Optimizing Image Compression Ratio for Generating Highly Accurate Local Digital Terrain Models: Experimental Study for Martian Moons eXploration Mission

Abstract

Recent technological advances have significantly increased the data volume obtained from deep space exploration missions, making the downlink rate a primary limiting factor. Particularly, JAXA’s Martian Moons eXploration (MMX) mission encounters this problem when identifying safe and scientifically valuable landing sites on Phobos using high-resolution images. A strategic approach in which we effectively reduce image data volumes without compromising essential scientific information is thus required. In this work, we investigate the influence of image data compression, especially as it concerns the accuracy of generating the local Digital Terrain Models (DTMs) that will be used to determine MMX’s landing sites. We obtain simulated images of Phobos that are compressed using the algorithm with integer/float-point discrete wavelet transform (DWT) defined by the Consultative Committee for Space Data Systems (CCSDS), which are candidate algorithms for the MMX mission. Accordingly, we show that, if the compression ratio is 70% or lower, the effect of image compression remains constrained, and local DTMs can be generated within altitude errors of 40 cm on the surface of Phobos, which is ideal for selecting safe landing spots. We conclude that the compression ratio can be increased as high as 70%, and such compression enables us to facilitate critical phases in the MMX mission even with the limited downlink rate.

1. Introduction

In situ observations from robotic explorations, such as the Hayabusa [1], Hayabusa2 [2], Rosetta [3], and OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer) [4] missions, have significantly contributed to expanding our understanding of the solar system. Subsequently, more deep space exploration missions are planned to be launched [5,6,7,8]. In these exploration missions, we can expect to obtain a large amount of scientific data relatively easily due to recent technological advances. However, the longer distances between spacecraft and the ground, coupled with limited transmission power constrained by several factors such as antenna size and power consumption, often result in significantly low downlink rates. Smart data handling strategies must, in this regard, be considered within the constraints of limited downlink rates to maximize scientific returns from future deep space exploration missions.

The limited downlink speed can be one of the biggest issues for the Japan Aerospace Exploration Agency (JAXA)’s Martian Moons eXploration (MMX) mission, which is scheduled to be launched in 2024 [9]. Specifically, this mission will explore the moons of Mars, Phobos, and Deimos to determine their origins and evolutions. There are several theories on the formation mechanisms of the two moons. The basic parameters, such as their small sizes, low bulk densities, irregular shapes, and low albedos, and the visible to near-infrared reflectance spectra lead to the captured asteroid origin theory, where primitive carbonaceous chondrites originating at the outside of Mars’s system could be captured by Mars’s gravity [10,11,12]. On the other hand, their orbital parameters, including the low orbital inclinations and eccentricities, and some numerical studies support the giant impact origin theory, where ejecta materials could accrete and form the moons after a giant impact on Mars [13,14,15,16,17,18,19].

To conclude this discussion about the origins, the MMX mission is planned to perform landings on Phobos (ideally two times on different sites) and collect surface materials ($\ge 10 \mathrm{g}$), which will be returned to Earth in 2029 and analyzed in laboratories [9]. Although previous missions such as the Hayabusa [1], Hayabusa2 [2], and OSIRIS-REx [4] missions performed touchdowns (instant contacts on the surfaces within a second) and collected samples from the surfaces of asteroids, the landing and sampling in MMX missions have become more challenging in that the spacecraft will have to safely land and stay for approximately 2.5 h on Phobos [20], where knowledge of the surface is limited. Nevertheless, Phobos is expected to contain plenty of topographic irregularities including slopes [21], craters [22,23,24,25,26,27], rock particles (i.e., boulders, cobbles, and pebbles) [28], and grooves [23,24,28,29,30,31]. The gravity of Phobos (~1/2000 G [32]) is also relatively higher than on any other small asteroids on which touchdowns were previously performed ($~{1/10}^5-{1/10}^4$ G [33,34,35,36,37]), so the landing site selection could be one of the most crucial phases for this mission.

Based on the current specifications of MMX spacecraft, we need to find flat regions with altitude differences smaller than 40 cm [38]. Although previous missions, such as the Mariner-9 [39], Viking-Orbiter [40], Mars Global Surveyor [28], Mars Express [41], Mars Reconnaissance Orbiter [42], and Emirates Mars [43] missions have observed Phobos or Deimos thus far, the resolutions of obtained optical images and three-dimensional shape models are insufficient considering this severe requirement for the landing sites. While some numerical studies have indicated the capability of finding smooth enough regions for the landing on Phobos [38], if we establish the safety of the spacecraft during landing as the ultimate priority, then the most practical strategy is performing in situ observations after the arrival and finding safe regions for the landings.

The MMX spacecraft is thus equipped with two optical cameras: the Telescopic Nadir Imager for GeOmOrphology (TENGOO) and the Optical RadiOmeter Composed of CHromatic Imagers (OROCHI) [44]. The high-resolution image capabilities of these cameras are critical for landing site selection. To map Phobos’s surface with a resolution of ~12 cm/pix from a quasi-satellite orbit (QSO) around the moon, the cameras have been designed to exhibit superior performance in comparison to optical cameras on previous sample return missions, such as AMICA of Hayabusa [45], ONC-T of Hayabusa2 [46], and OCAMS of OSIRIS-REx [47] missions. With a 3296 × 2472 pixel image size and a 16-bit depth, these specifications are significantly advantageous for minutely observing Phobos’s surface. However, this increased resolution results in a substantial image file size growth, with raw images potentially reaching 16.3 MB. Transmitting such large images to the ground could require over 1.1 h when utilizing the MMX’s typical telecommunication system with a speed of ~32 Kbps. This downlink duration is not practical given the limited observational period of the landing site selection, which is scheduled to be performed within approximately half a year and is severely constrained by illumination conditions determined by the relative positions of the spacecraft, Phobos, Mars, and the sun [20]. Additionally, the precise sample collection locations must be determined within the brief 2.5 h landing window, allowing under 1 h for downlinks.

One reasonable operation for transmitting such image data is to utilize data compression techniques, with numerous lossy compression algorithms that have been developed to reduce image file sizes significantly. Nonetheless, highly compressed images can become distorted and scientifically unusable. Optimizing image data handling, which will ensure data volume reduction without compromising scientific value, is, therefore, significant for future deep space exploration missions, including the MMX mission. While previous studies have analyzed the influence of data compression on images of exploration missions [48,49], to fulfill the requirements of the landing operations of the MMX mission, we mainly focus on the effect of image compression on the accuracy of local DTM generation to show whether such compressions lose any critical information necessary for selecting safe landing sites on Phobos (i.e., ~40 cm altitude differences).

2. Materials and Methods

2.1. Experimental Setup

Although previous studies showed the existence of various geological characteristics on Phobos, including craters, grooves, and boulders [23,24,28], the spatial resolutions of the images obtained by previous exploration missions are limited (lower than several meters per pixel), and the detail of the roughness is still unknown [38]. This knowledge gap will remain until the MMX spacecraft arrives at Phobos and reveals detailed surface structures through high-resolution images. Accordingly, we prepared simulated images of Phobos with both rough and smooth surfaces to accurately evaluate the influence of image compression on the selection of landing sites under various surface conditions of Phobos.

For the simulated images of a rough surface, we used the simulator for the OROCHI, an optical chromatic imager onboard the MMX spacecraft [44]. This OROCHI simulator has seven wide-angle bandpass imagers, with a pixel pitch of 5.86 $\mathsf{\mu }\mathrm{m}$ and a focal length of 12.5 mm, achieving an iFoV of 0.469 mrad/pix, which is similar to the iFoV of the OROCHI (0.44–0.46 mrad/pix [44]). The seven band-pass filters have wavelengths of 390 nm, 480 nm, 550 nm, 650 nm, 700 nm, 800 nm, and 950 nm, respectively (Figure 1a). Furthermore, these imagers are mounted on an aluminum frame and can operate simultaneously, allowing the camera to capture the same region on the Phobos surface in seven different colors, which is useful for determining suitable landing sites and identifying the uniformity or nonuniformity of the distribution of surface materials. In this study, we mainly focus on images obtained by the imager with the band-pass filter having the wavelength of 550 nm, a wavelength commonly used in previous exploration missions, including the Hayabusa and Hayabusa2 missions [45,46]. For the surface material, we used the University of Tokyo Phobos Simulant, Tagish Lake Based (UTPS-TB) [50]. This simulated Phobos regolith material is developed and processed using terrestrial soils and materials, exhibiting a reflectance spectrum similar to that of Phobos surface materials, which allows for the acquisition of images that closely resemble those anticipated from the MMX mission.

The images were obtained with the following experimental setup (Figure 1b). UTPS-TB was spread over a foundation with a size of approximately $60\times 120$ cm. The OROCHI simulator was fixed to a frame to prevent image blurring due to camera shake. This frame can be moved to capture images from different regions using the same imager. Images were taken from a height of approximately 70 cm directly above the foundation. A halogen lamp, whose wavelength domain was not covered by the seven band-pass filters, served as the light source, with an incidence angle (phase angle) of $30°$, an optimal angle for observing surface rocks. Each image had a size of $1920\times 1200$ pixels. Note that TENGOO and OROCHI use a 14-bit A/D converter, while the data are stored with a bit depth of 16 bits. To simulate this data structure, we converted 8-bit color images from the OROCHI simulator to 16-bit grayscale images, ensuring that each pixel value fell within the 14-bit depth range. Also, the OROCHI simulator images contained a dark surrounding frame due to the band-pass filters, which we excluded in the post-processing, as explained in Section 2.3.

With a similar procedure, we obtained simulated images of Phobos with a smooth surface (Figure 1c). In this experiment, we used a digital camera commercially available to simulate the same image size as OROCHI and TENGOO ($3296\times 2472$ pixels). We used a foundation with a size of $75\times 150$ cm having circular depressions, which simulated craters on Phobos. Also, we spread UTPS-TB over the foundation as a surface material. Images were obtained from a height of approximately 188 cm above the foundation. As for the procedure of the simulated images for the smooth surface, we converted 16-bit color images to 16-bit grayscale images to simulate the conditions of TENGOO and OROCHI.

2.2. Image Compression

The compression algorithm used in the MMX mission was specially developed by the manufacturer of the TENGOO and OROCHI. Although this algorithm is proprietary and not publicly available, we have verified that images compressed using this algorithm perfectly match with images compressed by the algorithm defined in the CCSDS 122.0-B-1. CCSDS 122.0-B-1 is a document, generally referred to as Blue Book, showing a recommended standard of image data compression specialized for use in spacecraft. Because the complexity of the algorithm defined in this book is sufficiently low, images can be compressed rapidly even with hardware onboard spacecraft, including the MMX. Thus, we used this algorithm to compress images in this study.

Note that the CCSDS 122.0-B-1 was recently updated to the CCSDS 122.0-B-2. Also, there is another algorithm defined in the CCSDS 123.0-B-2, along with other common algorithms such as JPEG, JPEG2000, JPEG-LS, which may offer better performance compared to the algorithm defined in the CCSDS 122.0-B-1. However, robustness and a significantly low probability of program errors or malfunction during image compression are essential requirements for the MMX mission. The algorithm adopted in the MMX mission, which has consistent outputs with the CCSDS 122.0-B-1, has passed countless severe tests performed by the manufacturer of the MMX spacecraft to show whether the algorithm fulfills these requirements. Therefore, we mainly focused on the algorithm defined in the CCSDS 122.0-B-1 in this work and performance comparisons with other compression algorithms could be a topic for further studies.

Image compression algorithms commonly perform two compression schemes: lossless and lossy compressions. In lossless compression, the original image data can be fully reproduced, while the compression ratio is substantially low (i.e., high data volume of a resulting product). Conversely, in lossy compression, the original image data cannot be fully recovered, but the compression ratio can be significantly high (i.e., low data volume of a resulting product). Considering the limited downlink rate of deep space exploration missions, including the MMX mission, low data volume of a resulting product is important, and thus, we mainly focused on the image-handling strategies using lossy compression. Note that some algorithms, including the one defined in the CCSDS 123.0-B-2, offer near-lossless compression, where the maximum error in the reconstructed image can be limited, while the data volume can be significantly compressed. However, the algorithm adopted in the MMX mission, as well as the one defined in CCSDS 122.0-B-1, does not support near-lossless compression. Therefore, in this study, we did not consider near-lossless compression.

The image compression algorithm defined in the CCSDS 122.0-B-1 (hereafter simply referred to as CCSDS) consists of two functional parts: a Discrete Wavelet Transform (DWT) module that performs decorrelation, and a Bit-Plane Encoder (BPE) which encodes the decorrelated data. The CCSDS supports two different types of DWT: integer-point DWT and float-point DWT, and a choice of DWT leads to slightly different procedures during image compression. The integer-point DWT requires integer arithmetic, and offers lossless compression, but it can also be used in lossy compression. Following the DWT, the wavelet coefficients are scaled using the weight factors before the encoding performed in the BPE. On the other hand, the float-point DWT requires floating-point calculations, and it can be used only for lossy compression. Following the DWT, the wavelet coefficients are rounded to the nearest integer before encoding in the BPE. Importantly, whether these two algorithms have consistent compression performances for images from extraterrestrial bodies, especially Phobos, has yet to be revealed. Therefore, this study examined both algorithms using integer and float points to determine the best compression scheme.

In practice, we used a public script published by the University of Nebraska (http://hyperspectral.unl.edu/download.htm) (accessed on 18 November 2023) for image compression using CCSDS. In this study, the compression ratio $p$ is defined as follows:

$$p=\left(1-\frac{{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}.}}{{\mathrm{S}}_{\mathrm{o}\mathrm{r}\mathrm{g}.}}\right)\times 100 \left[\%\right],$$

(1)

where ${\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}.}$ and ${\mathrm{S}}_{\mathrm{o}\mathrm{r}\mathrm{g}.}$ are the file sizes of compressed and original images, respectively. Note that during the CCSDS encoding process, only the number of bits per pixel specified by the user is utilized, leading to a partial reconstruction of the input image, which is essentially the compression process. Therefore, we controlled the compression ratio by adjusting the value that indicates the number of bits per pixel to be used during encoding.

2.3. Image Quality Assessment

We used several evaluation metrics to assess the influence of image compression on image quality, which included Peak Signal-to-Noise Ratio (PSNR), Signal-to-Noise Ratio (SNR), and Strucural SIMilarity (SSIM). PSNR is one of the most widely used image quality indices, representing the ratio between the maximum possible power of the image and the power of distorting noise that affect the quality of the image. PSNR is defined as

$$\mathrm{P}\mathrm{S}\mathrm{N}\mathrm{R}={\log }_{10}\frac{2^B-1}{\mathrm{M}\mathrm{S}\mathrm{E}} \left[\mathrm{d}\mathrm{B}\right],$$

(2)

where $B$ represents the dynamic range of an image (in bits). Also, $\mathrm{M}\mathrm{S}\mathrm{E}$ is Mean Squared Error, which is expressed as

$$\mathrm{M}\mathrm{S}\mathrm{E}=\frac{1}{w·h}\sum _i^{}\sum _j^{}{\left(x_{i, j}-{\widehat{x}}_{i, j}\right)}^2,$$

(3)

where $w$ and $h$ denote the image width and height, respectively. $x_{i, j}$ and ${\widehat{x}}_{i, j}$ represent the original and reconstructed pixel value in the $i$th row and $j$th column of the original and compressed images, respectively. The higher PSNR shows the higher quality of a reconstructed image.

SNR is also a common metric used not only for image quality analysis but for performance analysis of scientific instruments onboard spacecraft. Especially, we introduced SNR to evaluate the influence of image compression with the performance requirements of the camera onboard MMX [44]. In this study, SNR is defined as

$$\begin{array}{cc}\mathrm{S}\mathrm{N}\mathrm{R}\hfill & =\frac{{\mathrm{P}}_{\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{a}\mathrm{l}}}{{\mathrm{P}}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}}\hfill \\ & =\frac{\frac{1}{w·h}\sum _i^{}\sum _j^{}{x_{i, j}}^2}{\mathrm{M}\mathrm{S}\mathrm{E}}\hfill \end{array}$$

(4)

where ${\mathrm{P}}_{\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{a}\mathrm{l}}$ and ${\mathrm{P}}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}$ show the powers of the original image and the difference between the original and compressed images. The higher SNR also shows the higher quality of a reconstructed image.

Additionally, we analyzed the influence of image compression by using SSIM, which is also one of the most widely used image quality indices [51]. Essentially, the SSIM evaluates image quality based on three comparisons: luminance, contrast, and structure comparisons. SSIM values range from 0.0 to 1.0, where a higher value indicates better image quality. A value of 1.0 shows that a given image is identical to the original image. Importantly, compared to PSNR and SNR, SSIM is more specialized to evaluate image quality in terms of visual perceptions of objects in images [51], which is fundamentally important to recognize hazardous objects on Phobos and to identify the same objects or textures existing in multiple images in order to accurately generate local DTMs (i.e., key point matching, described in Section 2.4).

2.4. Generation of Local DTMs

Structure from Motion (SfM) is one of the most famous and widely used algorithms to generate three-dimensional shape models from images obtained by satellites, drones, and spacecraft, for instance. The planetary science domain has utilized SfM in addition to several other conventional techniques, such as aerial photogrammetric approaches based on stereo pairs [52], and small digital topography/albedo maps (L-map) determined from multiple images with stereophotoclinometry (SPC) [53]. A recent study revealed that the SfM’s accuracy is compatible with SPC [54]. In the MMX mission, SfM is considered a reasonable algorithm for generating local Digital Terrain Models (DTMs). Thus, we used SfM to generate local DTMs.

In practice, we utilized Metashape Pro (ver. 1.6.4), a commercial software program for generating three-dimensional shape models. We utilized parameters that are recommended for generating local DTMs with the highest possible accuracy as shown in

Table 1. Parameters used to generate local DTMs with high accuracy using Metashape.

Process	Parameter	Setting	Comments
Align photos	Accuracy	Highest	The program aligns photos with the highest accuracy.
	Generic preselection	On	The program makes low-resolution images and finds key points in order to decrease the process time.
	Reference preselection	On	The program generates a sparse point cloud by using the camera coordinates information input a priori.
	Key point limit	0	Key points will be generated without the limitation of the number of points.
	Tie point limit	0	Tie points will be generated without the limitation of the number of points.
	Adaptive camera model fitting	Off	When this parameter is set to be On, the camera parameters for fitting the distortion of the lenses will be determined, which is not necessary in this research.
Build dense cloud	Accuracy	Ultra high	The dense cloud is generated with the highest accuracy.
	Depth filtering	Mild	How aggressively the program filters outliers obtained from the depth computation. “Mild” is recommended.
Build mesh	Surface type	Arbitrary (3D)	“Arbitrary (3D)” means that the program generates a closed 3D shape model without any holes.
	Source	Depth maps	The program generates the mesh using all the information from the input images including assumed depth maps, which is recommended to use.
	Quality	Ultra high	The mesh is generated with the highest accuracy.
	Face count	100,000,000	We set the parameter large enough in order to generate meshes without any limitations of the number or meshes.

, although they significantly demand computational resources. To address this, we utilized high-end CPUs and GPUs (CPU of Core-i9 12900K and dual GPUs of GeForce RTX 3090) and reduced calculation times. Note that in the MMX mission, once we obtain images from the spacecraft, we need to generate countless local DTMs at the ground stations. This aims to quickly understand the detailed topographies of Phobos’s surface and select the best landing spots using these DTMs. Furthermore, such generation of the models should be performed repeatedly over ~6 months during the landing selection phase [20], as we need to update local DTMs when we obtain images with higher spatial resolutions or better observational conditions. Therefore, the process of generating multiple local DTMs with the highest possible accuracy, combined with the acceleration of processing time, as performed in this study, will be a crucial part of the preparation for the upcoming landing site selection phase in the MMX mission.

Local DTMs were created with Metashape through the following processes:

• Import images and image masks (i.e., binary images determining the processing areas) and set camera parameters (e.g., focal length and sensor pixel sizes).
• Georeference cameras by importing camera coordinate files, which define positions (coordinates) and orientations (directions) for each camera.
• Perform key point matching by identifying distinctive features in images that can be recognized in other images and matching the most prominent features across the image dataset.
• Perform bundle adjustment for three-dimensional geometry reconstruction using the network of matched features, incrementally adding images to update camera model parameters (e.g., focal length, radial distortion parameters) and camera orientations (i.e., positions, directions), and calculating three-dimensional coordinates for key points.
• Generate a sparse point cloud representing the three-dimensional coordinates of the most prominent features in the image dataset, realign images with large coordinate errors, and remove outliers by observing the point cloud from various directions.
• Build a dense point cloud by calculating depth and color information for each camera.
• Generate polygon meshes from the dense point cloud that express a detailed topography of the target shape.
• Generate image masks by selecting areas on the mesh with high confidence, created from many points in the dense point cloud. Using those image masks, regenerate the model.
• Generate the model’s texture by combining the original images seamlessly with the reconstructed polygon meshes.

Note that, to generate local DTMs with high quality, the amount of overlapping area in each image with other images is important. This scenario occurs because the large overlapping area leads to many reconstructed point clouds, resulting in a better quality of local DTMs. Thus, we first created models without any image masks (by Step 7). Then, we selected an area on each model where a large number of point clouds are reconstructed and generated image masks. Using these masks, we processed only portions in each image with large overlaps with others and improved the quality of local DTMs (Step 8).

3. Results

3.1. Phobos Simulated Images and Local DTMs

Figure 2 and Figure 3 show examples of the simulated images of Phobos with rough and smooth surfaces, respectively. Using the experimental setup with the rough surface, we obtained 10 images. The spatial resolution of these images is 0.379 mm/pix. On the other hand, by utilizing the experimental setup with the smooth surface, we acquired 44 images at a spatial resolution of 0.112 mm/pix.

Using these simulated images, we generated local DTMs for both rough and smooth surfaces (Figure 4a). For the rough surface model, we created a dense point cloud composed of 3,826,280 points, resulting in a mesh with 2,309,668 facets. The standard deviation of the elevation is 19.2 mm (Figure 5a). On the other hand, for the smooth surface model, we generated a dense point cloud containing 13,265,901 points, resulting in a mesh with 10,012,252 facets (Figure 4b). The standard deviation of the elevation is 8.99 mm, which is smaller than that of the rough surface model and indicates this model’s smoothness (Figure 5b). In this manner, we generated local DTMs having a substantially large number of facets, which are compatible with models that will be generated in the MMX mission. Note that generating local DTMs demanded ~3 min for the rough surface, compared to ~10 min for the smooth surface. They needed approximately 60% longer processing time if they were processed with a single GPU.

3.2. Influence of Image Compressions

We compressed the simulated images of the rough and smooth surfaces, employing different compression ratios using the two algorithms, CCSDS with float- and integer-point DWT (Figure 6 and Figure 7). Basically, the difference in image compression performance between the two algorithms is limited. In terms of processing speed, ~0.18 sec. was required for the rough surface simulated image and ~0.71 sec. for the smooth surface simulated image, consistently across both algorithms. Moreover, visual changes or distortions in simulated images are not distinctly noticeable until the compression ratio reaches 98%, and this result is consistently observed in both algorithms (Figure 6 and Figure 7).

The image quality evaluation performed using PSNR also demonstrates that the difference in distortion levels between CCSDS with float- and integer-point DWT is considerably limited (Figure 8). However, our quantitative analysis also reveals that image quality can decrease at varying rates as the compression ratio increases, depending on the surface characteristics depicted in the images (i.e., rough vs. smooth surfaces). Our result shows that simulated images of the smooth surface can be significantly affected by image compression even at lower compression ratios, whereas simulated images of the rough surface exhibit fewer distortions even at higher compression ratios, which suggests that the difference in surface roughness can be a more significant factor for the distortion due to image compression, rather than the difference in compression algorithms. Likewise, this result reflects the data processing performed using DWT.

Images inherently consist of both high-frequency and low-frequency structures. High-frequency structures correspond to details and textures in images, while lower-frequency structures represent broader and more gradual changes in an image, such as variations in brightness. In the CCSDS with the DWT, the wavelet coefficients representing the high-frequency structures are more aggressively quantized or truncated, especially at higher compression ratios. Consequently, these high-frequency components are more susceptible to distortion than the low-frequency ones. Figure 6 and Figure 7 also show this effect, where small topographic features and textures, which constitute the highest-frequency structures in our images, are highly distorted by image compression. Essentially, the simulated images for the smooth surface contain more information related to such small topographic features (high-frequency structures) compared to the simulated images for the rough surface. This ratio means the former is more susceptible to image compression at the same compression ratio.

Our analysis using SNR (Figure 9) also shows a consistent result, where the difference in the loss of image quality between the two compression algorithms is minimal and the simulated images for the smooth surface are more susceptible to image compression, compared to the simulated images for the rough surface. In the MMX mission, the OROCHI is mainly planned to be used to obtain high-resolution images of Phobos’s surface, and these images will be used to observe detailed topographies, generating the local DTMs. Kameda et al. [44] set the performance requirement of the OROCHI as SNR > 30 for an effective observation of Phobos’s surface and selection of the landing sites. To fulfill this requirement across all images, the compression ratio should be 70% or lower (Figure 9). Furthermore, our image quality assessment using SSIM (Figure 10) also shows that, if the compression ratio is 70% or lower, quality loss remains constrained across all images. With such compression ratios, we expect significant scientific information to be maintained. Therefore, we recommend compression ratios of 70% or lower to reduce the data volume and simultaneously retain important scientific information in the MMX mission.

4. Discussion

4.1. Effect of Image Compression on the Accuracy of Generating Local DTMs

With a compression ratio of 70%, we analyzed whether local DTMs contain critical errors (that is, over 40 cm altitude errors) to find safe landing sites for the MMX mission. We compared local DTMs generated from compressed images (compressed model) with the model generated from uncompressed images (original model). The error calculations were performed using CloudCompare (ver. 2.11.2), a public 3D point cloud and mesh-processing software. In the model comparison, we first accurately registered the dense point cloud of the compressed models to that of the original model by minimizing the distances between each point. Then, we computed those distances and recorded them as errors.

Figure 11 shows the compressed model for the rough surface, generated by 70% compressed images using CCSDS with float- and integer-point DWT. The models were each generated within a 2% difference in the number of dense points and meshes from the original model. Figure 12 represents the result of the smooth surface, with models generated with 3% differences in the number of dense points and meshes compared to those of the original. These results show that the qualities of the model generated are maintained, even when we used 70% compressed images.

Figure 11 and Figure 12 also show the errors of the compressed models from the original models. We showed that the compressed models for the rough surface could be generated with errors of $0.210\pm 0.145$ mm (CCSDS with float-point DWT) and $0.208\pm 0.146$ mm (CCSDS integer-point DWT), respectively. For the smooth surface, however, we could generate the models with errors of $0.205\pm 0.147$ mm (CCSDS with float-point DWT) and $0.200\pm 0.145$ mm (CCSDS integer-point DWT), respectively. In particular, the side with tall rock particles or the floors of the circular depressions tended to exhibit greater errors (partly due to inadequate imaging), resulting in a reduced number of dense points generated by the SfM.

In the MMX mission, the equatorial region (i.e., latitude $\le 30°$) of Phobos is planned to be primarily observed from the orbit named at QSO, which is approximately 20 km away from the surface, to reveal detailed topography and surface compositions and identify the best landing sites. Assuming the spacecraft typically obtains images with a resolution of ~12 cm/pixel using the TENGOO [20], which is sufficient to observe >20 cm-sized hazardous rock particles, and scaling our image up, the 1 mm errors in our analysis can be equivalent to ~31.7 cm errors for the rough surface and ~107 cm errors for the smooth surface on Phobos. These errors are based on our image resolutions of 0.379 mm/pixel for the rough surface and 0.112 mm/pix for the smooth surface. In this case, for the rough surface, the errors are equivalent to $6.66\pm 4.60$ cm (CCSDS with float-point DWT) and $6.59\pm 4.63$ cm (CCSDS integer-point DWT), respectively. On the other hand, for the smooth surface, the errors are equivalent to $21.9\pm 15.7$ cm (CCSDS with float-point DWT) and $21.4\pm 15.5$ cm (CCSDS with integer-point DWT), respectively. This result means that local DTMs generated from compressed images with a compression ratio lower than 70% are expected not to include an error of the altitude larger than 40 cm, regardless of the surface roughness on Phobos. This situation is ideal for determining safe landing and sampling sites on the surface of Phobos. Therefore, we can expect that the compression ratio can be increased as high as 70% in the MMX mission, ensuring the safety of the spacecraft.

Furthermore, we generated local DTMs using images processed with compression ratios of 60%, 80%, and 90%, to evaluate the feasibility of our recommended compression ratio of 70%. Figure 13a shows the result of an error assessment for the local DTMs of the rough surface, while Figure 13b represents the result for the local DTMs of the smooth surface. Overall, we quantitatively show that the local DTMs for the smooth surface contain larger errors compared to the models for the rough surface, which is consistent with our result of image quality assessment (Section 3.2), indicating that the simulated images for the smooth surface are more susceptible to image compression. For the rough surface, we can generate local DTMs with errors smaller than 40 cm on Phobos’s surface, using images compressed with these four different compression ratios. However, for the smooth surface, the local DTMs can contain errors larger than 40 cm on Phobos’s surface, if the compression ratio is larger than 70%. This result strongly supports the idea that the compression ratio should be 70% or lower, to avoid any critical loss of scientific information especially for selecting the best landing sites, and at the same time to effectively reduce image data volume transmitted to the ground. Note that for both rough and smooth surfaces, the difference in errors of generating local DTMs using CCSDS with float- and integer-point DWT is minimal and these errors fall within the error range of other algorithms. Consequently, we conclude that the compression performances of the two algorithms do not differ significantly, which is consistent with the result from our quantitative analysis of image quality by PSNR, SNR, and SSIM discussed in Section 3.2.

4.2. Implications for the Observation in the MMX Mission

Given the nominal image resolution from the QSO (~12 cm/pix), the image size of the TENGOO ($3296\times 2472$ pixels), and the area of the equatorial region (latitude $\le 30°$) of Phobos ($~936 {\mathrm{k}\mathrm{m}}^2$), more than ~3820 images (with >50% overlapping areas in each image for detailed analysis, including DTM reconstruction) are thought necessary to reveal detailed topography on Phobos for landing site selection. Transmitting all of those images would require ~180 days (~6.0 months), but such a duration can be shrunk into ~54 days (~1.8 months) using the compression ratio of 70%. This timescale is preferable for the landing site selection phase, currently planned to last approximately six months. Even so, downlink time for the TENGOO will be further constrained by several factors such as uplink communications, downlink of other science instruments onboard the MMX spacecraft, and availability of deep space communication facilities on the ground.

Note that the best compression ratio could change depending on various factors. These include differences in target image parameters such as image size, bit depth, and brightness/contrast. Also, the nature of the target surface, including the presence of fewer/more geological characteristics like craters, boulders (rocks), as well as varying albedo patterns, can play a crucial role. Furthermore, other criteria with varying acceptable local DTM errors and/or other compression algorithms can lead to a different optimal compression ratio. Therefore, determining the best compression ratio for each critical phase in future deep space exploration missions may require different or appropriate methods/criteria. This matter could be a topic for future research.

5. Conclusions

Low downlink rates can be one of the greatest limiting factors for deep space exploration missions, including the MMX mission. We thus prepared simulated images of Phobos using rough and smooth surfaces in a laboratory. We subsequently compressed those images using the CCSDS with float- and integer-point DWT candidate algorithms that can be used in the MMX mission. The image quality assessment performed by PSNR, SNR, and SSIM shows that the difference in the compression performances between the two algorithms is substantially limited. Notably, the loss of image quality can differ depending on the roughness of the surface in images. But, such loss of quality remains constrained if we compress images with a compression ratio lower than or equal to 70%.

We further compared the local DTMs generated using compressed and uncompressed images. Our result shows that the models can be generated with altitude errors smaller than 40 cm on Phobos, even if we compress images with a compression ratio of 70%. Thus, we can expect that the compression ratio can be increased as high as 70% in the MMX mission. Using this compression ratio, we can reduce the data volume without losing important scientific information. This approach can be significantly effective in the MMX mission, particularly during the landing site selection phase, which is one of the most crucial parts of this mission.