*5.1. Determination of the Threshold Dis and Searching Radius*

In the initial image matching process, the image geographic coordinates served as the constraint and the threshold *Dis* were determined by SSS location error. Usually, SSS is installed in a towfish and towed by a cable behind a surveying vessel for seabed surveying, which is shown in Figure 1a. During this process, the towfish positions can be estimated by Equation (6).

$$
\begin{pmatrix} \mathbf{x}\_{\text{towfish}} \\ \mathbf{y}\_{\text{towfish}} \end{pmatrix} = \begin{pmatrix} \mathbf{x}\_{\text{tresel}} \\ \mathbf{y}\_{\text{tresel}} \end{pmatrix} + \begin{pmatrix} L \cdot \cos \alpha \cdot \cos(A + \pi) \\ L \cdot \cos \alpha \cdot \sin(A + \pi) \end{pmatrix} \tag{6}
$$

where, (*xtowfish*, *ytowfish*) and (*xvessel*, *yvessel*) are respectively the coordinates of the towfish and vessel tow point, *L* is the cable length, α is the angle between the cable and horizontal direction, *A* is the vessel heading. Affected by the vessel velocity variation, the accuracies of vessel positions and heading data, the towfish position error *dtowfish* can be determined by Equation (7).

$$d\_{\text{bwfish}} = \sqrt{d \mathbf{x}\_{\text{bwfish}} ^2 + d y\_{\text{bwfish}} ^2} = \sqrt{d \mathbf{x}\_{\text{resed}} ^2 + d y\_{\text{resed}} ^2 + L^2 \cdot \sin^2 a \cdot da^2 + L^2 \cdot \cos^2 a \cdot dA^2} \tag{7}$$

where, (*dxtowfish*, *dytowfish*) and (*dxvessel*, *dyvessel*) are respectively the towfish and tow point position errors in *x* and *y* directions, *d*α is the variation range of the angle α, *dA* is the heading difference between the vessel and towfish. For most SSS measurements in offshore waters, the vessel position error is about 1~3m; the length of the cable is about 10~20m; the angle α is about 30◦ and its variation range is about 10◦; the heading difference between the vessel and towfish is about 1◦–5◦ [44]. After substituting these values into Equation (7), the *dtowfish* ranges roughly from 10 to 100 m. The above parameters will become bigger with the increase of surveying vessel size in open sea. In this experiment, the sea was calm and the vessel's course was steady. Thus, the *dtowfish* was about 18 m, which served as a referenced threshold in the initial image matching. To determine the optimal threshold, different thresholds in Equation (2) were used by referring to *dtowfish* and the matched results are shown in Table 4, which shows that the detected matched points increased as the threshold became larger but the number of correct ones peaked when the threshold was 20. Thus, the initial matched result was obtained with this threshold and followed by the finer matching.

**Table 4.** The matching results of different thresholds.


In the finer matching process, the template matching strategy was used and the searching radius for better matches was determined. A small searching radius is not enough for finding better matches while a large one will cost more time and the matched results may also not be the optimal. During the finer matching process, different searching radiuses were used and the matched results are shown in Table 5. This indicated that 20 m could be adopted as a suitable searching radius in the finer matching step as most correct matches were obtained when using this value.


**Table 5.** The matching results of different searching radiuses.
