | 32 | 195 | 30 | 257 | 82.2 |

Trees + grass | 0 | 7 | 169 | 176 | 80.1 | 3 | 24 | 149 | 176 | 82.8 |

Total | 72 | 217 | 211 | 500 | 75.8 | 83 | 237 | 180 | 500 | 74.3 |

User accuracy (%) | 64.2 | 73.9 | 96.0 | 78.0 | 71.6 | 75.9 | 84.6 | 77.4 | ||

Support Vector Machine | ||||||||||

4-Band Image | 8-Band Image | |||||||||

Reference | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) |

Roads | 22 | 41 | 4 | 67 | 59.5 | 23 | 18 | 1 | 67 | 62.2 |

Building | 15 | 210 | 32 | 257 | 83.3 | 13 | 210 | 34 | 257 | 90.5 |

Trees + grass | 0 | 1 | 175 | 176 | 82.9 | 1 | 4 | 171 | 176 | 83.0 |

Total | 37 | 252 | 211 | 500 | 75.2 | 37 | 232 | 206 | 500 | 78.6 |

User accuracy (%) | 32.8 | 81.7 | 99.4 | 71.3 | 34.3 | 81.7 | 97.1 | 71.0 | ||

Two-Sample Kolmogorov-Smirnov Test Statistics Classifier | ||||||||||

4-Band Image | 8-Band Image | |||||||||

Reference | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) |

Roads | 52 | 14 | 1 | 67 | 61.1 | 52 | 14 | 1 | 67 | 59.0 |

Building | 33 | 179 | 45 | 257 | 92.7 | 36 | 181 | 40 | 257 | 92.8 |

Trees + grass | 0 | 0 | 176 | 176 | 79.3 | 0 | 0 | 176 | 176 | 81.1 |

Total | 85 | 193 | 222 | 500 | 77.7 | 88 | 195 | 217 | 500 | 77.6 |

User accuracy (%) | 77.6 | 69.6 | 100 | 82.4 | 77.6 | 70.4 | 100 | 82.7 | ||

Student’s t-Test Statistics Classifier | ||||||||||

4-Band Image | 8-Band Image | |||||||||

Reference | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) |

Roads | 52 | 14 | 1 | 67 | 56.5 | 52 | 14 | 1 | 67 | 59.1 |

Building | 40 | 194 | 23 | 257 | 93.3 | 36 | 196 | 25 | 257 | 93.3 |

Trees + grass | 0 | 0 | 176 | 176 | 88.0 | 0 | 0 | 176 | 176 | 871 |

Total | 92 | 208 | 200 | 500 | 79.3 | 88 | 210 | 202 | 500 | 79.8 |

User accuracy (%) | 77.6 | 75.5 | 100 | 84.4 | 77.6 | 75.5 | 100 | 84.4 |

**Table 4.**Additional confusion matrix for k-NN and SVM classifiers; conducted with 22 attributes (4 spectral, 4 texture and 14 spatial attributes).

k-Nearest Neighbor | ||||||||||

4-Band Image | 8-Band Image | |||||||||

Reference | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) |

Roads | 40 | 20 | 7 | 67 | 68.9 | 44 | 20 | 3 | 67 | 74.6 |

Building | 16 | 202 | 39 | 257 | 83.1 | 14 | 213 | 30 | 257 | 81.9 |

Trees/grass | 2 | 21 | 153 | 176 | 76.9 | 1 | 27 | 148 | 176 | 81.8 |

Total | 58 | 243 | 199 | 500 | 76.3 | 59 | 260 | 181 | 500 | 79.4 |

User accuracy (%) | 59.7 | 78.6 | 86.9 | 75.1 | 65.7 | 82.9 | 84.1 | 77.6 | ||

Support Vector Machine | ||||||||||

4-Band Image | 8-Band Image | |||||||||

Reference | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) | Roads | Building | Trees + Grass | Total | Producer Accuracy (%) |

Roads | 32 | 25 | 10 | 67 | 88.9 | 35 | 30 | 2 | 67 | 87.5 |

Building | 4 | 226 | 27 | 257 | 87.9 | 5 | 231 | 21 | 257 | 87.1 |

Trees/grass | 0 | 6 | 170 | 176 | 82.1 | 0 | 4 | 172 | 176 | 88.2 |

Total | 36 | 257 | 207 | 500 | 86.3 | 40 | 265 | 195 | 500 | 87.6 |

User accuracy (%) | 47.8 | 87.9 | 96.6 | 77.4 | 52.2 | 89.9 | 97.7 | 79.9 |

^{2}and located 1.5 km west of the primary study area. This classification was conducted using a 4-band Worldview-2 image (Red, Green, Blue and NIR1 bands) and a new set of training samples for four land cover classes: roads (6), buildings (9), trees (7) and grass (9). With the k-NN and SVM classification methods only four spectral attributes were used.

**Figure 10.**The final classification image for all four classifiers related to the 8-band classification results presented in Table 4: (

**a**) k-NN; (

**b**) SVM; (

**c**) the two-sample Kolmogorov-Smirnov statistics based classifier; (

**d**) the Student’s t-test statistics based classifier.

**Figure 11.**The detailed subset of classification images represented in Figure 10 in relation to the satellite image that was used as an input for the classification process and was also considered as the ground truth image: (

**a**) pan-sharpened Worldview-2 image (shown as a false color composite); (

**b**) k-NN classifier; (

**c**) SVM classifier; (

**d**) the two-sample Kolmogorov-Smirnov statistics based classifier; (

**e**) the Student’s t-test statistics based classifier. Images reveal higher classification accuracies of the two proposed classifiers compared to the ground truth image.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Đurić, N.; Pehani, P.; Oštir, K. Application of In-Segment Multiple Sampling in Object-Based Classification. *Remote Sens.* **2014**, *6*, 12138-12165.
https://doi.org/10.3390/rs61212138

**AMA Style**

Đurić N, Pehani P, Oštir K. Application of In-Segment Multiple Sampling in Object-Based Classification. *Remote Sensing*. 2014; 6(12):12138-12165.
https://doi.org/10.3390/rs61212138

**Chicago/Turabian Style**

Đurić, Nataša, Peter Pehani, and Krištof Oštir. 2014. "Application of In-Segment Multiple Sampling in Object-Based Classification" *Remote Sensing* 6, no. 12: 12138-12165.
https://doi.org/10.3390/rs61212138