**5. Under what conditions the craters are not detected**

The higher the successful detection rate is, the lesser the false alarm rate will be. When the detection rate is 80%, the false alarm rate is just 17% whereas for the detection rate of 73%, the false alarm rate increases to 25%. The authors have plotted the graph of successful rate detection versus the false alarm rate as can be shown in Figure (18) below. The FAR (False Alarm Rate) is the percentage of non-signals that were detected as signals (craters) and is calculated based on the number of false alarms and the correct-rejections which can be formulated as [19]:

FAR = Num. Of False alarms/(Num. Of False alarms + Number of Correct-Rejections) (26)

The number of false alarm in this case can be referred to as a signal that was not presented but was mistakenly detected by the system whilst correct rejections can be referred to as a signal that was not presented and not detected by the system at all. The lesser false alarm rate in the system is, the better the system/algorithm will be. The main reason that brought these false alarms is the assumption of the sun angle that will lead to a faulty detection of true crater pair (true light patch connected to a true dark patch) hence will decrease the accuracy of the detection rate.

As in any true scenario, an image has to be captured first before the system can detect the safe landing sites that are free from hazards (craters). As mentioned before, this algorithm is assuming that the authors know the sun's direction and will be using the sun angle as one of the steps to detect the craters on the moon's surface. But, there will be some errors when the authors assume the sun angle without knowing its true direction. This assumption will affect the algorithm to pick up the wrong pairs (light patches will be connected to wrong dark patches and vice versa). Nowadays, the authors can obviously determine the sun elevation by many ways from the satellite system or LIDAR.

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

that lies on the **x** axis.

the signal strength [9].

formulated as [19]:

accuracy of the detection rate.

1. That is why those (1.0000,-0.0049,-0.0007) values when squared, summed them all and squared root them back, the authors will have more than 1. By theory, this value should be 1 and the reason for this error is maybe due to MATLAB that has rounded the value of 1.0000

Furthermore, in order to evaluate the error of the ellipse that the authors reconstruct, the ellipse itself has an error on the image. This is because of the digitization of a real shape that has an inherent loss of information c compared with the original shape. One should notice that there is no possibility that the original ellipse can be recovered from the digital ellipse but the errors can be optimized by increasing the picture resolution of an image. If the image is unclear or has a poor resolution, the authors can pre-process the image to reduce the presence of noise in the original image by using a smoothing technique [9]. This smoothing technique is carried out by implementing the low-pass filter to the original image. The main purpose is to attenuate the high-spatial frequencies by keeping the low spatial frequencies of

Besides, what cause the error are the uncertainties that appear from hardware (altimeter, satellite, or radar), software (MATLAB) and also the landing site topography itself. In a real situation, the sensor noise that comes from the altimeter also has to be considered a noise as

The higher the successful detection rate is, the lesser the false alarm rate will be. When the detection rate is 80%, the false alarm rate is just 17% whereas for the detection rate of 73%, the false alarm rate increases to 25%. The authors have plotted the graph of successful rate detection versus the false alarm rate as can be shown in Figure (18) below. The FAR (False Alarm Rate) is the percentage of non-signals that were detected as signals (craters) and is calculated based on the number of false alarms and the correct-rejections which can be

FAR = Num. Of False alarms/(Num. Of False alarms + Number of Correct-Rejections) (26)

The number of false alarm in this case can be referred to as a signal that was not presented but was mistakenly detected by the system whilst correct rejections can be referred to as a signal that was not presented and not detected by the system at all. The lesser false alarm rate in the system is, the better the system/algorithm will be. The main reason that brought these false alarms is the assumption of the sun angle that will lead to a faulty detection of true crater pair (true light patch connected to a true dark patch) hence will decrease the

As in any true scenario, an image has to be captured first before the system can detect the safe landing sites that are free from hazards (craters). As mentioned before, this algorithm is assuming that the authors know the sun's direction and will be using the sun angle as one of the steps to detect the craters on the moon's surface. But, there will be some errors when the

it will affect the accuracy of the results determined by the system.

**5. Under what conditions the craters are not detected** 

**Figure 18.** Relationship between successful detection rate and false alarm rate for the proposed craters detection algorithm

This algorithm is not effective on a noisy image with lots of tiny craters, undesired features that look like a crater, the craters' rims which are overlapping and segmented as well as a blurry image. Besides, an image with a too high or too low of sun elevation angle will make the system unable to differentiate the pattern (the light and the dark patches/blobs) and thus, influence the craters to be rarely detected by the system/algorithm. The algorithm will work accurately/efficiently with a sun elevation angle between 10 degrees to 50 degrees based on the experimentations under different image conditions earlier. With noisy image, the only way to reduce the tiny blobs is by using the function in MATLAB called '*bwareaopen*'. As discussed before, this function removes from a binary image all connected components (objects) that have fewer than G (set by the authors) pixels, producing another binary image. Figure (21) below is an example of the image if the algorithm does not apply the '*bwareaopen*' function to eliminate tiny blobs which makes the algorithm becomes ineffective while Figures (14) and (15) above show the detected craters after the function '*bwareaopen*' is applied. The detection rate falls to only 36% and the difference of accuracy is very obvious which is about 37%. To capture an image with a clear pattern of light and dark patches, it is vital as it is one of the most important features to improve the accuracy of the system detection.

Therefore, the image has to be taken by the spacecraft's camera under ideal sun elevation angle (not too low and too high) and a low noise image is a bonus.

However, for the advantages, the algorithm itself can detect the craters without knowing the main parameters such as the size (radius/diameter or the gradient of the craters). It is an uncomplicated detection algorithm and has a fast detection performance. Under a clear image (low noise, good lightning condition and ideal sun elevation angle) where the pattern is easily distinguishable, the accuracy will be much higher. Besides, the craters detection is independent of the shape detection whether it is a circle or an ellipse.
