**8. Conclusion and recommendation**

516 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

the authors take the solution 2 as a disc reconstructed position.

bounding ellipse algorithm. At the end of the experiment, the results from the reconstructed algorithm are satisfactory and similar to the results from the bounding ellipse algorithm. The positional error evaluated for both two solutions are shown in the table below. The one which has a low error will be taken as a true position. As can be seen in the results below, the positional errors are quite high from both solutions that are 8.8722 and 8.8715. Therefore,

**Figure 23.** Artificial image of ellipse processed using minimum bounding ellipse with Khachiyan

The positional errors are evaluated as shown in Table (3) below. Unlike before, the causes of the errors in the disc position are something similar to what were discussed in the previous 4.1.2.4 section. The positional error can be in any circumstances such as pixellation, the bounding ellipse algorithm error, MATLAB rounding figures as described before, uncertainties from the hardware and the like. These are the reasons why the authors tend to have quite a high number of errors on the position determination part. Besides, when the authors have the ellipse that is too eccentric, both the outputs of the reconstruction

The ellipse bounding algorithm also has an error in bounding the targeted patch. As can be seen in the Figure (26) above, the targeted ellipse is not totally bounded by the red lines and this will affect the output of the image plane ellipse parameter such as semi major axis and semi minor axis. Hence, these parameters will also affect the output of the reconstruction algorithm and will cause errors in the disc's position. In practice, the way to overcome this

Algorithm

algorithm will become complex.

This paper focuses primarily on the identification and detection of craters on a lunar's surface. To realize these goals, an algorithm to detect craters which happen to be the main hazardous features on lunar is proposed. The authors divided the evaluation of this algorithm into a flowchart as presented in the methodology section. First, using the original image of craters on the moon's surface, the authors convert the RGB image plane to HSV image plane and analyze only the Value parameter of a HSV plane. Further, the thresholding is applied to the image for classification using this Value and thresholding approaches by Sawabe et al. After these classifications of images between light and dark patches, the authors have labelled them and determined the centre of each patch using 'regionprops' function. This stage is then followed by a vital stage in determining the best craters of all using two proposed methods: the minimum distance determination and angle measurement. This is a new and simple method proposed by the authors in detecting craters as main hazardous features on the moon's surface.

For precise moon landing, the authors then proposed the geometrical analysis consisted of projection or reconstruction of the ellipse to a 2-D circle on an image plane. At this stage, the authors applied the bounding ellipse algorithm as a first step in modelling a crater as a disc. The authors then calculated all the ellipse parameters using the information embedded in the output of bounding ellipse algorithm, then drew the bounding ellipse around the targeted patch. This output will then be used in ellipse reconstruction algorithm in order to get the orientation, *p* and further position, *q* of the disc (crater) from the camera's projection.

There are some limitations that have to be stated here for further extension and modification. For the craters detection algorithm, it is dependent on the sun angles and these assumptions will lead to an error of detecting a true pair (light and dark pairing patch). In addition, there are uncertainties as discussed before from the software (MATLAB) and the hardware itself in a real application (altimeter to measure the altitude). The Hough method seems to give more precise results but have a constraint in the shape of a crater itself. For an instance, the reconstruction needs to analyze a crater as an ellipse model instead of a circle. In Hough ellipse transformation, the authors have to analyze the ellipse in 5 dimensions instead of 3 dimensions in a circle. These limitations make the Hough Transform method to be unreliable and make its computational method a burden to use together with this craters detection algorithm

For future works, this useful research can be extended to a crater pattern matching as described in the Literature Review section above. Craters Pattern matching is proposed by previous researchers to attain the position and velocity estimation of a spacecraft and a Lander during Entry, Descent and Landing (EDL) purposes and also for autonomous precision landing purposes. By making a pattern matching, one can get the differentiation between the position determined by the pattern matching and those from the reconstruction algorithm. The errors in the crater's position between these two methods can be evaluated to determine which is better in a real application. In reality, the lunar's surface is not flat and the camera parameters will not usually estimate perfectly. The image does require scaling, but the true amount is impossible to be identified without also knowing the camera's specifications (focal length and field of view). In most cases, the picture is not usually taken straight at the centre of the image and perspective distortion will have an effect as discussed before. As none of these are true in real applications, the need of the reconstruction algorithm to find the position of the crater is high. The crater's position determination and evaluation of this reconstruction algorithm were discussed in detail in the previous section. Then, the authors can determine the velocity of the spacecraft based on the position and the orientation of the crater. The idea is, if the authors can find the position and orientation in a single frame, then the velocities are the difference from one frame to the other one. Therefore, this research has a great valuable for future works. In addition, this research is a very worthy research indeed and has valuable benefits to any spacecraft missions in order to avoid the hazardous craters (feature proposed) and for a moon Lander to have a precise landing on a Lunar. Besides, the authors can compare the position determined using equation *q* and the position determined using the craters pattern matching and this will be a noble future work for new researchers.
