Active stereovision using invariant visual servoing

Vincent Brandou
and Anne-Gaëlle Allais
and Michel Perrier

IFREMER Centre de Mediterranee - BP 330
FR-83507 La Seyne-Sur-Mer Cedex

Email: Vincent.Brandou@ifremer.fr

Ezio Malis

and Patrick Rives

INRIA Sophia-Antipolis
2004 route des lucioles - BP 93
FR-06902 Sophia Antipolis

*Abstract*— The objective of this paper is to propose an in-
novative visual servoing method in order to improve the 3D
reconstruction of objects for quantitative measurements. The
method uses a stereovision system that allows us to obtain various
shots of an object, at regular intervals according to a predefined
trajectory. In our case, the stereo rig is equipped with two
different cameras, the first one is fixed while the other one
is mounted on pan and tilt. So, the intrinsic parameters are
not the same for the two cameras. To validate our approach,
first experiments have been conducted by simulation and under
laboratory conditions.

I. INTRODUCTION

The aim of our research is to develop, implement and test
an original robotic method dedicated to compute a metric 3D
reconstruction in order to describe and quantify biodiversity
in deep-sea fragmented habitats [17]. The objective consists
in applying techniques of computer vision to create tools
adapted to the exploitation of underwater images. Today, some
deep-sea vehicles are equipped with measuring devices and a
manipulator arm. Vision systems are often used to complete
information provided by acoustic sensors [12]. Taking advan-
tage of possibilities allowed by underwater vehicles, our goal
is to develop a methodology based on a vision system, to
obtain quantitative measurements through a 3D reconstruction
of underwater scenes.

The images used for the reconstruction are acquired when
the vehicle is deployed on the sea floor at a fixed and stable
attitude. The images are subject to several constraints linked
to the underwater environment. First of all, the observed
scenes are unknown, and the objects to be reconstructed in
these scenes are made up of random textures and shapes.
We only know that the objects are rigid and have a verti-
cal overall shape. Moreover, the refraction, the presence of
particles, the absorption and the problems of lighting in an
underwater environment considerably alter the image quality.
Noisy images and an unknown model of the object have a
knock-on effect on the 3D reconstruction accuracy. The idea
is thus to define a trajectory adapted to the type of object in
order to improve the reconstruction accuracy. The originality
of the method lies in the use of an active stereo rig (i.e.
with variable geometry) mounted on a 6 DOF manipulator
arm effector, which equips the underwater vehicle. The stereo
rig is equipped with two different underwater cameras, the
first one is fixed while the other one is mounted on pan &
tilt. The geometry configuration of the stereo rig allows us
to generate predefined trajectories and to acquire images at
regular intervals. Thus, the geometry configuration is fixed
in function of the desired task. This constraint yields to a

reduction of unknown variables in the reconstruction process
by bundle adjustment technique [19].

We show hereafter how the stereo rig geometry determines
the trajectory and the number of shots taken around the object
to be reconstructed. Consequently, we carried out research
related to the use of visual servoing techniques to improve the
3D object reconstruction. Many approaches have already been
proposed to solve the problem of vision-based control [2], [3],
[14]–[16]. All of them are based on the same scheme: target
definition, image feature selection, 2D/3D modeling, robot
geometric modeling and Jacobian matrix calculation. But even
if the principle basis is the same, the methods vary according
to the prior knowledge on the environment and the sensors.

In this paper, we propose a visual servoing method adapted
to the stereo rig in order to improve a 3D reconstruction.
Indeed, the intrinsic parameters of the two cameras are not
the same. Moreover, they are influenced by the characteristics
of the underwater environment such as the optical index,
which varies as a function of temperature, salinity, pressure,
or wavelength [12]. For example, the underwater vehicle used
for the final experiments is able to dive up to a depth of 6000
meters. In applications using different cameras, the intrinsic
parameters should be determined by a calibration process. It
is quite difficult to use a calibration pattern to calibrate the
cameras in such conditions. On the other hand, we would like
to avoid on-line self-calibration techniques which imply new
constraints on the robot displacement (i.e. a strong rotation of
the stereo rig is needed). Consequently, we have implemented
a visual servoing method which is invariant to camera intrinsic
parameters [8]. The visual servoing scheme proposed in this
paper has been completely validated by experiments.

II. TRAJECTORIES INDUCED BY THE GEOMETRY OF THE
STEREO RIG

Visual control is carried out with a system of stereovision
mounted at the tip of an instrumented arm of a robot (eye-in-
hand robotic system). It consists in capturing a reference image
with the right camera on a given position, and then converging
towards this position with the left camera (see Figure (1)). We
have shown that setting the geometry between both cameras
is equivalent to moving the coordinate system associated to
each camera on the surface of a cylinder. The demonstration
is based on the integration of infinitesimal displacements to
obtain a discrete displacement.

Let $T$, defined in the Euclidean special group of dimension three $SE(3)$, be the transformation matrix between the
position of the two cameras (see Figure (2)):

$$ T = \begin{pmatrix} \mathbf{R} & \mathbf{t} \\ \mathbf{0} & 1 \end{pmatrix} \qquad T \in SE(3) \qquad (1) $$

where $\mathbf{R}$ is the $(3 \times 3)$ rotation matrix, and $\mathbf{t}$ is the $(3 \times 1)$ translation vector. The rotation matrix can be written as a function of $\alpha$:

$$ \mathbf{R}(\alpha) = e^{[\mathbf{r}(\alpha)]\times} \qquad (2) $$

where $\mathbf{r}$ is the rotation vector corresponding to an angle $\alpha \in \mathbb{R}$ around a fixed axis specified by the vector $\delta$:

$$ \mathbf{r}(\alpha) = \frac{\delta}{\|\delta\|} \alpha \qquad (3) $$

with:

$$ \delta = \begin{pmatrix} \delta_{\text{tilt}} \\ \delta_{\text{pan}} \\ 0 \end{pmatrix} \qquad (4) $$

Similarly, the translation vector depends on $\alpha$ and the distance $l$ between the cameras:

$$ \mathbf{t}(\alpha, l) = -\mathbf{R}(\alpha) \begin{pmatrix} l \\ 0 \\ 0 \end{pmatrix} = -e^{[\mathbf{r}(\alpha)]\times} \begin{pmatrix} l \\ 0 \\ 0 \end{pmatrix} \qquad (5) $$

T can always be written as:

$$ \mathbf{T} = e^{\mathbf{A}} \qquad \mathbf{A} \in se(3) \qquad (6) $$

where $se(3)$ is the Algebra of Lie associated to the group of Lie, and:

$$ \mathbf{A} = \begin{pmatrix} [\omega] \times & \nu \\ \mathbf{0} & 0 \end{pmatrix} \qquad (7) $$

where $\omega$ is the $(3 \times 1)$ rotation speed vector, such that $||\omega|| < \pi$, and $\nu$ is a $(3 \times 1)$ translation speed vector. Let $[\omega] \times$ be the $(3 \times 3)$ skew matrix associated to vector $\omega$.

An infinitesimal displacement of the frame origin $\mathcal{O}$, which coincides with the center of projection $\mathcal{C}$ on the trajectory according to time $t$, standardized between 0 and 1, is defined by:

$$ \dot{\mathbf{C}}(t) = [\omega] \times \mathcal{C}(t) + \nu \qquad (8) $$

It can be shown that the integral of this equation can be written in the general form of the parametric equations of a cylinder:

$$ \mathcal{C}(t) = \mathbf{r}_0 + \cos(\theta)\mathbf{u} + \sin(\theta)\mathbf{v} + \mathbf{w}t \qquad (9) $$

with:

$$ \theta = ||\omega t||, \qquad \mathbf{r}_0 = \frac{\gamma}{||\omega||^2}, $$

$$ \mathbf{u} = \left(-\frac{\gamma}{||\omega||^2}\right), \quad \mathbf{v} = \left(-\frac{\zeta}{||\omega||^3}\right), \quad \mathbf{w} = \left(\nu + \frac{\zeta}{||\omega||^2}\right) $$

where:

$$ \gamma = \begin{pmatrix} -\nu_y \omega_z + \nu_z \omega_y \\ \nu_x \omega_z - \nu_z \omega_x \\ -\nu_x \omega_y + \nu_y \omega_x \end{pmatrix} $$

$$ \zeta = \begin{pmatrix} -\nu_x(\omega_y^2 + \omega_z^2) + \nu_y\omega_x\omega_y + \nu_z\omega_x\omega_z \\ \nu_x\omega_x\omega_y - \nu_y(\omega_z^2 + \omega_x^2) + \nu_z\omega_y\omega_z \\ \nu_x\omega_x\omega_z + \nu_y\omega_y\omega_z - \nu_z(\omega_y^2 + \omega_x^2) \end{pmatrix} $$

The three vectors $\mathbf{u}$, $\mathbf{v}$ and $\mathbf{w}$ are unit and form a direct trihedron. Including $\mathbf{r}_0$, they characterize the cylinder which defines the trajectory. Since $\mathbf{u}$, $\mathbf{v}$, $\mathbf{w}$ and $\mathbf{r}_0$ depend on the

various components of $\nu$ and $\omega$, which depend themselves on the transformation matrix $T(\mathbf{R}, \mathbf{t})$ linking the position of the two cameras (see Equations 1,6,7), we can say that the stereo rig geometry induces the trajectory.

Because point $\mathbf{r}_0$ is located on the cylinder axis, if we set the geometry of the stereo rig, we can also determine the distance to be applied between the cameras and the object under study.

Hence, it is possible to choose the geometry of the stereo rig with respect to the shape, the volume, and the orientation of the underwater object to be reconstructed. For example, with a fixed geometry of the stereo rig, the trajectory corresponds to a straight line in case of parallel cameras (no angle), a circle if we apply a pan angle, or an helicoid in case of a pan and tilt angle. For instance (see Figure (1)), a pan angle $\alpha$ and a distance $l$ force the stereo rig to describe a circular trajectory. We can also compose more complex trajectories if the geometry of the stereo rig is changed during the visual servoing.

Moreover, if one geometric configuration of the stereo head leads to one trajectory, a particular trajectory can be induced by various value combinations of angles and baseline lengths which have only an effect on the number of shots taken along the trajectory. It is thus necessary to ensure an overlapping of the camera fields of view to make possible visual servoing. Concerning the number of views necessary for the 3D reconstruction, we can mention research carried out by [13], [18] which makes possible to select a relevant subset of images from image sequences to estimate the epipolar geometry between the views and then to compute the 3D reconstruction. But these methods are only adapted for post-processing when a great deal of images have already been acquired. So they cannot be applied to determine the stereo rig geometry which is a requirement to visual servoing and image acquisition.

<figure><img src="image_1.png" /><figcaption>Fig. 1. Trajectory induced by the stereo rig geometry</figcaption></figure>

### III. VISUAL SERVOING APPROACH

The aim of visual servoing is to control the movement of the robot's end-effector using the information provided by vision sensors. A typical task consists in putting an "eye-in-hand" system in a given position with respect to an observed object [10]. Most visual servoing techniques are based on a "teaching-by-showing" approach [6]. In our case, given a reference image $\mathcal{I}^*$ taken by the right camera at the reference
<figure><img src="image_2.png" /><figcaption>Fig. 2. Perspective projections of a 3D point $\mathcal{X}$ on the two stereo rig cameras</figcaption></figure>

position $\mathcal{F}^*$, the goal is to reach the same position with the left camera.

Let us consider the pinhole camera model to perform a perspective projection of a 3D point $\mathcal{X} = (X, Y, Z, 1) \in \mathbb{P}^3$ to a virtual point $\mathbf{m} = (x, y, 1) \in \mathbb{P}^2$ in the frame $\mathcal{F}$ from the center of projection $\mathcal{C}$ (see Figure (2)). The relationship is defined by:

$$ \zeta \mathbf{m} = \frac{1}{Z} [\mathbf{R} \ \mathbf{t}] \mathcal{X} \qquad (10) $$

where $\zeta$ is the positive depth, $\mathbf{R}$ and $\mathbf{t}$ are respectively the rotation and the translation between frames $\mathcal{F}^*$ and $\mathcal{F}$ which set the stereo rig geometry. Point $\mathbf{m}$ gives the corresponding point $\mathbf{p} = (u, v, 1)$ measured in pixels in image $\mathcal{I}$:

$$ \mathbf{p} = \mathbf{K} \mathbf{m} \qquad \mathbf{p} \in \mathcal{I}(\mathcal{F}, \mathbf{K}) \qquad (11) $$

where $\mathbf{K}$ is the intrinsic parameter matrix of the left camera:

$$ \mathbf{K} = \begin{bmatrix} f & s & u_0 \\ 0 & rf & v_0 \\ 0 & 0 & 1 \end{bmatrix} \qquad (12) $$

where $u_0$ and $v_0$ are the coordinates of the principal point (in pixels), $f$ is the focal length (in meters), $s$ is the skew and $r$ is the aspect ratio. In the same way, points $\mathbf{p}^*$ are obtained in frame $\mathcal{F}^*$, but with different intrinsic parameters if the cameras are not the same.

Generally, using “camera-dependent” visual servoing methods [9] implies that the same camera is used to learn the reference image and to perform the visual servoing. If the cameras are different, the intrinsic parameters of these cameras must be precisely identified. Otherwise, the current image $\mathcal{I}$ converges towards the reference image $\mathcal{I}^*$, but with different camera positions. Note that the intrinsic parameters may significantly vary during the life of a vision system, and they can be changed intentionally when using zooming cameras [10]. We saw in section I, that it is difficult to calibrate cameras under underwater experimental conditions. So, we have used a visual servoing method allowing us to compute an error function invariant to camera intrinsic parameters $\mathbf{K}$ [8].

Let consider $n$ non-collinear 3D points of the observed object. These points are projected respectively in frames $\mathcal{F}^*$ and $\mathcal{F}$ to give points $\mathbf{p}_i^* = (u_i^*, v_i^*, 1)$ and $\mathbf{p}_i = (u_i, v_i, 1) \forall i \in 1, 2, \dots, n$. The latter are then projected into spaces $\mathcal{Q}^*$ and $\mathcal{Q}$ invariant to intrinsic parameters. To

carry out these projections, we need to compute the following $(3 \times 3)$ symmetric matrix:

$$ \mathbf{S}_p = \frac{1}{n} \sum_{i=1}^{n} \mathbf{p}_i \mathbf{p}_i^{\top} \qquad (13) $$

If the observed points are not collinear and $n > 3$, matrix $\mathbf{S}_p$ is symmetric positive definite and can be written, using a Cholesky decomposition:

$$ \mathbf{S}_p = \mathbf{T}_p \mathbf{T}_p^{\top} \qquad (14) $$

where $\mathbf{T}_p$ is a $(3 \times 3)$ non-singular upper triangular matrix, which allows us to compute points $\mathbf{q}_i \in \mathcal{Q}$:

$$ \mathbf{q}_i = \mathbf{T}_p^{-1} \mathbf{p}_i = (a_i, b_i, 1) \qquad (15) $$

In the same way, points $\mathbf{q}_i^*$ are computed with points $\mathbf{p}_i^*$. These new points are then contained in two vectors: $\mathbf{s}^* = (\mathbf{q}_1^*, \mathbf{q}_2^*, \dots, \mathbf{q}_n^*)$ and $\mathbf{s} = (\mathbf{q}_1, \mathbf{q}_2, \dots, \mathbf{q}_n)$. The camera has converged to the reference position when $\mathbf{s} = \mathbf{s}^*$. The derivative of vector $\mathbf{s}$ is written:

$$ \dot{\mathbf{s}} = \mathbf{L} \mathbf{v} \qquad (16) $$

where $\mathbf{L}$ is the $(3n \times 6)$ matrix of interaction, and the $(6 \times 1)$ vector $\mathbf{v}$ represents the Cartesian velocity of the camera.

The task function is:

$$ e = \hat{\mathbf{L}}^+(\mathbf{s} - \mathbf{s}^*) \qquad (17) $$

where $\hat{\mathbf{L}}^+$ is an approximation of the pseudo-inverse of $\mathbf{L}$ since $\mathbf{K}$ and $\zeta$ are unknown.

In order to control the movement of the camera by imposing the exponential convergence of the task function, the control law is:

$$ \mathbf{v} = -\lambda \mathbf{e}, \quad \text{where } \lambda > 0 \qquad (18) $$

This method has been tested with a stereo system, first by simulation, and afterwards by experiment, in order to generate large trajectories by repeating visual servoing. As it is shown in [9], the control law is stable even in the presence of calibration errors.

## IV. SIMULATION

The simulation allowed us to test the complete process of visual servoing. We have taken into account the real dimensions and parameters of the cameras (sensor dimension, pixel size and focal length), and of the robotic arm (such as joint limits, kinematic singularities, maximum articular velocities, axes dimension). The simulation of the arm makes possible to determine which trajectories can be performed within the robot workspace.

Figure (3) represents a trajectory simulation of the stereo rig carried by the robotic arm of the underwater vehicle. In Figure (3)(a) and Figure (3)(b), camera Cam1 is mounted on pan and tilt and is used to acquire reference images whereas camera Cam2 is fixed and is controlled during visual servoing. Both cameras have different intrinsic parameters. In these figures, the scatter plot stands for the 3D object such that it fits the shape of an underwater hydrothermal vent.

The camera trajectories, hence the stereo rig geometry, are chosen according to the size and the shape of the object under study. In this example, the trajectory is induced by a geometry of 0.3 meters between the cameras and a pan angle
<figure><img src="image_3.png" /><figcaption>Fig. 3. Simulation of trajectories</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 4. Projection of the scatter plot seen by the two cameras (red) in the invariant space (green)</figcaption></figure>

of 18 degrees. Figure (3)(a) and Figure (3)(b) show the side and the top view of the trajectory used for the simulation. The trajectory is marked by the successive positions of the reference camera in green points. It is composed of three quarters of a circle in order to cover the whole height of the object. To ensure the continuity of the trajectory, the stereo rig is U-turned at the end of a quarter of a circle. We can see that the arm cannot be manoeuvred all around the object if the vehicle is at a fixed location. So, to make the 3D reconstruction of an overall object, the underwater vehicle has to be landed at several positions.

Figures (4)(a) and (b) represents the scatter plot seen by both cameras, at the end of visual servoing once the controlled camera has converged towards the reference position. The picture on the right is image $I^*$ taken by the reference camera whereas the picture on the left is image $I$ taken by the controlled camera. We can notice that, because the intrinsic parameters are not the same for the two cameras, points $p$ do not match points $p^*$.

On the contrary, Figures (4)(c) and (d), the green scatter plot represents points $q$ and $q^*$ which are the projection of points $p \in I$ and $p^* \in I^*$ in space $Q$ and $Q^*$ invariant to intrinsic parameters. So, these intrinsics-free spaces are perfectly adapted to quantify the convergence of camera positions. These points are then used to compute the control law $v$ applied to the controlled camera.

Different trajectories adapted to various object shapes (cylinder, sphere, several plans, ...) have been simulated. Noise has been added to the point coordinates. The final aim for the use of simulation is to improve the robustness of the control law, and to observe the robot behaviour in order to prepare the experiments, and thus to prevent the real arm from damage.

## V. EXPERIMENTS

<figure><img src="image_5.png" /><figcaption>Fig. 5. Experimental conditions</figcaption></figure>

In this part we have chosen to present the first experiments led in laboratories which allowed us to validate the results obtained by simulation.

Experiments have been conducted using a 6 DOF arm to test the visual servoing loop under optimum conditions. Figure (5) represents an experiment carried out in laboratory with a baseline of 20 cm between the cameras, and a right camera pan angle of 15 degrees. With this geometry the stereo rig describes a circle around the object. Both cameras have different intrinsic parameters. The 3D target, located at approximately 1.3 m from the cameras, is composed of three plans with different normal vectors (Figure (5)(b)).
<figure><img src="image_6.png" /><figcaption>(a) End of the 1st servoing</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b) End of the 2nd servoing</figcaption></figure>

<caption>Fig. 6. Visual servoing</caption>

In order to compute the robot control law, features have to be extracted from images. We have focused our choice on a method based on a robust point extraction such as the SIFT algorithm [7]. These points are particularly robust to solve the difficult matching correspondence problem in underwater images of vent chimneys. Keypoints extracted from the reference and the current images are matched. A RANSAC algorithm [4] is applied to remove false matches. We then obtain points $\mathbf{p}^*$ (see section III) in the reference image, and points $\mathbf{p}$ matched in the current image of the controlled camera.

Points $\mathbf{p}$ are tracked in the current image until the left camera reaches the right camera position. The ESM tracking [1] algorithm has been chosen for these first experiments. But this method allows us to track only planar targets, therefore in the first experiments, the 3D target is made up of several plans. As soon as a new image is acquired, points are tracked and the command is computed and applied to the robot. To generate the command, the coordinates of points $\mathbf{p}^*$ and $\mathbf{p}$ are projected in invariant spaces $\mathcal{Q}^*$ and $\mathcal{Q}$, to obtain respectively points

<figure><img src="image_8.png" /><figcaption>Fig. 7. Task function of the 1st servoing</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Task function of the 2nd servoing</figcaption></figure>

$\mathbf{q}^*$ and $\mathbf{q}$, invariant to intrinsic parameters. At each iteration, points $\mathbf{q}$ are computed with the new coordinates of points $\mathbf{p}$.

When points $\mathbf{q}^*$ and $\mathbf{q}$ are superposed, task function $\mathbf{e}$ has converged exponentially towards zero (Figure (7) and Figure (8)). This is also illustrated in Figure (6), which represents the end of two successive displacements of the stereo rig, when the left camera position has reached the reference camera position. The starting position is represented in transparency, in order to show the superposition of the left camera on the reference position. Finally, we can see in Figure (7) and Figure (8) that the control law is stable in spite of noise and calibration error.

In pool trials are currently carried out in order to prepare the at sea trials. In Figure (9), we can see on the left the stereovision system made up of a frame in aluminium, two LED lights and two underwater cameras that are mounted on a baseline. One of these is a pan and tilt camera. On the right, the object is designed so that it is similar by its size, its shape and its texture to a section of a deep-sea vent. The results concerning these experiments will be presented in a future paper.

<figure><img src="image_10.png" /><figcaption>Fig. 9. In pool trials with the stereovision system and a 3D target</figcaption></figure>
## VI. DISCUSSION

Our application relates to supervised exploration of ocean floors but does not concern autonomous exploration as it is defined by [20]. Our aim is to collect in real time with the most effectiveness the data concerning an object identified by an operator in order to improve the 3D reconstruction in a post-processing stage. In our case, time constraint is of great importance since deep-sea experiments are generally heavy to set up and to carry out. That is why we cannot afford to spend much time merging different sources of information during visual servoing and image acquisition. The solution we propose is thus to use only vision sensors to perform a predefined trajectory. But some uncertainties are induced by noise in the image that leads to a shift of the camera positions from their theoretical positions. It is thus necessary to take these uncertainties into account and to correct them in order to improve the quality of the final reconstruction result. To reduce these uncertainties, the noise can be first reduced by filtering during visual servoing. Then, in a post-processing stage, we use an algorithm of minimization, such as a sparse bundle adjustment algorithm [19], initialized with the theoretical camera positions.

Although the method of visual servoing we propose does not require the knowledge of camera intrinsic parameters, the latter have to be estimated in order to carry out a metric reconstruction. They can be estimated by a self-calibration method which does not imply the use of additional material. This is a great advantage for applications using robots whose payload capacity is limited. Some methods are well-suited to our application as [5] because the constrained nature of the motion to perform the self-calibration corresponds to the type of trajectories described by visual servoing.

## VII. CONCLUSION

In this paper, we have presented an innovative visual servoing scheme in order to improve the 3D reconstruction of an unknown underwater object. The stereovision system we have specified allows us to generate predefined trajectories around the object under study, and thus to take pictures at regular intervals that are determined by the stereo rig geometry. Because the cameras are not necessarily the same and the intrinsic parameters may vary according to the environment, we have focused our attention on an intrinsics-free visual servoing method [9].

After the validation of our technique under laboratory conditions, tests under real underwater conditions are in progress. The at sea trials will bring additional constraints, yielding to a strong degradation of the images. These deteriorations are principally due to the presence of suspended particles and the problems of illumination in deep-sea environment associated to absorption that attenuates light. Moreover, the phenomenon of diffusion introduces a blur into the image [12]. Besides, the illumination of the objects by a lighting source rigidly linked to the cameras involves a variation of textures during the visual servoing because of the dropped shadow phenomenon. The noise in the image, the loss of the tracked points, the number of points and their distribution in the image can disturb the control law stability. But the first results obtained during in pool trials with the underwater stereovision system are pretty good and are promising for the future at sea trials. It thus will be very interesting to compare in a future paper the experiment

results obtained under optimal laboratory conditions with those obtained in the complex world of the ocean depths.

Future work will focus on a novel technique for metric reconstruction adapted to underwater objects. Owing to a regular distribution of the shots taken around the object, the camera position corresponding to the images can be used as prior knowledge for the 3D reconstruction. Indeed, the number of unknown variables is reduced, increasing the accuracy and the speed of the optimization process, hence improving the reconstruction [11].

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