Segmentation-based Multi-scale Edge Extraction to Measure the

Persistence of Features in Unorganized Point Clouds

Dena Bazazian, Josep R. Casas and Javier Ruiz-Hidalgo

Signal Theory and Communications Department, Universitat Polit

ecnica de Catalunya, Barcelona, Spain

Keywords:

Edge extraction, Multi-scale, Segmentation, Unorganized Point Cloud.

Abstract:

Edge extraction has attracted a lot of attention in computer vision. The accuracy of extracting edges in point

clouds can be a signiﬁcant asset for a variety of engineering scenarios. To address these issues, we propose a

segmentation-based multi-scale edge extraction technique. In this approach, different regions of a point cloud

are segmented by a global analysis according to the geodesic distance. Afterwards, a multi-scale operator is

deﬁned according to local neighborhoods. Thereupon, by applying this operator at multiple scales of the point

cloud, the persistence of features is determined. We illustrate the proposed method by computing a feature

weight that measures the likelihood of a point to be an edge, then detects the edge points based on that value

at both global and local scales. Moreover, we evaluate quantitatively and qualitatively our method. Experi-

mental results show that the proposed approach achieves a superior accuracy. Furthermore, we demonstrate

the robustness of our approach in noisier real-world datasets.

1 INTRODUCTION

The computer vision community has drawn attention

to 3D scene analysis in recent years, with data

captured with stereo and multi-camera systems, and

especially after the success of commercial depth

sensors, such as MS Kinect or Asus Xtion. The data

acquired by these devices, however, may contain

noise, outliers and, even if the projected points are

uniformly distributed on the image (at the pixel

level), the distribution tends to be highly non-uniform

in the 3D point cloud. The situation becomes more

complicated since the point clouds are unorganized:

the points in the cloud are not initially connected,

and information about surface normals has to be

computed with a certain amount of uncertainty. For

these reasons, the shape analysis of the measured

data-set becomes highly challenging in computer

graphics and computer vision.

Our research deals with the edge extraction problem

in surfaces represented by point clouds. Estimating

and identifying edges enables a better understanding

of the structural features of the underlying surfaces.

An edge is formed when two surfaces, which we may

approximate by planes, with sufﬁciently different

orientation meet. Hence, the planes deﬁned by

normal vectors of the surrounding points should be

estimated in order to determine an edge point. A

region of contiguous edge points is then deﬁned

as an edge region in the surface represented by the

unorganized cloud.

Edge extraction identiﬁes crucial characteristics

of the underlying geometry. It can be used to detect

feature points, and improves the performance of

geometry processing such as adaptive sampling,

segmentation, detection and scene analysis.

For edge extraction techniques, multi-scale schemes

improve noise sensitivity and add robustness against

the scale dependency of features. The rationale

behind this is to get an optimal scale for each point in

order to analyze the intrinsic structure around it.

In our approach, we segment the surface to explore

global classiﬁcation of edges and feature points.

One of the aspects of the multi-scale analysis is to

cope with false feature measurements arising from

the fact that part of the surface intersects the local

neighborhood.

The main contributions of this paper are the fol-

lowing. First, we put forward a new classiﬁcation

framework that allows for discrete surface analysis at

multiple scales. Second, we propose an optimal edge

extraction technique by considering a segmentation

of the surface in order to obtain a multi-scale descrip-

tion of edges in the point cloud. Third, we improve

the accuracy of the edge extraction technique in

Bazazian D., R. Casas J. and Ruiz-Hidalgo J.

Segmentation-based Multi-scale Edge Extraction to Measure the Persistence of Features in Unorganized Point Clouds.

DOI: 10.5220/0006092503170325

In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), pages 317-325

ISBN: 978-989-758-225-7

317

unorganized point clouds.

The remainder of the article is organized as follows.

Section 2 presents related work, followed by a de-

scription of our approach and architecture in Section

3. Section 4 reports the experimental results of our

approach, and conclusions are drawn in section 5.

2 RELATED WORK

The state of the art for edge extraction in point clouds

is summarized below. We group the various contri-

butions according to the different aspects of the prob-

lem: extraction of sharp features, estimation of nor-

mals, segmentation and multi-scale approaches.

2.1 Sharp Feature Extraction

Robust statistics have been exploited to extract sharp

features (Fleischman et al., 2005; Daniels et al., 2008;

Oztireli et al., 2009). A technique for edge detection

for the registration of point clouds was introduced by

Choi (Choi et al., 2013). Other authors have explored

just the detection of edge points (Sidiropoulos and

Lakakis, 2016) or the segmentation of larger geomet-

ric structures such as surfaces (Demarsin et al., 2007;

Xu et al., 2015), lines (Lin et al., 2015) and, more re-

cently, contour detectors based on classiﬁers (Hackel

et al., 2016) have also been proposed.

In unorganized point clouds, the geometry deﬁned

by the neighborhood of a point is almost the only

available information to extract features from. In this

line, several authors (Weber et al., 2010; Weber et al.,

2012; Gumhold et al., 2001; Feng et al., 2014) pro-

pose a region growing method that decomposes the

point cloud into clusters, and identiﬁes the regions

with sharp features based on the analysis of the nor-

mals. In these approaches, extracting sharp edge fea-

tures from a 3D point cloud requires the computation

of accurate normals from the neighborhood to gener-

ate high quality surfaces. This brings up the problem

of normal estimation, which is closely related to sharp

feature extraction, as we will discuss next.

2.2 Normal Estimation

Regression based estimation was ﬁrst proposed by

Hoppe (Hoppe et al., 1992). For each point in the

cloud, a least squares local plane is ﬁtted to its k near-

est neighbors using PCA. The normal at each point is

the eigenvector corresponding to the smallest eigen-

value of the covariance matrix (Lange and K., 2005).

By assigning Gaussian weights to the neighbors of

each point, Pauly and Gross (Pauly et al., 2003b;

Gross and Pﬁster, 2007) proposed a weighted version

of this basic approach. For noisy point clouds, Mi-

tra (Mitra and Nguyen, 2003) suggested an adaptive

neighborhood size based on local properties, such as

noise scale, curvature and sampling density. A sim-

ilar motivation led Wang (Wang and Feng, 2015) to

propose an algorithm to develop a normal estimation

method that rejects neighborhood outliers.

2.3 Segmentation

Various algorithms have been proposed for point

cloud segmentation as an indirect approach to extract

edges. Some methods are based on the surface such

as those by Zhang and Reisner (Zhang et al., 2013;

Reisner-Kollmann and Maierhofer, 2012), which at-

tempt to ﬁnd sets of points in the scene that ﬁt planes

and primitives. Moreover, Rabbani and Son (Rabbani

et al., 2006; Son and Kim, 2013) proposed a graph

based method which do not constrain users to model-

ing with primitives. In addition, Liu (Liu and Youlun,

2008) proposed a mapping of the normal of a point

cloud into a Gaussian sphere, producing a Gaussian

image; afterwards this spherical image can be clus-

tered to identify shapes. Furthermore, Kustra (Kus-

tra et al., 2014) proposed to ﬁnd the most probable

local quasi-ﬂat surface patches passing through each

point by using a clustering approach, and then merg-

ing these patches to classify the input points into man-

ifolds or noise.

2.4 Multi-scale

Deﬁning a proper neighborhood for each point in the

cloud raises the question of ﬁnding the right scale fac-

tor. Scale in computer vision has always been of ex-

treme importance, more so with true space 3D data

as in point clouds. It constitutes a limiting factor in

the automatic estimation of a point feature represen-

tation. Pauly (Pauly et al., 2003a) proposes a surface

variation method based on PCA at multiple scales,

and evaluates the likelihood of a point belonging to

a feature. Instead of surface variation, Ho (Ho and

Gibbines, 2009) adopts the rotation and translation

invariant local surface measure as a local geometric

property to compute the feature conﬁdence value and

suitable scales. In addition, according to the signiﬁ-

cance of the normals in the point cloud, the authors

in (Ioannou et al., 2015) proposed a multi-scale ap-

proach by computing the difference of normals. Fur-

thermore, to overcome the complexity of the noise in

the point cloud, Park (Park et al., 2012) proposes an-

other multi-scale technique based on tensor voting for

point clouds that contain random noise.

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

318

Figure 1: (a) The difference of normals (Ioannou et al.,

2015), and (b) the difference of surface variation (Pauly

et al., 2003a), illustrated with a jet-color map.

2.5 Our Contribution

Our goal is to analyze the persistence of a selected

unique segment by using different distances over mul-

tiple scales. The method we propose is designed to

extract edges in unorganized point clouds reliably and

accurately. In our work, we consider the segmenta-

tion method of Kustra (Kustra et al., 2014) in order to

explore a global classiﬁcation. Our contribution is a

new classiﬁcation framework by segmentation which

allows for discrete surface analysis at multiple scales

with the purpose of improving the accuracy of edge

extraction. The advantage of this approach is to cope

with false feature measurements when another surface

intersects the local neighborhood.

3 PROPOSED APPROACH

The following two subsections describe our pro-

posal. We present the motivation and the general

idea next, and then discuss the main technique for

the segmentation-based multi-scale edge extraction,

which is depicted in Algorithm 1.

3.1 Motivation and General Idea

We deﬁne a multi-scale operator based on the differ-

ence of normals according to Ioannou (Ioannou et al.,

2015) by using the estimated surface normal map of

a point cloud. Figure 1 (a) shows the difference of

normals when estimated for two different neighbor-

hood sizes. In order to measure the persistence of a

feature over all scales, we compute the surface vari-

ation (Pauly et al., 2003a) for each point at different

scales, as shown in Figure 1 (b).

If the structure of the larger neighborhood around a

center point is signiﬁcantly different from that of a

smaller neighborhood, then the direction of the two

estimated normals is likely to vary by a large amount.

In that case, a value between the two radii is often a

representative of the scale near the center point. We

illustrate how the difference of normals behaves for a

variety of neighborhood sizes in Figure 2.

Figure 2: The difference of normals computed for a series

of radii couples, illustrated with a jet-color map.

When increasing the values of the scale parameter, the

computed difference of normals may be unreliable in

case that a foreign surface intersects the local neigh-

borhood. In order to cope with this issue, we consider

Kustra’s global classiﬁcation technique (Kustra et al.,

2014). As shown in Figure 3, it is possible to segment

the surface in order to obtain a global analysis of the

point cloud.

When the local analysis neighborhood in the point

cloud is deﬁned by Euclidean distance, part of a for-

eign surface may be considered in the local neighbor-

hood. For instance, for a sample point located on the

bunny’s ear, some neighbors at large scales may come

from other surfaces, as shown in Figure 4 (a). In or-

der to overcome this drawback, we propose to replace

the Euclidean by geodesic distance, as shown in Fig-

ure 4 (b). This approach also allows the global classi-

ﬁcation of the whole point cloud considering the dif-

ferent patches of the segmentation, as shown in Fig-

ure 4 (c).

3.2 Overview of Our Algorithm

Our main objective is to face the challenge in edge

extraction related to varying neighborhood sizes for

multi-scale analysis and, in particular, to avoid con-

sidering foreign surface patches in the local neighbor-

hoods. We consider three steps in the proposed strat-

egy: ﬁrst, we segment the point cloud into different

patches in order to avoid considering non-local points

in the neighborhood; second, we propose a multi-

scale operator to explore the scale of each segment;

third, we extract edges according to the appropriate

neighbor size of each segment. The details of the pro-

posed technique are explained next and presented in

Algorithm 1.

3.2.1 Segmentation

The ﬁrst step in our algorithm is the global segmenta-

tion of the point cloud. We use the technique pro-

posed in (Kustra et al., 2014), which considers the

global connectivity structure of the point cloud. Ac-

cording to Kustra’s method, we ﬁrst cluster the Gauss

map of the neighborhood by using the geodesic dis-

tance on the Gaussian sphere between the normals of

the map. Then, we extract the curved manifolds from

Segmentation-based Multi-scale Edge Extraction to Measure the Persistence of Features in Unorganized Point Clouds

319

Figure 3: Extracting manifolds from the point cloud (Kustra

et al., 2014).

the patch connectivity graph via a multiple-source

ﬂood ﬁll. Segmentation results look like shown in

Figs. 3 and 4 (c).

3.2.2 Multi-scale

In order to ﬁnd out the adaptive neighborhood size on

the point cloud we consider a multi-scale method ac-

cording to the size of each segment. First, the area of

each segment in the point cloud is calculated accord-

ing to the position of the associated points in the 3D

Cartesian coordinate system. Afterwards, we explore

the adaptive scale by considering an iterative proce-

dure for each segment. We start from a small scale

such as 0.1 times the area (this value was a propor-

tionate scale in our experiments with various shapes).

Then, we compute the probability of being an edge

for each sample point according to the surface varia-

tion method (Pauly et al., 2003a), which is based on

the eigenvalues of the covariance matrix. The surface

variation σ

) at point p

with neighbor size of n is

deﬁned as:

) =

+ λ

(1)

where λ

, λ

and λ

are the eigenvalues of the covari-

ance matrix of p

and λ

≤ λ

The surface variation σ

) for each sample point

allows to distinguish the points belonging to a ﬂat

surface from those belonging to an edge in the point

cloud. Since the smallest eigenvalue of the covari-

ance matrix for ﬂat surfaces is zero, then the value of

the surface variation for ﬂat surfaces would also be

zero. Accordingly, we deﬁne the probability of being

an edge as:

P(p

) =

)

(S)

, (2)

where P(p

) is the probability of being an edge for the

sample point p

in the considered segment, and σ

)

is the surface variation of p

. The value Θ

(S) in the

denominator stands for the largest surface variation

for the running segment of the point cloud. Thus, if

the surface variation is zero, then that sample point is

deﬁnitely not an edge. The larger the surface varia-

tion, the higher the probability of that sample point

Figure 4: Estimating the neighbors of a sample point on the

ear of bunny at large scales: (a) far away neighbors may be-

long to foreign surfaces when Euclidean distance is used;

(b) geodesic distance is a better choice to explore large lo-

cal neighborhoods; (c) the point cloud can be segmented to

distinguish different surfaces.

being an edge. This procedure is then repeated at pro-

gressively larger scales of the running segment, in or-

der to measure the persistence of the p

’s feature ac-

cording to the probability variation, as described in

Algorithm 1- procedure 2.

3.2.3 Edge Extraction

As a last step, we extract edges according to the fast

technique proposed in (Bazazian et al., 2015), which

is also robust for edges in very small dihedral an-

gles. Bazazian’s edge extraction technique analyzes

the variation of eigenvalues of the covariance ma-

trix (via the surface variation parameter); afterwards,

the points with zero or almost zero surface variation

are considered as non-edge points. Instead of con-

sidering a single scale for whole the point cloud as

in (Bazazian et al., 2015), we are able to improve the

fast and robust edge extraction by deﬁning an appro-

priate local scale for each segment of the point cloud

via our multi-scale approach.

4 EXPERIMENTAL RESULTS

We performed experiments with synthetic point

cloud geometries, as those in Figure 3 and 10, and

classical point cloud models, as those in Figure 5.

Synthetic geometries allow estimating the accuracy

of the algorithm according to a known ground-truth.

Figure 5 displays progressive iterations in the esti-

mation of an adaptive scale for the three point cloud

models of Bunny, Buddha and Dragon.

In order to explore the appropriate neighborhood

size, we describe the application to the Bunny model.

To this end, ﬁrst we segment the point cloud into the

four patches. Next, according to the iterations which

have been explained in section 3.2, we explore the

best adaptive scale to extract the edges in the point

cloud. The appropriate neighborhood size for each

segment will depend on its area. Figure 6 illustrates

the variation of neighborhood sizes of each Bunny’s

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

320

Figure 5: Iteration of Extracting Edges for the point clouds of Bunny, Buddha and Dragon.

segment at each iteration. In this plot we show

the average number of points which are included

in each radius surrounded by a sample point. The

plot demonstrates the sensitivity of determining the

neighborhood size for small segments of a point

cloud, which leads to considering almost all the

points of the segment as neighborhood points.

Moreover, Figure 7 illustrates how the different

Bunny segments behave differently for edge de-

tection with varying neighborhood sizes. We can

observe that when increasing the size of the neighbor-

hood, the number of extracted edge points increases

in all the segments. The ﬁgure shows also that at

some neighborhood sizes, such as for instance 0.95,

there is a larger probability of false positives for

small segments than for large segments. This also

proves the need of the multi-scale approach, as edge

detection with the same neighborhood size for all

the segments of a point cloud (which have different

actual scales) is prone to error. Hence, we propose

to deﬁne the neighborhood size for each segment

proportional to its scale, in order to get more precise

results of edge extraction.

For the comparison of the percentage of edge points,

we have estimated the probability of being an edge

depending on the various segments of Bunny across

the various scales. The probability of being an edge is

computed according to the ﬂuctuations of the surface

variation at each segment. As shown in Figure 11,

for those segments with small area (ear and head) at

large scales (neighbor size 1.35 or 1.50), edge points

are either undetected or just very few are detected.

Almost all points of small area segments are detected

as edge points at large scales. In these plots we

demonstrate the different behavior of the variation of

neighborhood sizes according to the various segments

of a single shape. We illustrate that considering an

appropriate neighbor size for each segment of a point

cloud is essential for edge detection.

For the quantitative evaluation of the proposed

algorithm, we perform experiments with artiﬁcial

geometric point clouds such as the intersection of

three planes in Figure 3 (left). In this point cloud

each plane is considered as a single segment of unit

area. In Figure 8 we show ten iterations for exploring

the adaptive scale for this surface, by computing the

F1-score deﬁned as:

= 2 ×

Precision × Recall

Precision + Recall

(3)

where Relevant is deﬁned as the points which are la-

beled as ground-truth, whereas Precision is deﬁned

as how many selected points are relevant and Recall

is deﬁned as how many relevant points are selected.

Precision and Recall are computed as:

Precision =

T P

T P + FP

Recall =

T P

T P + FN

(4)

where T P stands for True Positives representing the

number of correctly detected points, FP stands for

Segmentation-based Multi-scale Edge Extraction to Measure the Persistence of Features in Unorganized Point Clouds

321

Algorithm 1: Segmentation-based Multi-Scale Edge Ex-

traction.

1: procedure 1: SEGMENTATION

2: Input: A point cloud C which samples a surface S ⊂ R

3: Output: A set of segment manifolds S of C

4: for all points v ∈ C do

5: Estimate the normals at v, call them n

6: end for

7: Create a graph G = (V,E) with V = C and initially

E :=

8: for all v ∈ C do

9: for all w ∈ C such that v and w are neighbors in

S do

10: compute the angle between ∠n

11: if ∠n

≤ T for some threshold value T

then

12: E := E ∪{v, w}

13: end if

14: end for

15: end for

16: Explore a ﬂood-ﬁlling over the patch connectivity

stored in G and compute segments S

17: end procedure1

18: procedure 2: MULTISCALE

19: Input: A segment S ∈ S

20: Output: The adaptive scale (neighborhood size) N

21: area

:= area of S, N

:= 0, p

:= 0, ∆ := 1000

22: for i = 1 to 10 do

23: Let N

:= (0.1 ∗ area

) + (i ∗ 2 ∗ (area

/100))

24: p

:= the probability of being an edge in C at

level N

computed according to the surface variation

25: Compute persistence: ∆

:= p

− p

i−1

26: if ∆

≤ ∆ then

27: ∆ := ∆

, N

:= N

28: end if

29: end for

30: Return N

31: end procedure2

32: procedure 3: EDGE EXTRACTION

33: Input: A segment S ∈ S and N

34: Output: set of edge points F of S

35: F :=

36: for each sample point P ∈ S do

37: Compute the surface variation V

at P at scale

38: if V

≥ T

for some threshold value T

then

39: F := F ∪ {P}

40: end if

41: end for

42: end procedure3

False Positives representing the number of wrongly

detected points, FN stands for False Negatives, rep-

resenting the number of false rejections, i.e. points

that belong to the ground truth but are not detected

by the edge extraction technique.

Furthermore, to prove the robustness contributed by

the segmentation step to the edge extraction process,

we have compared our technique with the method

in (Bazazian et al., 2015). To this end, we consider

Table 1: Comparing the accuracy of edge extraction for the

Multiple-Tetrahedron ﬁgure with segmentation (our pro-

posed algorithm) and without segmentation (the technique

of (Bazazian et al., 2015)).

Multiple Tetrahedron Precision Recall F1-Score

With Segmentation 0.786 0.825 0.805

Without Segmentation 0.651 0.842 0.734

an unorganized point cloud which is a Multiple-

Tetrahedron, as shown in Figure 10. We propose this

shape for two reasons: ﬁrst, as a synthetic shape, the

ground-truth of edge points is available. Second, it

comprises 4 different tetrahedrons of different surface

sizes, to demonstrate the advantage of the segmen-

tation approach on the different sizes of each segment.

Table 2: Evaluating the accuracy of edge extraction for the

Multiple-Tetrahedron model perturbed with 10% additive

Gaussian noise. Our proposed method refers to the line

where calls with segmentation, whereas the method pro-

posed in (Bazazian et al., 2015) is called by without seg-

mentation.

Multiple Tetrahedron with Noise Precision Recall F1-Score

With Segmentation 0.476 0.824 0.603

Without Segmentation 0.405 0.826 0.543

Table 1 shows the F1-score: we compare the accu-

racy of our proposed technique (which is by segmen-

tation) with the technique of (Bazazian et al., 2015)

(which is without segmentation). We demonstrate that

performing segmentation as a pre-process of the edge

extraction yields to higher accuracy. By segmenting

the point cloud into different patches, we avoid tak-

ing non-local neighbors into account. In addition, by

considering an appropriate scale for each segment of a

point cloud, we eliminate false positive results which

are due to the scale incompatibility. As shown in Ta-

ble 1, by employing segmentation as a prerequisite of

edge extraction process we obtain a higher accuracy.

Moreover, in order to examine the robustness of our

proposed method to noisier real-world datasets, we

show the results for noisy models perturbed with addi-

tive 10% Gaussian noise. As it is shown qualitatively

in Figure 9 the edges are extracted accurately, al-

though there are noisy points surrounding the Bunny.

Thus, the results in this case are almost the same as in

the model without noise. Furthermore, to verify the

results quantitatively, we have added 10% Gaussian

noise to the Multiple-Tetrahedron and computed the

accuracy. We have evaluated our proposed method

using the F1-score. In Table 2 it is shown that even

when adding noise the accuracy of edge extraction

with segmentation is higher than without segmenta-

tion.

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

322

Figure 6: Plot of the Average of the area and number of

neighbors for each segment of the Bunny.

Figure 7: The different segments of Bunny behave dif-

ferently for edge extraction with progressive neighborhood

sizes.

5 CONCLUSION

In this paper we have presented a segmentation-based

technique for multi-scale edge extraction. We have

focused on the challenge of edge detection when for-

eign surfaces get into local analysis neighborhoods.

A global segmentation based on geodesic distance al-

lows segmenting different regions of a point cloud.

This allows exploring the best scale for each segment

and improves the accuracy of edge extraction.

We have illustrated the importance of determining the

best scale as a prerequisite for the edge extraction pro-

cess. Consequently, we propose a multi-scale tech-

nique that ﬁnds the appropriate neighborhood size for

the analysis, instead of setting a single scale for whole

the point cloud. This is the basis for the superior accu-

racy of the proposed method in the quantitative eval-

Figure 8: Comparison of the F1-Score for the various neigh-

borhood sizes in order to explore the adaptive scale for a

segment of the point cloud corresponding to the intersec-

tion of 3 planes.

Figure 9: Comparing the Edge Extraction technique of

Bunny with Gaussian Noise and without noise.

Figure 10: The geometric shape of Multiple-Tetrahedron.

uation results we present.

We have also proven that the segmentation of the

point cloud, makes feasible to deﬁne the scale of

each segment before ﬁnding the optimal neighbor-

hood size. This eliminates false positives due either

to the incompatibility of neighborhood sizes and seg-

ment scales or non-local neighbors. Accordingly, it

yields an improved precision in edge detection.

We have quantitatively compared the accuracy of re-

Segmentation-based Multi-scale Edge Extraction to Measure the Persistence of Features in Unorganized Point Clouds

323

Figure 11: Probability of being an edge according to the various segments of the Bunny over various scales.

sults in the analysis of synthetic objects for which

we do have ground truth. Furthermore, by adding

Gaussian noise to the artiﬁcial point clouds, we have

demonstrated that the presented approach is more ro-

bust in noisier real-world datasets.

Experimental results show quantitatively and qualita-

tively that our algorithm can deal with different un-

organized point cloud surfaces, can complete surface

segmentation and then apply multi-scale edge extrac-

tion robustly.

Moreover, the proposed algorithm is able to deter-

mine independently the neighborhood size of each

segment in a point. This makes it possible to perform

a precise and semi-automatic edge extraction proce-

dure for point cloud analysis.

The contributions of this paper are in two main as-

pects: ﬁrst, we declare that considering a single

neighbor size for all the segments of a point cloud is

prone to error, particularly for small segments. There-

fore, in order to have an accurate edge extraction sys-

tem, it is essential to assign an appropriate neighbor

size for each segment of the point cloud. The sec-

ond aspect is that we propose a robust semi-automatic

edge extraction algorithm based on surface segmenta-

tion.

As future work, we aim to exploit the algorithm pro-

posed in (Rieck and Leitte, 2014) in order to analyze

the skeleton of a surface according to the persistent

homology in order to obtain the multi-scale descrip-

tion in a point cloud.

ACKNOWLEDGMENT

This work has been developed in the framework of

projects TEC2013-43935-R and TEC2016-75976-R,

ﬁnanced by the Spanish Ministerio de Economia y

Competitividad and the European Regional Develop-

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

324

ment Fund (ERDF).

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