Calibration of a Telecentric Structured-light Device

for Micrometric 3D Reconstruction

Mara Pistellato

, Andrea Albarelli

and Filippo Bergamasco

DAIS, Universit

a Ca’Foscari Venezia, 155, via Torino, Venezia Italy

{mara.pistellato, ﬁlippo.bergamasco, albarelli}@unive.it

Keywords:

Camera-projector Calibration, Structured-light Scanning, Telecentric Lenses, Micrometric Surface

Reconstruction.

Abstract:

Structured-light 3D reconstruction techniques are employed in a wide range of applications for industrial

inspection. In particular, some tasks require micrometric precision for the identiﬁcation of microscopic surface

irregularities. We propose a novel calibration technique for structured-light systems adopting telecentric lenses

for both camera and projector. The device exploits a ﬁxed light pattern (striped-based) to perform accurate

microscopic surface reconstruction and measurements. Our method employs a sphere with a known radius as

calibration target and takes advantage of the orthographic projection model of the telecentric lenses to recover

the bundle of planes originated by the projector. Once the sheaf of parallel planes is properly described in

the camera reference frame, the triangulation of the surface’s object hit by the light stripes is immediate.

Moreover, we tested our technique in a real-world scenario for industrial surface inspection by implementing

a complete pipeline to recover the intersections between the projected planes and the surface. Experimental

analysis shows the robustness of the proposed approach against synthetic and real-world test data.

1 INTRODUCTION

Structured-light approaches adopt a controlled light

source with known geometry to locate the same ma-

terial point from different views, recovering its depth

via triangulation (Pistellato et al., 2015). A classi-

cal example is the well-known phase-shift method

(Zuo et al., 2018; Pistellato et al., 2018), widely

used in several applications with appropriate unwrap-

ping algorithms (Pistellato et al., 2019a; Pistellato

et al., 2019b). Such approaches are portable solu-

tions which can be easily integrated in industrial set-

tings, allowing for high precision measurements with-

out touching the artefact (Xu et al., 2011b; Xu et al.,

2011a). In these scenarios the adoption of a precise

measurement system is a key element to assess the

quality of the manufactured objects during construc-

tion, specially because an accurate and extensive con-

trol also reduces potential issues that may emerge dur-

ing the subsequent production steps.

Fringe projection is often employed in the con-

text of microscopic applications, where the acquired

https://orcid.org/0000-0001-6273-290X

https://orcid.org/0000-0002-3659-5099

https://orcid.org/0000-0001-6668-1556

Telecentric lens

Object

Bundle of planes

generated by the

pattern

Stripe pattern projected

onto the object surface

Stripe pattern

Scheimpflug

adjustment

Stripe pattern

observed by

the camera

Figure 1: Picture and geometric schema of our telecentric

camera-projector 3D reconstruction device.

440

Pistellato, M., Albarelli, A. and Bergamasco, F.

Calibration of a Telecentric Structured-light Device for Micrometric 3D Reconstruction.

DOI: 10.5220/0010841700003122

In Proceedings of the 11th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2022), pages 440-448

ISBN: 978-989-758-549-4; ISSN: 2184-4313

object features’ size ranges from millimetres to mi-

crons. This is the case of several tasks, as quality

control (Weckenmann et al., 2006), weld pool surface

depth measurement (Saeed and Zhang, 2007), lami-

nated plastic wrinkles evaluation (Yao and Xu, 2007),

electrical components or small coins reconstruction

(Li et al., 2014; Liu et al., 2015). Additional exam-

ples include the work presented in (Bergstr

om et al.,

2011; Rosendahl et al., 2010) for an object shape ver-

iﬁcation system using structured-light and stereo cor-

respondences, while (Li and Zhang, 2017), proposes

to combine fringe projection with binary defocusing

technique (Lei and Zhang, 2009) for 3D microscopic

proﬁlometry. When the acquisition speed is a limiting

factor, ﬁxed patterns are typically used in the form of

random distributions (Chen et al., 2018) or binary and

coloured codes (Zhou et al., 2017). Shape from single

stripe pattern is proposed in (Winkelbach and Wahl,

2002), where authors devise surface normals from the

stripes observed by a single camera. All the afore-

mentioned applications require an initial calibration

to assess the geometric relations between the compo-

nents involved in the acquisition.

Such process has a direct impact on the quality of

the reconstruction, particularly for industrial-related

applications, where accuracy is a critical requirement.

In the speciﬁc case of telecentric surface reconstruc-

tion, the narrow ﬁeld-of-view of the lenses requires a

specialised method as well as a speciﬁcally-designed

calibration target. Common approaches can employ

a small planar target with a grid dot pattern that can

be easily detected and identiﬁed by the imaging sys-

tem (Li et al., 2014; Li and Zhang, 2015; Chen et al.,

2014; Bergamasco et al., 2011), complex 3D targets

(Liu et al., 2017), or none (Bergamasco et al., 2014).

In this paper we describe a structured-light de-

vice based on telecentric fringe projection proﬁlom-

etry for micrometic measurements. Our setup com-

bines a telecentric camera and projector with a ﬁxed

pattern composed by equally spaced parallel lines.

Both camera and projector imaging systems are af-

fected by negligible lens distortion and are charac-

terised by an orthographic projection model. The ad-

vantages of employing a single striped pattern are sev-

eral: ﬁrst, we need a single shot to reconstruct the

scene, thus the acquisition and computation speed are

signiﬁcantly increased. Moreover, the system does

not require accurate gamma calibration and it does not

suffer from particular scene features like non-uniform

albedo or materials. The contribution is twofold: ﬁrst,

we propose a novel calibration solution involving the

observation of a sphere with a known radius in differ-

ent positions. The intersections of the parallel planes

generated by the projected pattern with the spherical

surface originate a series of coaxial 3D circles that are

projected as ellipses on the camera image plane. Such

curves can be exploited to geometrically compute the

system parameters and obtain the correct pixel scale

by ﬁtting the 3D sphere. The second contribution con-

sists in a speciﬁc case-of-study where the described

sensor is employed to reconstruct the internal surface

of industrial gearwheels. The overall accuracy and

low cost of such approach makes it a potential substi-

tute for the classic contact measuring for quality as-

sessment in industrial applications. Indeed, it is par-

ticularly suitable for the inspection of smooth surfaces

requiring micrometric precision.

2 CALIBRATION TECHNIQUE

Considering their orthographic imaging model, tele-

centric lenses are particularly convenient to measure

small objects. In an orthographic camera the centre

of projection is located at inﬁnity, so that rays com-

ing from the captured object intersect the image plane

orthogonally (Hartley and Zisserman, 2003). This im-

plies that the projection on the image plane is not af-

fected by the object’s depth, and thus the size of each

pixel corresponds to a certain length in the real world,

making straightforward to measure distances along x

and y axes. On the other hand, depth computation and

3D reconstruction are not immediate and require spe-

cialised approaches.

Our device is sketched in Figure 1: the projector

casts on the scene a ﬁxed pattern consisting in a series

of equally-spaced straight lines. Such lines generate

a bundle of equispaced parallel planes P in 3D space,

that are orthogonal to the projector’s image plane. We

deﬁne the stride ∆ as the distance between any two

consecutive planes. This value is proportional to the

lines distance on the projector’s image plane, but it is

scaled by a multiplicative unknown factor. Such scale

depends on the combination of (i) the magnifying fac-

tor of the telecentric lens and (ii) the inclination of

the projector’s focus plane (Scheimpﬂug adjustment),

that needs to be aligned with the camera image plane

to obtain the optimal depth-of-ﬁeld.

The planes orientation with respect to the camera

coordinate system and their stride are unknown, thus

we identify three parameters that need to be estimated

by the calibration process:

1. the normal vector n =





of all the

parallel planes in the bundle P with respect to the

camera reference frame;

2. The scale factor s between camera pixels and the

real world units (i.e. pixel’s size in millimetres).

Calibration of a Telecentric Structured-light Device for Micrometric 3D Reconstruction

441

Figure 2: Left: telecentric projector (in blue) generates a parallel sheaf of planes P intersecting a known sphere used as

calibration target. Such intersections result in coaxial circles in space which (due to self-occlusions) are observed as a set of

arcs by the camera. Right: each circle is projected to the image plane as the ellipse E

. The normal n can be obtained by

rotating the vector z around the axis a

, but two alternative solutions (n

′

and n

′′

) are equally valid and must be disambiguated.

3. The stride ∆.

All the planes in the bundle are identical, and

therefore is not possible to distinguish their abso-

lute offset (or numbering) within the projector im-

age plane. For this reason, we assume to only recog-

nise their relative order (i.e. which one comes after

another) but not their absolute index with respect to

the ﬁrst one, which generally depends by the depth

of the observed object. So, without loss of general-

ity, we can assume that P contains an inﬁnite set of

planes P

= (p

, n), P

= (p

, n), . . . (parameterised as

a point p

and the normal vector n) such that p

= ∆ni.

During the calibration process, a sphere with

known radius r is imaged so that a subset of N planes

originated from the projector are cast on the sphere’s

surface. The intersection of parallel planes with with

the sphere generates N circles in 3D space that ex-

hibit some particular properties: (i) they are are coax-

ial since all the slicing planes are parallel, (ii) their

3D centres lie on a line L in space, and (iii) L is

orthogonal to the parallel sheaf of planes (i.e. line

direction has the same orientation as n). Since the

sphere self-occludes the projected light rays, only N

arcs A

. . . A

of the full circles are visible on the sur-

face. Such N 3D circle arcs are therefore imaged by

the camera as portions of N 2D ellipses E

, ..., E

. For

each ellipse E

with i = 1, ..., N, the plane bundle nor-

mal vector n can be recovered up to two equally pos-

sible conﬁgurations.

Let C

be the i

circle generated by the intersec-

tion of the i

plane in P and the sphere. Since we

are using an orthographic camera, C

projects to an

ellipse E

having a

and b

as major and minor axes

respectively (see Fig. 2). The length of a

is equal

to the radius r of the sphere, so if we rotate the bun-

dle of planes P around the axis a

the eccentricity of

changes. In particular, as shown in (Bergamasco

et al., 2020; Pistellato et al., 2019c), the ratio between

the semi-axes is a function of the angle θ between the

normal n and the camera z-axis:

cos θ =

||b

||a

. (1)

In this setting, the bundle normal n can be ob-

tained by rotating the vector z = (0, 0, 1)

around the

axis a

with two equally possible angles:

1,2

= ± arccos

||b

||a

. (2)

As a consequence, each ellipse E

generates two

equally possible normal vectors n

′

and n

′′

. Note that

also −n

′

and −n

′′

are valid solutions but can be ig-

nored in the disambiguation process since they repre-

sent the same plane.

The 3D line L connecting all the circles’ centres

projects onto the camera image plane as the 2D line l

passing through the ellipses centres. The disambigua-

tion of the correct n exploits the geometry of l to ﬁlter

out the wrong plane normals. Indeed, we recall that

n is parallel to the axis L and that all normal vectors

generated by the N ellipses must be oriented to the

same direction. So, among all the alternatives, we

keep the normal vectors whose angles formed with

the axis L is minimum.

Finally, since the ellipses centres are the ortho-

graphic projections of the 3D circles centres, the

stride value can be computed from the relative dis-

tance (in pixels) between adjacent ellipses centres on

the image plane. The relation between such distance

and the stride value is the following:

∆ =

sin(β)

(3)

ICPRAM 2022 - 11th International Conference on Pattern Recognition Applications and Methods

442

Inlier Detection

Curve Extraction

and Ellipse Fitting

Calibration

• Stride

• Planes Normal

Triangulation

and Sphere Fitting

Image Acquisition

and Preprocessing

Figure 3: Our proposed calibration pipeline. From left to right: (i) Stripe pattern is projected and a known calibration sphere

is exposed to the camera in different positions. Thresholding, skeletonization, and ﬁltering is applied to cluster each arc. (ii)

Ellipses are robustly ﬁtted to arc points (via RANSAC) and a selection procedure is used to extract a subset of inlier ellipses

whose centers are uniformly distributed on a straight line. (iii) Plane bundle stride and normal is estimated is §2. (iv) 2D arc

points are triangulated by intersecting the corresponding exiting camera rays with the recovered plane bundle. A sphere is

ﬁtted to the obtained 3D points.

where β is the angle formed by the plane normal n

and the camera z-axis, and d is the distance (in cam-

era pixels) between two consecutive projected cen-

tres. Note that, due to the orthographic projection,

this is the equivalent of computing the hypotenuse of

a right-angled triangle.

Once the stride ∆ and plane normal n are com-

puted, points composing the 3D arcs A

. . . A

can be

triangulated by simply intersecting the exiting cam-

era rays passing through ellipses E

. . . E

with the

3D planes in P . Let e

∈ R

be the j

2D point of

the ellipse E

. Its 3D position g

is given by:

− e

)









. (4)

The obtained point cloud is then ﬁtted to a sphere

model S, obtaining a radius r

, expressed in camera

pixels. Since the acquired sphere has known radius,

the scale between pixels and world units is simply

given by

s =

. (5)

Finally, to obtain a robust parameter estimation

the procedure is repeated for different sphere loca-

tions. The ﬁnal parameters are computed by aver-

aging the resulting values, excluding the acquisitions

for which the RMS of the distance between the ﬁtted

sphere and the 3D points is above a threshold.

Note that the relative position of the triangulated

points is correct, but their absolute depth can be re-

covered up to an unknown multiple of the stride since

the planes are not distinguishable one from the other.

In other words, matching between a certain 2D point

and the bundle plane from which it was originated

is somehow arbitrary. This is not a showstopper for

many industrial applications, especially when the goal

is to recover the shape of the surface and not its po-

sition, which is often the case with quality assurance.

In cases where the absolute position of the surface is

also needed, it would be straightforward to set an ab-

solute numbering for stripes, for instance by using a

special marker embedded in the pattern.

2.1 Implementation Details

The whole calibration procedure is sketched in Fig-

ure 3. We start by projecting the stripe pattern to

the calibration sphere placed at different random posi-

tions in front of the camera. Stripe contour points are

extracted by applying a series of image ﬁlters: ﬁrst,

5 binary images are obtained by applying 5 differ-

ent threshold levels to the original image. The skele-

tonization for each binary image is computed, as de-

scribed in (Lee et al., 1994), to generate a set of 5 bi-

narized skeleton masks. Then, the skeleton masks are

summed into an accumulator in which morphologi-

cal dilation is applied to join the isolated portions of

each arc (ie. close small holes of the original skele-

ton masks). Finally, the accumulator is thresholded

to extract all the connected components representing

candidate ellipse arcs to be tested.

To provide a reliable an accurate ellipse ﬁtting, we

adopted a RANSAC-based approach as described in

(Halır and Flusser, 1998). We ﬁltered all the ellipses

with less than 80% inliers among the point data, con-

sidering a RANSAC inlier distance of 2 camera pix-

els. In this way, all the extracted arcs that are not

ellipses in the image are automatically discarded.

An additional inlier selection is then performed

over the set of ellipses by ﬁtting a line through their

centres and checking their relative distance in pixels.

Then, the ellipses whose centres are not uniformly

distributed along the line are discarded (See. Alg.1).

In Figure 3 (third image) the inlier ellipses used to

Calibration of a Telecentric Structured-light Device for Micrometric 3D Reconstruction

443

Figure 4: Calibration absolute errors on a synthetic scene. 2D ellipse points are perturbed with a zero-mean Gaussian random

noise with standard deviation σ

. For each noise level, the calibration is repeated several times measure the error against the

ground truth.

Algorithm 1: Ellipse inlier detection.

. . . c

← centres of E

. . . E

ﬁt a line l trough c

. . . c

via RANSAC

S ← set of indices i such that dist(c

, l) < t

ˆc =

|S |

∑

i∈S

l ← ﬁt a line through points in S

K ← ⟨⟩

for i ∈ S do

ˆc

← project c

add ˆc

in K

end for

Sort points in K according to their signed distance

to ˆc

m ← |K | − 1

Compute ⟨

. . .

⟩ where

= ∥K

k+1

− K

∥

D ← median(⟨

. . .

⟩)

Inliers ← points in K s.t. dist(

, D) < t

calibrate the system are displayed.

At this point, the selected ellipses are used to com-

pute the plane normal and the stride value as de-

scribed in the previous section. In practice, every el-

lipse gives a independent estimation of n and ∆. We

simply average all such estimations to reduce the er-

ror. Then, the points belonging to the ellipses are tri-

angulated and used to ﬁt a 3D sphere with a standard

linear least-squares approach. Finally, the pixel scale

s is recovered as in (5). Figure 3 (right) shows an

example of the resulting triangulated points and the

corresponding ﬁtted sphere.

3 EXPERIMENTAL EVALUATION

In order to evaluate the performances and the stability

of the proposed method, we designed a set of syn-

thetic and real-world experiments. First, we tested

the accuracy of the parameter estimation from a single

shot, introducing some noise and varying the system

conﬁguration. Then, we exploited our setup to vali-

date the algorithm stability in the case of real-world

applications.

3.1 Synthetic Validation

Synthetic tests give us the full control over the scene,

allowing for a systematic validation of the proposed

technique. We ﬁrst decided to test the accuracy of

the calibration method against acquisition noise, then

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444

20 30 40 50 60 70

Projector Angle

0.2

0.4

0.6

0.8

Abs Error (rad)

Angle Absolute Error

20 30 40 50 60 70

Projector Angle

Abs Error (px)

-3

Sphere Fitting RMS

Figure 5: Results on a synthetic scene increasing angle between camera and projector.

we analysed the behaviour of the system varying the

relative position between projector and camera. In our

synthetic tests we simulated a conﬁguration similar

to the real setup, with a virtual orthographic camera

and projector. The projector emits a set of 20 parallel

planes with a ﬁxed stride equal to 0.5 (camera px),

and the camera captures a sphere with a radius equal

to 3 pixels.

In the ﬁrst experiment we ﬁxed the projector ori-

entation to 45 degrees with respect to the camera z-

axis. Then, we randomized the sphere position (sim-

ulating a real acquisition) and perturbed the projected

2D points of each ellipse with a zero-mean Gaussian

noise with standard deviation σ

. Results are shown

in Figure 4, where the absolute errors with respect to

the ground truth are plotted. We increased the error

standard deviation σ

applied to 2D points and mea-

sured (i) the angle error with respect the plane nor-

mals, (ii) the stride error, (iii) the sphere radius esti-

mation error, and (iv) the Root Mean Square (RMS)

error of the triangulated points with respect to the

sphere surface.

We repeated each test 100 times, with different

sphere locations, using only one picture to calibrate

the system. As expected, the errors increase linearly

with the noise. In particular, for relatively small per-

turbations, the angle absolute error is smaller than

0.05 radians, and the sphere radius estimation error is

below 0.03 pixels, that is the 2% of the actual radius.

As a second test, we analysed the impact of the

relative angle between the projector and the camera.

Indeed, since the observed portions of ellipses are

fundamental to devise the ﬁnal system parameters,

we studied such effect on our synthetic setup to de-

sign an optimal conﬁguration for our real-world pro-

totype. To do so, we basically repeated the previous

test, this time varying the relative angle between the

camera and the projector z-axes. Note that with an

angle close to 0 degrees the camera observes straight

lines, because the plane normals are orthogonal to its

z-axis, while when the angle is 90 degrees the camera

should observe circle arcs. Results of this tests are

shown in Figure 5. Interestingly, the projector angle

exhibits a very high impact on the plane normal es-

timation, with an optimal orientation equal to 45 de-

grees. Other measurements are slightly affected by

such angle, as shown for the sphere RMS.

3.2 Real-world Results

In our real-world tests we employed a camera-

projector pair, both equipped with telecentric lenses.

The camera acquires greyscale images with a 12

MPixels resolution, and we used a line pattern with

a physical stride of 0.05 mm. The devices were

mounted on a solid structure with a relative angle of

approximately 45

◦

, in a way that the plane of focus

for both camera and projector are aligned to a com-

mon area of interest (see Fig. 1 and 7). The sphere

used for calibration is a smooth ceramic bearing ball

with a diameter of 8 mm and a declared surface toler-

ance of 0.7 microns.

We evaluated the accuracy and repeatability of the

calibration varying the number of sphere acquisitions.

A total of 30 images were acquired, varying the po-

sition of the sphere in the camera-projector frustum.

Then, we used a cross-validation approach working

as follows. The set of 30 images is divided in m par-

titions. For m times, one partition is used for calibra-

tion and the remaining m − 1 for testing. The opera-

tion is repeated varying the number of partitions (and

consequently the number of image samples used for

calibration, in x-axis) and plotted in Fig.6. Each test

was repeated 20 times, and the standard errors are also

shown as error bars.

We can observe that the normal estimation er-

ror between calibration and test set is in the order

of 4.4 · 10

−3

radians, the stride error lower than 1.5

Calibration of a Telecentric Structured-light Device for Micrometric 3D Reconstruction

445

5 10 15 20

Number of Samples

4.2

4.3

4.4

4.5

4.6

4.7

4.8

Angle Error (rad)

-3

Normal Error

5 10 15 20

Number of Samples

0.9

1.1

1.2

1.3

1.4

Error (px)

Stride Error

5 10 15 20

Number of Samples

3.2

3.4

3.6

3.8

4.2

4.4

4.6

4.8

Error (px)

Radius Error

Figure 6: Calibration parameters estimation errors varying the number of acquisitions. From left to right: planes normal

absolute error (rad), stride absolute error (px), and radius error (px).

camera pixels and sphere radius absolute error consis-

tently lower than 4 camera pixels for a number of cal-

ibration samples greater than 5. Moreover, the RMS

of triangulated points over the ﬁtted sphere is below 1

px for the majority of the acquired images. Consider-

ing that the computed scale (ie. the camera pixel size)

s is 3.24 · 10

−3

mm/px, such error is approximately

6.5 microns.

We also tested the 3D reconstruction accuracy by

means of the RMS error between the reconstructed

3D points and the ideal sphere calibration target.

Overall, it ranges from 0.3 to 1.7 pixels, correspond-

ing to 5 microns on average.

Figure 7: Our prototype setup to analyse the internal gear-

wheel’s surfaces.

4 APPLICATION: INDUSTRIAL

SURFACE ANALYSIS

In this section we present an industrial application of

our setup to acquire and analyse the internal gear-

wheel surfaces during the ﬁnal steps of their produc-

tion (Fig.7).

Gearwheels manufacturing is a ﬁeld in which pre-

cision and repeatability is critical since the gear’s

teeth need to perfectly ﬁt the shape of other similar

components in a mechanical machinery.

When illuminated by our stripe projector and ac-

quired by the camera, the teeth surface appears as a

semi-shiny material, characterised by diffused micro-

scratches as shown in Fig. 8a.

For this application we ﬁrst apply a sequence of

image ﬁlters so that the line pattern proﬁles are accu-

rately extracted.

The result of image pre-processing task is shown

in Figure 8b, where each extracted curve is high-

lighted in yellow. For each detected curve, a spline is

ﬁtted and then adjacent curves are identiﬁed in order

to enumerate each subsequent projector plane. The

actual teeth reconstruction is carried out by triangu-

lating the detected splines. This is done ﬁrst by uni-

formly sampling a set of discrete 2D point from each

curve, and then by intersecting each point with the

corresponding plane of P . The procedure generates a

3D point cloud composed by the union of individual

sampled curves, shown in Figure 8c.

Then, adjacent curves are analysed to ﬁnd point-

to-point correspondences between them. This is per-

formed by running the Iterative Closest Point (Besl

and McKay, 1992) algorithm between two adjacent

curves to ﬁnd their optimal alignment. The point

matches given by the last iteration of ICP are used to

synthetize additional points by uniform sampling 3D

points on the straight lines connecting them.

Finally, Delaunay 2D triangulation (Chen and

ICPRAM 2022 - 11th International Conference on Pattern Recognition Applications and Methods

446

(a) (b)

Figure 8: Gearwheel teeth analysis. (a) image acquired by the camera. (b) Striped-pattern curve detection. (c) 3D point

cloud obtained by triangulating each stripe. (d) Final tooth surface reconstruction (colour denotes z-coordinate to highlight

the curvature).

Bishop, 1997) is applied to join the 2D points projec-

tions on the camera image plane and obtain a dense

triangulated surface. An example of the ﬁnal result is

shown in Fig. 8d.

5 CONCLUSIONS

In this paper we proposed a micrometric calibration

process for telecentric camera-projector setups, em-

ploying a ﬁxed-striped pattern. We used a known

spherical target to retrieve the geometrical character-

istics of the system with a precision that can reach the

order of microns. Since such targets are easy to man-

ufacture and not expensive compared to their dimen-

sional accuracy, the whole procedure can be carried

out with a limited effort and costs. Synthetic and real-

world experiments conﬁrm both the stability of our

method and its level of accuracy.

Additionally, we described a case-study of such a

system, by means of a complete pipeline for micro-

scopic surface acquisition and reconstruction involv-

ing micrometric gearwheel surface measurements.

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