# A Two-Stage Registration Strategy for Thermal-Visible Images in Substations
## 2 Proposed Methodology
### Second Registration
#### 2.2.2 Adaptive-Downsampling-Unit PIIFD  
PIIFD was originally designed to register blurred multi-modal retinal images. The thermal-visible-image registration with a monitoring video as the information source that was studied in this paper also has the problem of poor image quality, and registration occurs between images of different modes. Therefore, PIIFD was selected as the descriptor of feature points.  
However, the scale difference between the medical images registered by the PIIFD algorithm is usually very small, and the local window, with a size of 40 \(\times\) 40 pixels, in the feature point field is used for feature description, so the scale invariance cannot be realized at the beginning of the design. For the thermal image and visible-light image pair, due to the large difference in scale in the parameter setting of the sensor, the local feature information is quite different, which makes the traditional PIIFD unable to describe it effectively.  
In order to solve the above problems, MS-PIIFD achieves multi-scale feature description by constructing a Gaussian pyramid of the image. It gradually downsamples the original image and blurs the images at different scales, and then obtains the neighborhood information of Harris corners in the whole scale space for feature description. This method is used to complete the registration task of multi-modal remote sensing images at different scales, and has good scale invariance.  
However, MS-PIIFD relies too much on experimental experience to set parameters when constructing the scale space of the image, which is feasible for highly fixed remote sensing images. However, the monitoring camera that is used for fire detection will produce displacement or adjust the internal parameters of the sensor under different conditions  
Figure 3: Process of the second registration.  
according to the actual needs. These changes will result in varying scales in the output image.  
In order to cope with this situation, this paper proposes adaptive downsampling unit PIIFD to solve the problems caused by this special scenario. Figure 4 shows how ADU-PIIFD gradually reconstructs the scale space. Once the sensor parameter's interval changes, the comprehensive registration index \(\lambda_{i}\) under different downsampling times is recalculated, and the index is defined as follows:  
\[\lambda_{i}=(P_{i}\omega_{p},\frac{\omega_{t}}{ART_{i}}) \tag{4}\]  
where \(i\) is the number of downsampling images; \(P\) is the matching accuracy, which is calculated using the ratio of the correct matching number of corresponding points to the total matching number. \(\omega_{p}\) is the additional weight of the matching accuracy, and the default setting is 0.5. \(ART\) is the average running time of the extracted descriptor, \(\omega_{t}\) is the additional weight of the average running time, and the default setting is 0.5. The best comprehensive registration index can be defined as:  
\[\lambda_{k}=\max\{\lambda_{1},\lambda_{2}\cdots,\lambda_{i}\} \tag{5}\]  
where \(k\) is the number of target downsamplings.  
After selecting the optimal downsampling unit, the scale pyramid of the image in this cycle is constructed, and the optimization process is activated at the beginning of each cycle. In addition, the different requirements of practical engineering can be met by adjusting the proportion of additional weights.