# Image-Based Automated Width Measurement of Surface Cracking

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Step I: Preliminary Filtering

#### 2.2. Step II: Binary Segmentation

_{min}corresponding to the minimum distance between a point and its neighbor.

_{min}according to k given in Equation (4):

#### 2.3. Step III. Profile Width

_{i}be the i-th vector comprising the intensity levels of length t. The width of the crack can be calculated as (Equation (5)):

## 3. Results

- (1)
- No clear distribution: Samples V/3 and V/4 show this case. In these samples, it was possible to extract only a limited number of measurement points due to the small number of cracks present in the sample. Thus, it is not possible to associate the data with a specific distribution. This limitation of the method is a particular point for future improvement.
- (2)
- Normal distribution: This phenomenon is present in samples with a regular cracking pattern. It is clearly observed in samples A/1, A/2, and A/3. Additionally, in sample A/2, the number of measurements was increased from 75 to 606 through parameter k (Figure 10). By increasing the number of measurements, it is possible to observe a normal behavior and a lower error in relation to the manual process (p-value 0.906 versus p-value 0.308).
- (3)
- Bimodal distribution: This phenomenon can be clearly observed in samples No Fiber/1, A/4, and A/5 (Figure 13). These samples exhibit two types of cracks (coarse and fine), which have a vertical and/or horizontal cracking behavior. In some cases, a greater width was found in the horizontal cracks. However, it is worth mentioning that all the cracks have internal angles that can only be appreciated in images with a higher magnification (Figure 13a).

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

_{i}be the i-th canonical basis vector of dimensions (m × 1), i.e., e

_{i}= [0, ⋯, 0, 1, 0, ⋯, 0] with a value of 1 at the i-th position and the rest with zeros. Operator $\sqcap \left(\xb7\right)$ can be defined as Equation (A1):

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**Figure 1.**Crack-width comparator gauge (CWCG) for measuring the crack width; image resolution 14.7 pixels/mm.

**Figure 2.**Test image with cracks and shadowed regions; original image area (500 mm × 500 mm), sub-image area (82 mm × 82 mm), resolution 11.5 pixel/mm, shadow region area (25 mm × 25 mm): Arrow: detail of a suspected fault region that is actually a shadow.

**Figure 3.**The proposed three-stage algorithm for crack width estimation. The partial results for each imagen of the algorithm are described in Section 2.1,Section 2.2,Section 2.3.

**Figure 4.**Preliminary filtering step: (

**a**) original image captured with a Canon XTI Rebel 6i camera, (

**b**) L-channel from the L*a*b space, and (

**c**) coherence filter applied to the L-channel; sample area 500 mm × 500 mm.

**Figure 5.**(

**a**) Vector w

^{+}in the original image, (

**b**) the maximum index for Equation (2), (

**c**) the coherence filter output, and (

**d**) binary segmentation; sample area 500 mm × 500 mm.

**Figure 6.**(

**a**) A section of the binary image, (

**b**) the Euclidean distance transform on the binary image (in pseudo-color), (

**c**) application of the top-hat filter to the distance transform, and (

**d**) topological skeleton applied to the top-hat image (zoom area 12.8 mm × 12.8 mm).

**Figure 7.**Central points after the neighbor spacing stabilization process; central point area equal to 28.3 mm × 28.4 mm.

**Figure 8.**(

**a**) Sub-region and line profile superimposed on the angle normal to the crack, (

**b**) intensity levels of the profile, and (

**c**) width estimation by clustering.

**Figure 9.**Plain mixture specimen with optimum calculation of the crack width and optimum angle of orientation according to the curvature.

**Figure 10.**Control point spacing according to the k-means parameter k: (

**a**) k = 10, d

_{min}= 8.5, d

_{avg}= 3.238 mm, (

**b**) k = 15, d

_{min}= 13.5, d

_{avg}= 3.236, (

**c**) k = 20, d

_{min}= 16.5, d

_{avg}= 3.364, and (

**d**) k = 40, d

_{min}= 38, d

_{avg}= 3.158.

**Figure 11.**Dataset of samples generated from ECMs reinforced with different fiber types and a plain ECM. Samples were taken with two light sources: natural and artificial (area under analysis 500 mm × 500 mm).

**Figure 12.**Results of the proposed method on the dataset of Figure 11 (area under analysis 500 mm × 500 mm).

**Figure 13.**Zoom on the analyzed images (

**a**), zoom area: 8.3 mm × 8.4 mm), (

**b**), zoom area: 61.5 mm × 61.5 mm), and (

**c**), zoom area: 51.3 mm × 51.3 mm).

Automatic Measurement | Manual Measurement (30 Points) | t-Test Comparison | Image Features | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Image Code | Count | Mean (Pixel) | std (Pixels) | Mean (Pixels) | std (Pixels) | Z-Score | p-Value | Light Type | k | Fiber Type |

V/1 | 30 | 5.35 | 1.99 | 5.26 | 1.44 | −0.25 | 0.801 | Midday sun | 20 | Vegetal |

V/2 | 30 | 9.90 | 4.95 | 9.55 | 2.04 | −0.43 | 0.671 | Midday sun | 20 | Vegetal |

V/3 | 10 | 6.42 | 1.43 | 6.56 | 2.08 | 0.20 | 0.842 | Light (3000 K) | 10 | Vegetal |

V/4 | 5 | 4.48 | 0.54 | 4.32 | 1.11 | −0.50 | 0.624 | Light (3000 K) | 20 | Vegetal |

S/1 | 39 | 7.37 | 4.72 | 6.21 | 4.65 | −1.03 | 0.308 | Afternoon Sun | 20 | Industrial |

A/1 | 75 | 7.28 | 2.40 | 7.80 | 1.87 | 0.88 | 0.386 | Afternoon Sun | 20 | Animal |

A/2 | 606 | 7.61 | 3.72 | 7.80 | 1.87 | 0.11 | 0.906 | Afternoon Sun | 10 | Animal |

A/3 | 95 | 8.38 | 3.26 | 8.83 | 3.06 | 0.49 | 0.622 | Light (3000 K) | 20 | Animal |

A/4 | 192 | 23.15 | 9.39 | 22.71 | 8.22 | −0.31 | 0.761 | Midday sun | 10 | Animal |

A/5 | 234 | 17.86 | 7.15 | 17.67 | 7.79 | −0.38 | 0.699 | Light (3000 K) | 10 | Animal |

NoFiber/1 | 95 | 12.43 | 6.36 | 12.47 | 7.39 | −0.39 | 0.694 | Afternoon Sun | 20 | No Fiber |

NoFiber/2 | 308 | 14.37 | 6.42 | 14.83 | 8.14 | 0.22 | 0.827 | Light (3000 K) | 20 | No Fiber |

TOTAL | 1719 regions |

Technique | Noise Removal | Length Estimation | Route Tracing (Tortuosity) | Light Source Setup | Spatial Width Distribution | Ref |
---|---|---|---|---|---|---|

Edge distance + Linear fit | None (automatic threshold) | No | No | Yes | No | [15] |

Percolation + Binarization | Percolation processing | No | No | No | No | [16] |

Percolation + Neighbor boundary | Percolation processing | No | No | No | No | [22] |

Skeletonization between two points | None (clumping process) | No | Yes | No | No | [23] |

Digital image correlation (DIC) | None (automatic threshold) | Yes | No | Yes | No | [2] |

Top-Hat + Otsu Binarization | Gaussian function-based spatial filter | No | No | No | No | [5] |

Feature extraction and SVM algorithm | Steerable Filter | Yes | No | No | No | [4] |

Genetic Algorithm | Multi-sequential image filter | Yes | Yes | No | No | [13] |

Deep Learning | Fast-RCNN + TuFF | No | No | No | No | [29] |

Hessian structure propagation | None | No | Yes | No | No | [27] |

Deep Learning | YOLO | Yes | No | Yes | No | [33] |

filtering + edge searching. | Frangi filtering | Yes | No | No | No | [26] |

Bwdist transform + Arc Length | Morphological operations (Aperture) | Yes | Yes | Yes | No | [24] |

M2GLD | Min-Max Gray Level Discrimination | No | No | No | No | [25] |

Proposed technique | L*a*b + Coherence Filter | Yes | Yes | No | Yes |

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**MDPI and ACS Style**

Carrasco, M.; Araya-Letelier, G.; Velázquez, R.; Visconti, P.
Image-Based Automated Width Measurement of Surface Cracking. *Sensors* **2021**, *21*, 7534.
https://doi.org/10.3390/s21227534

**AMA Style**

Carrasco M, Araya-Letelier G, Velázquez R, Visconti P.
Image-Based Automated Width Measurement of Surface Cracking. *Sensors*. 2021; 21(22):7534.
https://doi.org/10.3390/s21227534

**Chicago/Turabian Style**

Carrasco, Miguel, Gerardo Araya-Letelier, Ramiro Velázquez, and Paolo Visconti.
2021. "Image-Based Automated Width Measurement of Surface Cracking" *Sensors* 21, no. 22: 7534.
https://doi.org/10.3390/s21227534