HERA Centroiding Image Processing Algorithm Based on the

Normalised Correlation with a Lambertian Sphere

Stancu Florin Adrian

, Marcos Avilés Rodrigálvarez

, Andrea Pellacani

, Ángel Palomino Aguado

Aída Alcalde Barahona

, Francesco Pace

, Paul Băjănaru

, Víctor Manuel Moreno Villa

and Jesús Gil-Fernández

GMV Innovating Solutions, SkyTower, 246C Calea Floreasca, Bucharest, Romania

GMV Aerospace and Defence, Issac Newton 11, Tres Cantos, Spain

ESTEC-ESA, Keplerlaan, Noordwijk, Netherlands

Keywords: Planetary Defence, Image Processing, Image Correlation, Visual Based Navigation, Guidance Navigation and

Control.

Abstract: HERA is the spacecraft built by the European Space Agency (ESA) to visit and characterise the Didymos

binary asteroid system after the impact performed by the NASA Double Asteroid Redirection Test (DART)

mission. A visual-based Guidance Navigation and Control (GNC) system is developed for HERA to ensure

safe ground, semi-autonomous and autonomous navigation around Didymos. For a better characterisation of

the asteroids after DART post impact a close approach is foreseen. To ensure autonomous navigation during

the close approach a visual-based GNC solution is developed by GMV, where dedicated image processing

algorithms are implemented. Three main image processing algorithms are proposed to be used based on the

distance of HERA spacecraft with respect to the Didymos system: normalised correlation with Lambertian

sphere, centre of brightness with masking and feature tracking. This paper will briefly introduce the HERA

mission and GNC, focusing more on the normalised correlation with a Lambertian sphere. Synthetic images

generated based on Didymos (the main asteroid) and Dimorphos (the moon) are used for representative

simulations. Performances are reported from a functional point of view until software (SW) implementation.

1 INTRODUCTION

HERA mission is the European component developed

by ESA within the Asteroid Impact and Deflection

Assessment mission, which is an international

collaboration that materialised with the development

of two spacecraft: DART and HERA. DART is the

kinetic impactor launched in 2021 and it successfully

impacted Dimorphos in September 2022. HERA is

equipped with the necessary instruments to

characterise asteroids and evaluate the crater

generated by DART’s impact. It will be launched in

October 2024 and is expected to reach the Didymos

system in January 2027. The Didymos binary system

is composed of Didymos, the main asteroid, and

Dimorphos, the moon of the system. HERA embarks

several payloads, like the Image Processing Unit

(IPU), Asteroid Framing Camera (AFC) and Juventas

CubeSat. Juventas is a six-unit CubeSat designed to

operate in the close proximity of the Didymos system

and take more risks. Similar to HERA, Juventas

satellite is equipped with a visual-based navigation

solution developed as well by GMV, with the

objective to enhance navigation autonomy. A detailed

description of Juventas’ GNC architecture can be

found in (Ovejero et al., 2023) and (Stancu et al.,

2023).

HERA mission starts with the launch and early

operation, where two launch windows have been

identified in 2024 as the main date and a backup date

in 2026. The next phase is the interplanetary transfer,

where the HERA spacecraft is heading towards the

Didymos binary system. The third phase is the

rendezvous of HERA spacecraft with the Didymos

system. The final stage is composed of multiple

proximity operations: the early characterisation phase

of the binary system, the payload deployment phase

where the CubeSats are released, the detailed

characterisation phase of the Didymos system, the

Adrian, S., Rodrigálvarez, M., Pellacani, A., Aguado, Á., Barahona, A., Pace, F., B

anaru, P., Villa, V. and Gil-Fernández, J.

HERA Centroiding Image Processing Algorithm Based on the Normalised Correlation with a Lambertian Sphere.

DOI: 10.5220/0012899200003822

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics (ICINCO 2024) - Volume 2, pages 109-116

ISBN: 978-989-758-717-7; ISSN: 2184-2809

109

close operation phase near the asteroids, the

experimental phase performing fly-bys and extended

operation phase which will conclude with the end-of-

life landing on Didymos.

The mission requires multiple levels of autonomy

from semi-autonomous mode to autonomous

navigation which can be obtained using a visual-

based GNC system with dedicated image processing

techniques feasible to be applied on asteroid shapes

and surfaces. The visual-based GNC system allows

HERA spacecraft to perform a close approach to

Didymos in safe conditions in an autonomous

manner. The autonomous operation is achieved

through the translation navigation technology

implemented inside the GNC systems. A navigation

filter design based on an Extended Kalman is

implemented and details can be found in (Palomino et

al., 2023). The most important payloads contributing

to this data fusion technique are the laser altimeter,

the inertial measurement sensor, and the AFC acting

like a pseudo-sensor (because the navigational

information is extracted by the image processing

algorithms). Three types of image processing

technologies are implemented, which can be used in

different scenarios: centroiding using normalised

correlation with a Lambertian sphere, centre of

brightness and feature tracking.

This paper focuses on the development of the

HERA’s image processing technologies, providing

in-depth details of the centroiding using normalised

correlation with a Lambertian sphere algorithm.

Considering ESA’s mission lifetime cycle definition,

HERA is currently in phase D.

2 IMAGE PROCESSING

TECHNOLOGIES ONBOARD

HERA

The image processing approach is a key technology

to ensure the close autonomous operation of HERA

spacecraft near the Didymos system. The image

processing algorithms are designed to use images in

the visual spectrum. The first image processing

algorithm is the centroiding using correlation with a

Lambertian sphere (CLAMB). This technology can

be applied only on Didymos, when the complete

asteroid is in the camera’s field of view (FoV) and the

range is as baseline higher than 9.5 km. The objective

of the algorithm is to estimate the centre of Didymos

in the image frame. In Figure 1 the CLAMB outputs

are presented for one frame, in blue being represented

the estimated centre and radius of Didymos.

Figure 1: Robustness to Dimorphos presence in FoV.

The second technology is based on centre of

brightness with masking and can be applied to both

Didymos or Dimorphos. Masking is the process of

removing the unwanted body from the image to avoid

altering the centre of brightness position.

The last technology is based on feature tracking

which detects and tracks features in consecutive

images. The algorithm is based on the well-known

Kanade Luca Tomasi feature tracker, adapted by

GMV to fulfil functional and SW requirements of

HERA spacecraft.

All three image processing algorithms are

implemented directly in C and are wrapped under a

single-entry point function called IP-SW. The

HERA’s main onboard computer is a LEON3

processor which is a radiation-tolerant 32-bit

processor. The IP-SW is scheduled to run on the

second core of LEON3.

In Figure 2 the simplified architecture of the

visual-based GNC is depicted, focusing on the

general inputs/outputs and image processing chain.

The GNC is implemented as a C application software

(ASW) and together with the IP-SW form the visual-

based GNC system.

Figure 2: Simplified visual-based GNC system architecture.

The GNC-ASW and the IP-SW interact between

them and with other components via the central

software (CSW). The GNC-ASW is in charge of

selecting which image processing algorithm is needed

to run and ensure auxiliary inputs to IP-SW (for

example the sun position). The image processing is

extracting navigational information from the images,

which is routed by CSW to GNC-ASW. The images

ICINCO 2024 - 21st International Conference on Informatics in Control, Automation and Robotics

110

are obtained from AFC with a predefined periodicity

defined by the proximity operation stage, with the

scheduled requirement time of IP-SW execution up to

a maximum of 48s.

For development and testing purposes a

Functional Engineering Simulator (FES) was created

from the beginning of HERA visual-based GNC

system prototyping and maintained until phase D.

The FES is integrating both the GNC and the image

processing algorithms, but also models of real sensors

or actuators. The images are generated by a synthetic

image generator called PANGU. The FES is used to

run extensive Monte Carlo (MC) simulations and to

evaluate the fulfilment of requirements.

3 SYNTHETIC IMAGE

GENERATION

The asteroids' shape and dimension are known from

ground observations, knowledge that has been

improved based on the scientific data acquired by the

DART mission. To increase the representativeness of

the vision-based GNC system validation and

verification, the image processing algorithms are

tested using synthetic image datasets. Nowadays, one

of the most powerful synthetic image generators for

space applications is the Planet and Asteroid Natural

Scene Generation Utility (PANGU). PANGU is

capable of creating high-resolution models of planets

and asteroids, but also rendering images. Moreover,

PANGU can integrate camera models and generate

representative images given any position or

orientation of the spacecraft, sun, planet or asteroid.

PANGU is designed and validated for space image

processing algorithms, therefore is natural to model

and integrate the Didymos system scene in this

application.

Figure 3: PANGU Didymos system, (Stancu et al., 2021).

Information about HERA Didymos reference

model is provided in ESA-TECSP-AD-017258. The

Didymos system is modelled starting from real data

and subsequently integrated into PANGU. The

resolution of real models of the asteroids is artificially

increased to comply with the image processing pixel

ground sampling distance (GSD) needs.

It is important to note that a hyper-realistic

generation of Didymos system implementation in

PANGU was evaluated with good results from

resemblance with a real asteroid, but finally it was

discarded due to considerable computation time to

initialise and generate images, in order of minutes per

one image. This increased realism did not translate

into any differences from the image processing

algorithms' performance point of view.

Figure 4: Hyper-realistic PANGU Didymos in comparison

with the Bennu asteroid.

The scene creation and the camera model,

faithfully replicating the AFC characteristics, from

Figure 2 are handled by PANGU. The most important

configuration parameters of the AFC are: a FoV of

5.5 degrees, a sensor dimension of 1020x1020 pixels,

a grayscale image in the visual spectrum, and a pixel

depth for navigation images of 1 byte.

4 CENTROIDING USING

NORMALISED CORRELATION

WITH A LAMBERTIAN

SPHERE

The CLAMB objective is to determine the estimated

geometric centre of Didymain in the image, thus

providing to the navigation filter information about

the Line of Sight (LoS) towards the centre of the

asteroid. The proposed algorithm shall cope with at

least the following scenarios: Dimorphos may appear

in the image, Didymain has an irregular shape,

various illumination conditions, Didymain and

Dimorphos revolutions around their axis, defective

pixels, high image background noise and photo

response non-uniformity.

The following generic sequence of steps is

performed, and later detailed in this chapter:

1. Image preprocessing.

HERA Centroiding Image Processing Algorithm Based on the Normalised Correlation with a Lambertian Sphere

111

2. Image binning, if necessary.

3. Estimate the rough angular size of Didymos

from the image.

4. Correlate the image with different radiuses

of Lambertian spheres.

5. Determine the sphere radius that maximises

the normalised correlation.

6. Perform a correlation between the input

image and the Lambertian sphere generated

with the radius determined at point 5.

The image preprocessing is the initial correction

step that prepares the images for further processing.

The raw image can be affected by high background

noise and photo response non-uniformity, but also by

defective pixels. The background noise can be easily

corrected by subtracting from the raw image the bias

matrix, while the photo response non-uniformity is

corrected by a multiplication gain matrix containing

specific amplification factors for each pixel in part, as

defined in equation (1). The gain and bias matrix are

determined during the camera calibration procedure.

𝐼



=(𝐼−𝐵)∘ 𝐺 (1)

where 𝐼

×

is the raw image from AFC of 𝑚×𝑛

dimension (padded with zeros until next power of 2

dimension),

represents the image number of rows,

𝑛 represents the image number of columns, with the

property that

m=n

, 𝐼



×

is the corrected image,

𝐵

×

is the bias matrix, 𝐺

×

is the gain matrix and

∘ denotes element-by-element matrix multiplication.

Next, the defective pixel correction is performed

based on a predefined list of bad pixels. A defective

pixel can be either a hot or a cold pixel. The correction

is performed for every bad pixel in part by

considering the average of the pixel neighbourhood,

using a median kernel.

A robustification method in the case of the

presence of asteroid residue due to DART impact is

currently being evaluated. A morphological opening

operation is considered to remove small objects.

The image binning is useful to reduce the

computation load on the processor, and it represents

a downscaling of the image to reduce dimension.

Eventually, 𝐼



is defined to contain all the

preprocessing, background noise and photo response

non-uniformity correction, defective pixel correction,

morphological opening and image binning.

The rough angular size of Didymos is estimated

by counting the bright pixels in the image, which

represents the area of Didymos seen in the image,

𝐴



. To avoid considering possible artefacts

present in the image, a bright pixel is defined to be a

pixel with a value higher than a threshold. A

multiplication phase angle factor is computed

because the asteroid could not be fully illuminated

due to the sun phase angle, considering spacecraft-

camera-sun geometry. Using the phase angle factor

and the 𝐴



the estimated area is corrected and is

approximated with a circle to deduct the coarse radius

in pixels, 𝑟



. An additional measurement can be

computed based on the 𝑟



, namely the apparent

range to Didymos, by knowing the Didymos real

diameter in meters, the image dimension in pixels

(considering a square image), and the camera's field

of view.

The algorithm baseline is to correlate the image of

Didymos with several radiuses of Lambertian

spheres, thereby detecting the best correlation. The

Lambertian spheres are generated starting from

𝑟



by applying a multiplication factor. The

multiplication factors can be detected automatically

or can be set manually. The simulation shows that

multiplication factors between ± 25% from 𝑟



are sufficient to detect the best correlations.

The generation of the Lambertian sphere is based

on Lambert cosine law where the amount of light

reaching on the surface of a body is computed based

on the angle between the surface normal, N, and the

light direction, L:

cos(𝜃) =

‖

∙

‖

𝐿

‖

(2)

The correlation is the technique proposed to

determine the offset between two images and is based

on the Fast Fourier Transform (FFT), which implies

the transformation of the Didymos corrected image

and Lambertian sphere image in the frequency

domain.

The FFT correlation is performed as follows:

𝐶



=𝐼



 𝐼



(3)

where 𝐼



×

is the FFT transform of the Didymos pre-

processed image, 𝐼



×

is the FFT transform of

the Lambertian sphere model rotated 180 degrees,

and  represents the convolution operator which is a

matrix multiplication element by element for

complex numbers. The correlation will be repeated in

a number of times equal to the Lambertian sphere

candidates, defined by the multiplication factors.

To go back to the spatial domain, the inverse fast

Fourier transform (IFFT) on 𝐶



is applied,

followed by an FFT shift to shift the zero-frequency

components, finally obtaining the correlation

𝐶

×

The 2-D fast Fourier transform is well covered in the

scientific literature, however as a guideline, the reader

can reference to the Matlab implementation of fft2,

ifft2 and fftshift.

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At this point the correlation peak can be detected,

its row and column position providing the estimated

centre of Didymos. Because multiple Lambertian

spheres are correlated to obtain the optimal radius, see

Figure 6, the normalised correlation is proposed. The

output of one correlation chain represents the row and

column offset of Didymain, the peak normalised

correlation value and the Lambertian sphere radius.

Intuitively all this information will be obtained for all

the Lambertian sphere candidates, which will further

be used to determine the optimal radius that will

maximise the correlation. Figure 5 depicts the

correlation chain for one Lambertian sphere,

preliminary results being available in terms of

estimated asteroid centre and radius in the image

frame, even though not optimal.

Figure 5: Correlation chain.

One final correlation is done for the sphere radius

that maximises the correlation. The radius is

determined based on information from previous

correlations by fitting a quadratic function, equation

(4), and selecting the best three Lambertian spheres

that provide higher correlations. These correlations

are noted in Figure 6, 𝐶



being the best correlation,

𝐶



and 𝐶



are 𝐶



left and right neighbours.

𝐶



=𝑎𝑟



+𝑏𝑟+𝑐

(4)

where 𝑟 is mapped as the radius and as

𝐶



the

correlation.

By finding the best quadratic approximation the

vertex can be found

, 𝐶



, and in consequence the best

radius, 𝑟



is:

𝑟



=−

𝑏

2𝑎

)

Based on the 𝑟



, a new Lambertian sphere is

generated and correlated with the input image, to

obtain the optimal estimation of the Didymain’s

centre in the image frame.

At this step, the estimated centre can be corrected

for lens distortion, by using the Brown-Conrady

model. It shall be noticed that specific polynomial

coefficients are used, correcting the estimated centre

from a distorted position to an undistorted position in

the image frame.

Figure 6: Quadratic approximation.

5 FPGA BASED IMAGE

PROCESSING UNIT

The IPU is a GNC payload developed with direct

applicability for the HERA mission. The unit is

dedicated to the processing of the images taken by the

AFC and it acts as an experimental aid for the on-

board autonomous GNC.

The IPU provides isolation of image processing

function and interfaces function, as it is relying on a

two Field Programmable Gate Arrays (FPGA)

architecture, with allocated external volatile and non-

volatile memories. It includes one small and low-

power consumption European FPGA: the rad-hard

BRAVE NG-Medium, dedicated to interface control

and monitoring, while the other one is a powerful

FPGA that performs as a computer vision co-

processor. The Processing FPGA is the high-density

rad-hard Xilinx V5QV FPGA.

The SpaceWire interfaces allow telemetry and

telecommand exchange between IPU and the on-

board computer(s) via one nominal and one redundant

SpaceWire links making use of the Packet Utilization

Service (as per ECSS-E-ST-70-41-C). Alternatively,

IPU can communicate with 2 separate instruments.

The two FPGAs included by IPU allow flexibility

and many options for the design and implementation

of complex functionalities, such as high-data rate

interfaces management and hardware accelerators.

HERA Centroiding Image Processing Algorithm Based on the Normalised Correlation with a Lambertian Sphere

113

Different computer-vision accelerators which are not

used in the same moment of time can be used during

the mission by replacing bitstreams in the processing

FPGA in-flight to save a potentially needed of second

FPGA unit. The image processing techniques used by

IPU – implemented in VHDL (and already stored

before flight into the flash memory of the unit) are:

CLAMB and feature tracking algorithm.

Figure 7: IPU exploded view.

The design, development and integration of the

computer-vision algorithms for IPU are facilitated by

the architectural design of the processing FPGA code,

which provides an internal interfacing wrapper. IPU

also includes pre-processing/correction functions for

the image received from the navigation camera.

The development of the HERA IPU payload was

incremental, including several models like: elegant

breadboard, engineering model, engineering qualified

model and flight model. The IPU has a total weight of

2.1 kg and it fits inside an envelope of 332 x 195 x 40

mm. Detailed information about IPU can be found in

(Băjănaru et al., 2021).

6 FUNCTIONAL AND SW

PERFORMANCES

To quantify the CLAMB performances, the

experimental close fly-by scenario is considered,

where all image processing technologies are used

individually, by starting with CLAMB, then centre of

brightness and ending with feature tracking. This

analysis focuses on CLAMB taking advantage of the

fact that the range varies considerably from

approximately 20 km down to about 8.5 km. The FES

plays a critical role in this analysis, using the real-

world block to extract reference information that

consists at least of spacecraft and Didymos attitude

and position at each step of the simulation. The FES

real-world data is used to compare the estimated

measurement of CLAMB in terms of range, Didymos

centre and radius. The first metric to be evaluated is

the apparent range estimation, represented in Figure

8 using an orange line, with respect to the real range

of Didymos computed based on FES data, blue line.

From Figure 8, it can be noticed that a rough

estimation of the range is obtained where Didymos

shape uniformity has a direct impact on the stability

of the metrics. The CLAMB estimated range is not

used by the GNC but is a valuable input for the Fault

Detection and Isolation system.

The following performances are derived for the

estimated range and provided, in the form of mean

range absolute error, standard deviation (STD) of the

range absolute errors and the range relative mean

error:

Table 1: CLAMB apparent range estimation performance.

Range absolute

mean error [m]

Range absolute

error STD [m]

Range relative

mean error [%]

427.6 305.1 2.9

Figure 8: Real Didymos range vs CLAMB estimated range.

The CLAMB estimated centre in the image frame

of Didymos is the most important output of the

algorithm being directly used by GNC to maintain the

asteroid inside the FoV.

Figure 9: Real vs estimated centre on x axis.

Range [m]

X [pix]

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Figure 10: Real vs estimated centre on y axis.

The Figure 9 and Figure 10 present the

performances on the x and the y axes, respectively,

where the FES data is used to compute the reference

centre of Didymos in the image frame for every image

in part, blue line, with respect to CLAMB estimated

centres, orange line. Top left corner image reference

frame is used, x pointing to right and y pointing down.

From Figure 9 and Figure 10, it can be observed that

Didymos uniformity has a direct impact on the

accuracy of the CLAMB centre estimation. This is a

direct impact of the approximation with an ideal

spherical shape when generating the Lambertian

sphere. Another observation is the gradual error

increasing in centre estimation caused by the close

approach to Didymos, see Figure 8, and by the

variation of sun phase angle starting from 90 deg at

the beginning of the scenario and reaching almost 70

deg. However, the sun phase component error is very

small due to the quadratic fitting optimisation

procedure presented in equation (4).

The main component error is caused by the

gradual approach to Didymos, thus reducing the

range which affects the pixel GSD. The GSD is

represented in meters, and is higher when the camera

is further away from the surface that AFC is seeing,

and lower when approaching the surface. Due to this

phenomenon, the centre estimation error in meters

remains almost constant.

Table 2: CLAMB centre estimation performance.

Axis

Centre absolute mean

error [pix] / [m]

Centre absolute error

STD [pix] / [m]

x 13.4 18 9.9 13.5

y 7.6 9.5 7.3 7.6

In Figure 11 it can be noticed that the image is

taken with initial knowledge of the spacecraft,

moment of time when HERA’s AFC is not pointing

towards the centre of Didymos. The CLAMB is able

to estimate the centre of the Didymos, blue star,

which can be observed as well in the initial peak from

Figure 9 and Figure 10. By making use of this

measurement, the GNC is able to command HERA

spacecraft and recursively maintain the asteroid in the

centre of the image in the next frames.

Figure 11: First frame close fly-by, blue star estimated

centre, blue circle drawn based on estimated radius.

The optimised estimated radius presented in

equation (5) can be considered as well as an output of

CLAMB, see Figure 12.

Figure 12: Real Didymos radius vs CLAMB estimated

radius.

Similarly, based on FES data and AFC

configuration the radius of Didymos asteroid can be

approximated, blue line, and considered as a

reference to compare the CLAMB estimated radius,

orange line. The following performances are derived

for the CLAMB radius estimation:

Table 3: CLAMB radius estimation performances.

Radius absolute

mean error [pix]

Radius absolute

error STD [pix]

24.83 14.33

From Figure 12, the presence of a constant bias

can be observed, caused by the CLAMB correlation

and radius optimisation procedure which tends to use

Y [pix]

Radius [pix]

HERA Centroiding Image Processing Algorithm Based on the Normalised Correlation with a Lambertian Sphere

115

a Lambertian sphere radius that circumscribes

Didymos. This is the reason behind the decision to

use 𝑟



to compute apparent range estimation.

As specified in section 2, the IP-SW wraps all the

image processing under a single-entry point function,

scheduled to run on the second core of LEON3.

Taking into consideration that HERA is phase D,

consolidated implementation requirements are

imposed. The IP-SW is using less than 20 MB

memory during runtime, excluding inputs/outputs

and tuneable parameters. After SW optimisations

performed by GMV the CLAMB implementation is

using less than 3 MB of run-time memory. For the

perspective of time execution, the TSIM-LEON3

emulator is used, set at 80 MHz. The execution time

of CLAMB is determined for a subset of images using

TSIM-LEON3. From Figure 13 the maximum

execution time of CLAMB is up to 6.4 seconds during

initialisation, mentioning that morphological opening

is not included.

Figure 13: TSIM execution time.

7 CONCLUSIONS

This paper presents a detailed design of an image

processing technique specific for asteroid centroid

detection, that can be approximated with a spherical

shape. The algorithm is based on the correlation with

a Lambertian Sphere and is robust to various

illumination conditions, Dimorphos appearance in

FoV, and until a certain point robust to Didymos

shape irregularity. The image processing algorithm

offers the possibility to perform autonomous

navigation around the Didymos binary system, thanks

to the vision-based GNC system. The performances

at pixel level are determined and reported for the

range, centre and radius estimations of CLAMB. The

IP-SW optimisation of CLAMB allows to run the SW

in 6.4 seconds on a LEON3 processor. The CLAMB

algorithm was previously tested with success in a

mock-ups and camera were used, see (Pellacani et al.,

2019). Extensive MC campaigns have been

performed to test the visual-based GNC system,

including the current baseline design of CLAMB and

are reported in (Palomino et al., 2023).

ACKNOWLEDGEMENTS

The work presented in this paper is part of ESA

HERA mission, expressing gratitude to the entire

HERA mission team, particularly OHB as prime

contractor and ESA as a client that has made possible

the implementation of this mission and supported

GMV through the whole process.

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