SERG -- Topics

Mathematical Morphology Processing of Radar Images for Damage Detection of Concrete

 

Tzuyang Yu, Associate Professor, Ph.D.

 

Proposed Damage Detection Method

 

Principle

A damage assessment method for quantitatively compariong synthetic aperture radar (SAR) images using mathematical morphology (MM) is proposed. This method is consisted of two steps;

  1. Feature extraction— The back-projection images are rendered with continuous response levels, in which both background and defect signals are involved. To extract the characteristic shape of a back-projection image, the image is first trans- formed into a binary image based on a threshold value nthv. Two morphological operations, erosion and dilation, are sub- sequently applied to the binary image to obtain a feature- extracted version of the original back-projection image. These morphological operations are defined by

    2.                 (1)

                       (2)

    where I(x, y) = back-projection images; \epsilon_K = erosion operator functioning with the erosion structure K ; K_r = eroded set operating at position r; \delta_V = dilation operator functioning with the dilation structure V; V_r = dilated set operating at r, and Ø = empty set. Eq. (1) represents the erosion operation in MM, while Eq. (2) represents the dilation operation in MM. An eight-node element is adopted for both ero- sion and dilation structures, as shown in Fig. 1.

    Fig. 1. Eight-node element for morphological operations

     

    The feature extraction operation on I(x, y) is performed on the binary version of I(x, y) in this method, denoted by I_BW(x, y|n_thv). The operation is defined by

                    (3)

    where I^(x, y|n_thv) = feature-extracted binary image characterized by a threshold value nthv; n_thv = threshold value related to the level of the extracted edge in the image. It is the maximum magnitude level in the image, at which the characteristic shape of the image is preserved.

  2. Feature quantification — A quantitative index used in this paper to globally characterize I^(x, y|n_thv)is Euler’s number, n_E. The variation of n_E with respect to the incident angle is interesting and investigated here. For each I^(x, y|n_thv) obtained at a given incident angle \theta, n_E is defined by

                    (4)

    where n_obj(θ|n_thv) = number of objects in I^(x, y|n_thv); and n_hol(θ|n_thv)= number of holes within the objects in I^(x, y|n_thv). With a fixed value of n_thv, n_E(θ) can be obtained.

 

The presence of damage introduces additional defect signals into back-projection images globally, and changes the maximum amplitude locally. Logically, the presence of a defect creates a defect scattering signal, leading to an increasing n_hol. The value of n_E(θ) is subsequently altered. Given same nthv and same inspection domain \Omage_s, the fluctuation of defect scattering signals will create more holes than objects, thus resulting in small n_E(θ). The purpose of using mathematical morphology is to quantify such change. Additionally, in view of the angular sensitivity of defect signals, it is believed that damage assessment based on single measurement (or image) is unlikely to be reliable. Multiple images (more information) are needed to confirm the speculation on one suspicious image. For this reason, an averaging (low-pass) filter is applied to the n_E(θ) curve, which is defined by

                           (5)

where n^f_E(θ) = filtered nE curve; and L = length of the filter (data points used in the filter). The purpose of this filter is to remove local fluctuations from the original n_E curve in order to (1) avoid false alarms at local level and (2) obtain globally consistent results. Additionally, the length of the filter suggests the required amount of angular measurements. The length of the filter also relies on the resolution of the image. For high resolution images, small L values are expected.

 

Application

SAR Imaging

The proposed damage assessment method is validated using the farfield ISAR measurements of two GFRP-confined concrete cylinder specimens. Detailed description of these specimens and radar imaging details can be found at Synthetic Aperture Radar (SAR) Imaging of Concrete Specimens and Structure. Imaging result of an artificially damaged spceimen AD1 is shown in Figs. 2 and 3 for HH and VV polarizations, respectively.

Fig. 2. Reconstructed images of the intact and damaged sides of specimen AD1—HH polarization (? = 15°)

Fig. 3. Reconstructed images of the intact and damaged sides of specimen AD1—VV polarization (θ = 15°)

 

Determination of Threshold Value

In generating the feature-extracted images I^(x, y|n_thv) the value of nthv must be determined. The value of nthv is decided when the variation of Euler’s number n_E is at critical stage. When small n_thv values are chosen, all or most of the signals are preserved, leading to a feature-extracted image I^(x, y|n_thv) dominated by low amplitude signals. When large n_thv values are chosen, I^(x, y|n_thv) will be dominated by high amplitude signals. Consequently, the computed Euler’s number n_E in these two extreme cases does not represent/reflect the main feature of the image. To avoid the use of misleading n_thv, the pattern of n_E is provided, as shown in Figs. 4 and 5, in which n_thv is normalized to the maximum amplitude of I^(x, y|n_thv).

Fig. 4. Variation of n_E with respect to n_thv of the damaged-side images of specimen AD1

 

Fig. 5. Variation of n_E with respect to n_thv of the intact-side images of specimen AD1

 

Fig. 4 shows the variation of n_E versus n_thv computed from the intact-side backprojection images of specimen AD1. Fig. 4(a) is produced from Fig. 2 (a) and Fig. 4(b) from Fig. 2(a).

 

In Figs. 4(a) and 4(b), fluctuation of n_E in the region where nthv is small (0 < n_thv < 0.4) is attributed to background signals, while in another region of large n_thv (0.73 < n_thv < 1) the fluctuation of n_E is caused by the disturbance of high amplitude signals. In both regions, the computed n_E does not represent the main feature of the image. To avoid using misleading values of n_E , the critical n_thv should be determined as the maximum nthv outside these two regions. As indicated in Figs. 5(a) and 5(b), critical n_thv is 0.81 for the images by using both HH and VV polarized signals. In Figs. 4(a) and 4(b), critical n_thv is 0.73.

 

Calculation of Euler's Number, n_E

Fig. 6 shows the reconstructed back-projection images I(x, y) and their feature-extracted version I^(x, y|n_thv) of specimen AD1 by using HH polarized signals at full bandwidth. With the selection of critical n_thv, the generated I^(x, y|n_thv) captures the main feature of the original back-projection images I(x, y). The feature-extracted images using VV polarized signals also provide similar result and are not repeatedly shown here. The Euler’s number of the intact-side image I^(x, y|n_thv = 0.81) is n_E = -1. For the damaged-side image I^(x, y|n_thv = 0.73), n_E = -2.

Fig. 6. Back-projection images and their feature-extracted version of specimen AD1 (HH polarization, full bandwidth, θ =15°)

 

Following the same procedure described above, I^(x, y|n_thv) can be produced for other incident angles, resulting in the intact-side and damaged-side curves n_E(θ) of specimen AD1, as shown in Fig. 7. The nEð?Þ curves in Fig. 7 demonstrate the sensitivity and effectiveness of incident angle with respect to the damage indication by using Euler’s number. Since the scattering caused by defects is angle-dependent, evaluating the structure by using images at several incident angles is needed. This leads to theapplication of an averaging filter to obtain n^f_E(θ) curves.

Fig. 7. Original n_E(θ) curves of the intact and damaged surfaces of specimen AD1

 

Effect of Filtering

Fig. 8 shows the n_E(θ) by using a filter length (data points) of L = 3. In Fig. 8, the filtering processing produces a clear separation between the intact-side and damaged-side n_E(θ) curves, except in the specular dominant region [? ? (-10°, 10°)]. The values of n_E(θ) of the intact-side images are in general greater than the ones of the damaged-side images since the presence of defect signals creates more holes in the images, resulting in smaller values of n_E(θ). In addition, the filter length is related to the required amount of angular measurements for achieving a globally consistent assessment. In this case, at least three angular measurements (data points) are needed for each comparison between the images of intact and damaged structures.

Fig. 8. Filtered nE curves of the intact and damaged surfaces of Specimen AD1

 

Conclusion

  • Pattern recognition of the reconstructed images by using morphological operations provides a quantitative evaluation tool for distinguishing the responses of intact and damaged structures using radar images.
  • In producing the feature-extracted images of structures, the critical threshold value (n_thv) must be determined. This step is important to reliably render a representative version of the original back- projection image for the image quantification by using Euler’s number (n_E).

  • As evaluated by using a global index (Euler’s number, n_E), the presence of a defect results in the fluctuation of defect scattering signals in the images, creating more holes in the images and leading to a smaller n_E(θ).

 

 

Reference

  • Yu, T. A distant damage assessment method for multi-layer composite systems using electromagnetic waves, Journal of Engineering Mechanics, ASCE 2011; 137 (8): 547-560; doi:10.1016/j.conbuildmat.2007.09.009 (pdf)