### 1 Introduction

### 2 Detection Theory of Induction Thermography

### 2.1 Principle of IT

*δ*is the penetration depth,

*σ*is the electrical conductivity,

*μ*is the permeability, and

*f*is the excitation frequency. The skin depth equation is used to calculate the lift-off of the copper coil and specimen. The excitation frequency,

*f*, and the penetration depth,

*δ*, have an inverse relationship, so lift-off must be set considering the set excitation frequency. Where can be calculated as:

*μ*

_{0}means the permeability magnetic field constant in a vacuum state, the constant value is 4

*π*× 10

^{−7}[H/m].

*μ*

*is the relative magnetic permeability, and means a scale by which the degree of magnetization of the material can be compared. Magnetic flux density, which is the magnetic field induced in a space filled with a material such as an iron core in a coil wound with wire, varies depending on the material.*

_{r}*ρ*is the density,

*c*

*is the heat capacity,*

_{p}*λ*is the thermal conductivity, and q is the heating power. The heat due to joule’s heating, q, can be expressed as:

*J*is the current density,

*E*is the electrical field vector. Fig. 1 shows the principle that when a current flows through the copper coil, the magnetic field is formed around it and the current is induced in the magnetic material.

### 2.2 Theory of GF-based FFT

*H*(

*u*,

*v*) is the frequency domain of GF, (

*u*,

*v*) is coordinate of frequency domain,

*u*

_{0}and

*v*

_{0}are center position of GF,

*σ*

*and*

_{u}*σ*

*are standard deviation of gaussian distribution.*

_{v}*F*(

*u*,

*v*) is the image with the FFT applied to thermal image

*F*(

*x*,

*y*) and

*G*(

*u*,

*v*) is the image of frequency domain. And then, if the inverse transform is performed on

*G*(

*u*,

*v*) again, it is as follows.

### 2.3 Principle of VDSR Algorithm

### 3 Experimental Setup

### 3.1 Description of the Laboratory Setup

### 3.2 Steel Specimen

### 4 Results of Inductive Thermography

### 4.1 Acquiring 2D Thermal Image and Trend Analysis

### 4.2 Thermal-noise Removal Using GF-based FFT

### 4.3 Resolution Improvement Using VDSR

### 4.4 Binarization Applied Morphology Operation

*t*is the thresholding value,

*ω*

_{0}(

*t*) and

*ω*

_{1}(

*t*) mean the cumulative probabilities of classes 0 and 1, respectively.

*m*

_{0}(

*t*) and

*m*

_{1}(

*t*) mean the cumulative average of classes 0 and 1, respectively.

*arg*max is the variable

*t*with maximum value. The otsu algorithm selects the optimal binarization threshold by calculating the maximum value.

### 4.5 MOT-based Slit Detection

### 5 Conclusions

1) After acquiring thermal images for each moving speed, thermal contrast was analyzed through the profile. It can be seen that the faster the moving speed, the higher the thermal contrast between the defective area and the sound area.

2) The problem of localized thermal concentration was solved using the FFT algorithm based on gaussian filtering. In addition, the resolution of the image was improved using the VDSR deep learning. The PSNR value evaluated the quality of the entire area rather than the ROI, so there was no significant difference. However, when the VDSR algorithm was applied, the NIQE value was greatly improved. Typically, it improved to 124.066% at 5 mm/s and 132.209% at 15 mm/s.

3) The otsu algorithm with morphological calculation was used to acquire a binarized image with pixel noise removed. Binarization conversion of the image to which the VDSR algorithm was applied was performed using the otsu algorithm. In addition, pixel noise was removed using the morphology calculation techniques bwareaopen, strel, and imfill functions.

4) The MOT algorithm was used to track the slits in images to which the VDSR was applied. Although all slits could be traced, there were frame sections where blob analysis was affected by the coil, and confusion occurred.