b. Parameter Settings

For the Harris detector, the threshold of the Harris operator is normalized between 0 and 1, and it is set to 0.1 in the following experiments. For the SAR-Harris detector, the first scale is set as σ = 2, the constant between two adjacent scales is set as *k* = 21/3, the number of the scale layer is set to 8, and the arbitrary parameter is set as *d* = 0.04. Based on our previous experience, the threshold in the keypoint detection of the simulated optical image is set between 1 and 5, and that of the SAR image is set between 5 and 10. Other parameters used in the experiments follow the parameter settings suggested in Reference [25]. The m+M-Harris and UMPC-Harris are both based on PC. For fairness, the parameters of the PC method are tuned to the same value at each noise level. The PC is calculated in four scales and six orientations. The wavelength of the smallest filters is set from 3 to 5 pixels, according to different images. The scaling factor between successive filters is set to 1.6. In the experiment, the parameters are selected as *Sn* = 4, *Sm* = 5, *nop* = 20, and the number of moments of the PCM is selected as *n* = 5 and *h* = 0.5. The array of parameters *kt* is [−1, −0.5, 0, 0.5, 1].

#### 3.1.3. Influence of Noise Level on Proposed UMPC-Harris Detector

To assess the robustness of the feature detector to noise, the HR optical images are utilized to generate simulated optical and SAR images by adding Gaussian noise and speckle noise, respectively. The simulated optical image is obtained by adding Gaussian white noise with 0 mean and 0.01 variance. In the simulated SAR images, the noise level is defined to describe the degree of multiplicative noise. The multiplicative noise with a different number of looks is simulated from one-look to nine-look in the simulated SAR image. It decreases with an increase in the SAR number of looks. A high number of looks refers to a small noise level in SAR images. The simulated images are shown in Figure 8.

**Figure 8.** Simulated images. (**a**) Group 1 HR optical image; (**b**) Group 1 simulated optical image; (**c**) Group 1 simulated SAR image (five-look); (**d**) Group 2 HR optical image; (**e**) Group 2 simulated optical image; (**f**) Group 2 simulated SAR image (five-look); (**g**) Group 3 HR optical image; (**h**) Group 3 simulated optical image; (**i**) Group 3 simulated SAR image (five-look).

With the SAR noise level ranging from 1 to 9, the repeatability rate of the UMPC\_Harris detector is compared to three other detectors, Harris, Sar-Harris, and m+M-Harris. For fairness, each detector extracts approximately 600 pairs of points by adjusting the threshold, and the average value of ten calculations is taken as the experimental result. The curves of the repeatability rate with the SAR noise level in the three groups are shown in Figure 9.

**Figure 9.** Repeatability rate with different SAR noise level. (**a**) Group 1; (**b**) Group 2; (**c**) Group 3.

The repeatability rate of the UMPC-Harris is the highest among the four detectors in the three groups, and it is more robust to noise than the other detectors. SAR-Harris and m+M-Harris have similar repeatability rates as that of the SAR noise level. Their repeatability rates are between 0.5 and 0.3. When the SAR noise level is high, the repeatability rate of the UMPC-Harris is still higher than 0.4. When the SAR noise level is small, the differences between the two simulated images caused by noise are small, and hence, the three methods show good performance, except for the Harris detector. The repeatability rate of the Harris detector is lower than 0.4, and it decreases rapidly with an increase in the SAR noise level. It is difficult for the Harris detector to deal with multiplicative noise in SAR images directly.

#### 3.1.4. Influence of Radiometric Changes on Proposed UMPC-Harris Detector

To assess the robustness of the feature detector to nonlinear radiometric differences, HR optical images are utilized to generate an image with non-uniform radiometric differences. This is achieved by multiplying the HR optical image by a variable coefficient according to the change of the image column. The results are shown in Figure 10.

**Figure 10.** Results of original image and non-uniform radiometric differences.

The four detectors are tested on these images. Each detector extracts approximately 600 pairs of keypoints by adjusting the threshold properly, and the experiment results are shown in Figure 11. Furthermore, the repeatability rate of the four detectors are presented in Table 1.

**Figure 11.** Comparison of keypoint detection. (**a**) Harris; (**b**) SAR-Harris; (**c**) m<sup>+</sup>M-Harris; (**d**) UMPC-Harris.

**Table 1.** Repeatability rate of the detectors on the images with non-uniform radiometric differences.


The repeatability rate of the UMPC-Harris is the highest among the four detectors. One can see that the keypoints detected by UMPC-Harris are distributed more uniformly over the image than other detectors, which illustrates that the UMPC-Harris is more robust to radiometric variation and it further indicates that the UMPC-Harris can be applied to keypoint detection for images with radiometric differences.

#### 3.1.5. Results and Discussion of the Proposed UMPC-Harris Detector

The results of corner detection by UMPC-Harris on a pair of optical and SAR images are shown in Figure 12. They include images of a suburban in Weinan, Shaanxi, China. The size of the optical image and SAR image are 863 × 761 and 858 × 761, respectively. The optical image is obtained by Google Earth, and the SAR image is obtained by Airborne SAR. The resolutions are both 3.2 m/pixel. The comparison results indicate that the UMPC-Harris detector is able to extract uniformly distributed in the entire image and avoid missing keypoints at the border of the block.

**Figure 12.** Corner detection results of UMPC-Harris. (**a**) Optical image; (**b**) SAR image; (**c**) UMPC-Harris on optical image; (**d**) UMPC-Harris on SAR image.

The comparison of the repeatability rates of the four detectors indicates that the proposed UMPC-Harris detector has the highest repeatability rate. It is more robust to noise and it has better resistance to radiation differences. The reasons are listed below.


#### *3.2. Performance Experiments of Proposed ROS-PC Registration Algorithm*

To evaluate the performance of the ROS-PC, it is compared with two other state-of-the-art algorithms, namely OS-SIFT [28] and RIFT [39]. The OS-SIFT is a feature-based method, and ROEWA and Sobel operators are used to calculate consistent gradients for optical and SAR images. The RIFT is a PC-based method that detects corners and edge points on the PC map, and it proposes a MIM for feature description. Both the OS-SIFT and RIFT exhibit good performances on multi-sensor image registration. The comparative programs are obtained through their respective academic home pages. Subjective and objective criteria are used to evaluate the performance of the registration algorithm.

#### 3.2.1. Evaluation Criteria of the Registration Algorithm

The checkboard mosaic image and enlarged sub-images are displayed to observe the effect and details of image registration. For each test image pair, each algorithm is executed ten times, and the average of the ten results is computed as the final result. The following evaluation criteria are used to analyze the performance of the algorithm objectively and quantitatively.

Root mean square error (RMSE): This criterion is used to measure the accuracy of the image registration algorithm and is computed by the following method.

First, approximately 20 pairs of corresponding points are manually selected from the optical and SAR images to estimate the affine transformation matrix H. The coordinates of *ith* correctly matched keypoints are (*xoi*, *<sup>y</sup>oi*),(*xsi*, *<sup>y</sup>si*). The RMSE is computed as [26]:

$$RMSE = \sqrt{\frac{1}{N\_{\text{cor}}} \sum\_{i=1}^{N\_{\text{cor}}} \left( \mathbf{x}\_i^o - \left( \mathbf{x}\_i^s \right)' \right)^2 + \left( y\_i^o - \left( y\_i^s \right)' \right)^2} \tag{21}$$

where *Ncor* is the number of correctly matched keypoints after the fast sample consensus (FSC) [43], ((*xsi*),(*ysi*)) and it denotes the transformed coordinates of (*xsi* , *ysi*) by the estimated transformation matrix H.

Number of correct matches (NCM): The NCM is the number of correctly matched keypoints after the FSC. If the NCM of an image pair is less than four, the matching is considered to have failed.

A small RMSE indicates that the accuracy of optical and SAR image registration is high. A large NCM indicates that there exist more correctly matched keypoints, thereby resulting in a more accurate transformation matrix H.

3.2.2. Datasets and Parameter Settings of the Registration Algorithm
