# On Attribute Thresholding and Data Mapping Functions in a Supervised Connected Component Segmentation Framework

## Abstract

**:**

## 1. Introduction

## 2. Background and Related Work

#### 2.1. Graph-Based Connected Component Segmentation

#### 2.2. Constrained Connectivity

**Figure 1.**An abstract image, segmented with the $\alpha $w-CC method illustrating its general characteristics, with (0,0)-CC shown in (

**a**), (1,1)-CC in (

**b**), (1,2)-CC in (

**c**)

**,**and (2,3)-CC in (

**d**).

**Figure 2.**An image subset (

**a**) segmented with ($\alpha $w-CC) to show its common characteristics on real imagery, with the local and global range parameters set to 25 and 75 (

**b**), 25 and 75 with a region growing filter (

**c**), and to 50 and 200 (

**d**), respectively. The red polyline indicates an example element a user might be interested in.

#### 2.3. Metaheuristics

#### 2.4. Empirical Discrepancy Metrics

**Table 1.**The three empirical discrepancy metrics employed to measure the quality of generated segments against the provided reference segments.

Metric | Formulation | Reference |
---|---|---|

RWJ | $1-{\displaystyle \sum _{i=1}^{n}}\frac{\left|R{\displaystyle \cap}{S}_{i}\right|}{\left|R{\displaystyle \cup}{S}_{i}\right|}\times \frac{\left|R{\displaystyle \cap}{S}_{i}\right|}{\left|R\right|}$ | [6] |

RBSB | $\frac{\left|R{\displaystyle \cup}S\right|-\left|R{\displaystyle \cap}S\right|}{\left|R\right|}$ | [48] |

PD_OCE | $1-{\displaystyle \sum _{i=1}^{n}}\frac{\left|R{\displaystyle \cap}{S}_{i}\right|}{\left|R{\displaystyle \cup}{S}_{i}\right|}\times \frac{\left|{S}_{i}\right|}{{{\displaystyle \sum}}_{j=1}^{n}\left|{S}_{j}\right|}$ | [6,49] |

#### 2.5. Sample Supervised Segment Generation

## 3. Method

#### 3.1. Method Details

**Figure 4.**An example of an 11-dimensional parameter set traversed by the CC + Map + Attr full method variant. Example parameters within each constituent are written vertically.

#### 3.2. Mapping Functions

**Figure 5.**Example output of the three used mapping functions on an arbitrary test image (

**a**). Parameters were assigned random values. The red polyline denotes an example element of interest; (

**b**) shows output of the SS function (note the creation of sharp gradients);(

**c**) shows output from the transformation matrix, while (

**d**) shows the output from the GT function. Note the non-linear stretch of the output from the GT function.

#### 3.2.1. Spectral Split

#### 3.2.2. Transformation Matrix

#### 3.2.3. Genetic Transform

#### 3.3. Attributes

**Table 2.**Implemented attributes for consideration in the context of CC segmentation, specifically in the CC + Attr and CC + Attr + Map method variants.

Attribute | Range | Description |
---|---|---|

Area | [0..500] | Segment area measured in number of pixels |

Standard Deviation | [0..255] | Segment spectral standard deviation |

Perimeter | [0..500] | Number of pixel edges forming the perimeter |

Smoothness (SMT) | [0..30] | Perimeter/sqrt(area) |

Compactness (CMP) | [0..30] | Perimeter/bounding box edge length |

Gray level difference Histogram, five bins (CH1–5) | [0..500] Bins: CH1:[0..5], CH2:(5..10], CH3:(10..15], CH4:(15..20], CH5:(20..255] | Number of edge weights falling within specified bins. Five bins are defined. |

**Figure 6.**An image subset segmented with the local range parameter set to 50 and the global range parameter set to 200. Additional constraining attributes are introduced, specifically area, with a value of 800 (

**a**) and CH1 (

**b**) with a value of 300.

## 4. Data

**Figure 7.**The three image analysis tasks defined for evaluating the method variants, namely, thematically correctly segmenting tents in the Bokolmanyo problem (

**a**) and metal-roofed structures in the Jowhaar (

**b**) and Hagadera (

**c**) problems.

**Table 3.**The datasets, with accompanying metadata, used for evaluating the method variants (adapted from [6]).

Test Site | Target Elements | Sensor | Spatial Resolution | Reference Segments | Channels | Date Captured |
---|---|---|---|---|---|---|

Bokolmanyo ^{1} | Tents | GeoEye-1 | 0.5 m | 28 | 1, 2, 3 | 24/8/2011 |

Jowhaar ^{1} | Structures | GeoEye-1 | 0.5 m | 40 | 1, 2, 3 | 26/02/2011 |

Hagadera ^{2} | Structures | WorldView-2 | 0.5 m | 38 | 4, 6, 3 | 07/10/2010 |

^{1}GeoEye, Inc.

^{©}2011, provided by e-GEOS S.p.A., under GSC-DA, all rights reserved.;

^{2}DigitalGlobe, Inc.

^{©}2010, provided by EUSI under EC/ESA/GSC-DA, all rights reserved.

## 5. Experimental Evaluation

#### 5.1. Parameter Interdependencies

**Table 4.**Interdependency test of the method constituents for the Bokolmanyo problem. Note that all constituents affect one another. The mapping function affects all parameters most frequently.

Bokolmanyo | Mapping Function | CC | Attributes | ||||||
---|---|---|---|---|---|---|---|---|---|

GT1 | GT2 | GT10 | Local | Global | Area | Std | CH2 | ||

Mapping function | GT1 | 15 | 19 | 2 | 0 | 3 | 0 | 2 | |

GT2 | 36 | 29 | 3 | 0 | 2 | 3 | 2 | ||

GT10 | 38 | 12 | 4 | 0 | 2 | 1 | 3 | ||

CC | Local | 6 | 13 | 11 | 1 | 2 | 0 | 1 | |

Global | 31 | 15 | 24 | 12 | 6 | 0 | 2 | ||

Attributes | Area | 19 | 28 | 22 | 2 | 1 | 0 | 3 | |

Std | 21 | 25 | 32 | 1 | 1 | 11 | 2 | ||

CH2 | 13 | 11 | 9 | 1 | 0 | 1 | 0 |

Jowhaar | Mapping Function | CC | Attributes | ||||||
---|---|---|---|---|---|---|---|---|---|

GT3 | GT4 | GT9 | Local | Global | Perim | Smooth | CH1 | ||

Mapping function | GT3 | 33 | 20 | 3 | 0 | 1 | 0 | 1 | |

GT4 | 8 | 9 | 4 | 0 | 0 | 1 | 0 | ||

GT9 | 19 | 34 | 4 | 2 | 1 | 1 | 1 | ||

CC | Local | 13 | 16 | 11 | 7 | 0 | 2 | 0 | |

Global | 17 | 18 | 20 | 12 | 10 | 0 | 4 | ||

Attributes | Perm | 20 | 24 | 18 | 2 | 3 | 1 | 6 | |

Smooth | 8 | 3 | 2 | 1 | 0 | 0 | 0 | ||

CH1 | 12 | 14 | 16 | 2 | 0 | 5 | 1 |

Hagadera | Mapping Function | CC | Attributes | ||||||
---|---|---|---|---|---|---|---|---|---|

GT6 | GT7 | GT8 | Local | Global | CH3 | CH4 | CH5 | ||

Mapping function | GT6 | 27 | 15 | 3 | 3 | 3 | 1 | 3 | |

GT7 | 29 | 25 | 5 | 1 | 4 | 1 | 2 | ||

GT8 | 23 | 33 | 7 | 4 | 1 | 0 | 1 | ||

CC | Local | 10 | 7 | 9 | 4 | 3 | 1 | 4 | |

Global | 27 | 13 | 20 | 6 | 4 | 0 | 0 | ||

Attributes | CH3 | 6 | 3 | 3 | 0 | 0 | 1 | 4 | |

CH4 | 4 | 3 | 2 | 0 | 0 | 0 | 0 | ||

CH5 | 3 | 2 | 0 | 0 | 0 | 1 | 0 |

#### 5.2. Search Surface Complexity

**Figure 8.**Two-dimensional parameter plots, or search surfaces, demonstrating parameter interactions between method constituents: (

**a**) illustrates the interaction of the alpha parameter from the CC constituent and that of a mapping function parameter, while (

**b**) shows the interaction of alpha with the CH1 attribute.

**Table 7.**Performance of the four search methods on the four method variants. In the simpler CC method variants (CC and CC + Attr), no benefit is noted from using more advanced search methods. In the case of the higher dimensional method variants (CC + Map and CC + Attr + Map), using an advanced search method becomes necessary.

CC | CC + Attr | CC + Map | CC + Attr + Map | |
---|---|---|---|---|

RND | 0.429 ± 0.000 | 0.448 ± 0.000 | 0.186 ± 0.012 | 0.193 ± 0.015 |

HC | 0.442 ± 0.009 | 0.535 ± 0.144 | 0.507 ± 0.083 | 0.538 ± 0.159 |

PSO | 0.429 ± 0.000 | 0.448 ± 0.000 | 0.167 ± 0.012 | 0.163 ± 0.008 |

DE | 0.429 ± 0.000 | 0.448 ± 0.000 | 0.161 ± 0.003 | 0.163 ± 0.003 |

**Figure 9.**Search method profiles for the four method variants, namely CC (

**a**), CC + Attr (

**b**), CC + Map (

**c**), and CC + Attr + Map (

**d**). Note the increased performance of DE and PSO when considering the CC + Map and CC + Attr + Map method variants.

#### 5.3. Method Variant Performances

**Table 8.**Method performance on the Bokolmanyo problem. Note the improved results with the CC + LIN and CC + Attr + LIN method variants under all metric conditions.

CC | CC + Attr | CC + LIN | CC + Attr + LIN | ||
---|---|---|---|---|---|

RWJ | Avg | 0.465 ± 0.000 | 0.520 ± 0.035 | 0.239 ± 0.020 | 0.235 ± 0.026 |

Min | 0.465 | 0.476 | 0.211 | 0.200 | |

RBSB | Avg | 0.299 ± 0.000 | 0.308 ± 0.009 | 0.262 ± 0.235 | 0.185 ± 0.034 |

Min | 0.299 | 0.301 | 0.136 | 0.144 | |

PD_OCE | Avg | 0.538 ± 0.009 | 0.556 ± 0.030 | 0.233 ± 0.016 | 0.244 ± 0.026 |

Min | 0.526 | 0.514 | 0.199 | 0.205 |

**Table 9.**Method performance on the Jowhaar problem. The method variant employing a data mapping function (CC + SS) performed the best under all metric conditions.

CC | CC + Attr | CC + SS | CC + Attr + SS | ||
---|---|---|---|---|---|

RWJ | Avg | 0.551 ± 0.003 | 0.784 ± 0.001 | 0.411 ± 0.009 | 0.757 ± 0.013 |

Min | 0.548 | 0.783 | 0.392 | 0.739 | |

RBSB | Avg | 0.622 ± 0.000 | 0.652 ± 0.003 | 0.418 ± 0.058 | 0.616 ± 0.023 |

Min | 0.622 | 0.649 | 0.348 | 0.581 | |

PD_OCE | Avg | 0.684 ± 0.002 | 0.825 ± 0.006 | 0.549 ± 0.032 | 0.807 ± 0.021 |

Min | 0.683 | 0.816 | 0.506 | 0.769 |

**Table 10.**Method performances on the Hagadera problem. The top performing method variant is metric dependent.

CC | CC + Attr | CC + GT | CC + Attr + GT | ||
---|---|---|---|---|---|

RWJ | Avg | 0.614 ± 0.000 | 0.631 ± 0.008 | 0.492 ± 0.013 | 0.509 ± 0.012 |

Min | 0.614 | 0.619 | 0.468 | 0.494 | |

RBSB | Avg | 0.737 ± 0.000 | 0.511 ± 0.014 | 1.633 ± 1.061 | 0.522 ± 0.045 |

Min | 0.737 | 0.486 | 0.526 | 0.460 | |

PD_OCE | Avg | 0.705 ± 0.001 | 0.684 ± 0.005 | 0.617 ± 0.023 | 0.616 ± 0.028 |

Min | 0.704 | 0.678 | 0.579 | 0.553 |

^{®}Xeon

^{®}E5-2643 3.5 GHz processor with single-core processing). Attribute calculations were done incrementally in the CC framework, which is more efficient than calculating attributes independently for each new level of the local range parameter. The optimal achieved parameter values are also reported. Similar to related work [6], near optimal parameter value combinations exist owing to segmentation algorithm and mapping function characteristics.

**Figure 10.**Exemplar optimal segmentation results focused on a random reference segment. The rows depict the CC, CC + Attr, CC + Map, and CC + Attr + Map method variants respectively (in order). The columns denote the three problems, Bokolmanyo, Jowhaar, and Hagadera (in order). (

**a**) RWJ: 0.574; (

**b**) RWJ: 0.524; (

**c**) RWJ: 0.787; (

**d**) RWJ: 0.683; (

**e**) RWJ: 0.524; (

**f**) RWJ: 0.806; (

**g**) RWJ: 0.104; (

**h**) RWJ: 0.506; (

**i**) RWJ: 0.787; (

**j**) RWJ: 0.063; (

**k**) RWJ: 0.437; (

**l**) RWJ: 0.549.

**Table 11.**Average computing times for experimental runs and resulting method parameters. Note the increased computing time of method variants employing attributes.

Problem | Method Variant | Time | Alpha | WGlobal | Area | Std | Perimeter | Smoothness | Compactness |
---|---|---|---|---|---|---|---|---|---|

Bokolmanyo | CC + Map | 2062.304 ± 248.996 | 187.600 ± 68.646 | 53.600 ± 15.601 | NA | NA | NA | NA | NA |

CC + Attr | 3083.551 ± 237.328 | 173.300 ± 66.331 | 196.000 ± 44.838 | 247.500 ± 142.417 | 50.442 ± 58.470 | 369.900 ± 196.794 | 21.483 ± 7.688 | 19.803 ± 7.439 | |

Jowhaar | CC + Map | 2182.659 ± 193.999 | 165.900 ± 82.538 | 155.200 ± 19.136 | NA | NA | NA | NA | NA |

CC + Attr | 4136.116 ± 498.270 | 98.900 ± 52.297 | 203.500 ± 43.775 | 392.000 ± 85.249 | 133.289 ± 60.647 | 620.500 ± 241.420 | 18.379 ± 6.910 | 22.466 ± 4.331 | |

Hagadera | CC + Map | 2168.177 ± 226.159 | 101.700 ± 65.052 | 148.300 ± 29.803 | NA | NA | NA | NA | NA |

CC + Attr | 5409.293 ± 352.444 | 187.400 ± 68.704 | 240.300 ± 21.525 | 342.100 ± 81.266 | 162.601 ± 86.782 | 574.700 ± 271.998 | 23.573 ± 7.351 | 19.940 ± 6.113 |

**Figure 11.**Search method profiles for the different problems under different metric conditions. Note that for the simpler Bokolmanyo problem near-optimal results are achieved relatively early on in the search process. In the more complex problems, the methods need substantially more iterations in finding the achievable optimal parameter set.

**Figure 12.**Friedman rank test with a Nemenyi post hoc test conducted on results from Table 8, Table 9 and Table 10. Confidence interval is set to 95%. A Critical Difference (CD) of 0.349 is generated (ranking). All method variants deliver statistically significant different results. Generally speaking, the CC + Map method variant was found most useful.

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

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Fourie, C.
On Attribute Thresholding and Data Mapping Functions in a Supervised Connected Component Segmentation Framework. *Remote Sens.* **2015**, *7*, 7350-7377.
https://doi.org/10.3390/rs70607350

**AMA Style**

Fourie C.
On Attribute Thresholding and Data Mapping Functions in a Supervised Connected Component Segmentation Framework. *Remote Sensing*. 2015; 7(6):7350-7377.
https://doi.org/10.3390/rs70607350

**Chicago/Turabian Style**

Fourie, Christoff.
2015. "On Attribute Thresholding and Data Mapping Functions in a Supervised Connected Component Segmentation Framework" *Remote Sensing* 7, no. 6: 7350-7377.
https://doi.org/10.3390/rs70607350