Ijartes v1-i2-005

International Journal of Advanced Research in Technology, Engineering and Science (A Bimonthly Open Access Online
Journal) Volume1, Issue2, Sept-Oct, 2014.ISSN:2349-7173(Online)
Surface Reconstruction Using Cloud Points
Isha1, Ashok Kumar2
_______________________________________________
ABSTRACT- Surface reconstruction from point clouds is
motivated by a number of computer-aided geometric design,
point-based graphics, computer vision and scientific
visualization applications due to the wide availability of
point-cloud data, which may be obtained from modern laser
scanners or image-based techniques. Among most of the
existing methods, orientation information is essential during
the reconstruction process and directly affects the quality of
the approximation of the output surfaces. While a number of
existing surface reconstruction methods are capable of
producing satisfactory results in terms of efficiency and
quality from point cloud. We are using crust algorithm. The
algorithm is based on the three-dimensional Voronoi
diagram and Delaunay triangulation, it produces a set of
triangles that we call the crust of the sample points. All the
vertices of the triangles are sample points in fact, all the
triangles appear in the Delaunay triangulation of the sample
points. At the input of the described algorithm we have an
unsuccessful result of work of a surface reconstruction
algorithm and at the output there is a set of correctly
reconstructed regions. This algorithm detects and marks
points of correctly triangulated regions. The crust algorithm
also removes wrong edges and triangles and we also working
on reducing the size of the file. The algorithm can also
improve some errors which are caused by the generation of
redundant edges and triangles, but the crust algorithm
doesn’t create new edges and triangles. We are using
umbrella filtering for filtration purpose. Filtration is based
on noise threshold and redundant threshold value this is the
enhancement of crust algorithm.
_______________________________________________
KEYWORDS: Surface Reconstruction, Crust Algorithm,
Umbrella Filtering, Point Cloud.
________________________________________________
_______________________________________________
First Author Name: Isha, Electronics & Communication Department, ACE
& AR, Mithapur, India.
Second Author Name: Ashok Kumar, Electronics& Communication
Department, ACE & AR, Mithapur, India
________________________________________________
1. INTRODUCTION
Surface reconstruction is the process to achieve three-dimensional
complex surface model quickly and accurately
from three-dimensional data collected like a sample, and then
it is widely used in reverse engineering. Three-dimensional
data collected by measuring device is usually dense, so it is
called Point Cloud data [3]. Point cloud data can be
considered as an aggregation of the points in three-dimensional
space, and each point cloud data has three
coordinates of x, y, z. According to the different types of data
the point cloud data can be divided into two forms first is
Ordered point cloud and the second is Scattered point cloud.
Reconstruction of ordered point cloud is that constructing the
surface of points sample from the verge of object to
approximate the original surface most. For scattered point
cloud, if the reconstructed surface can show the shape of the
original point cloud, we take it as the result of the surface
reconstruction. There has been very considerable amount of
research in the past decade on the development of techniques
for surface reconstruction from points. However, only few
attempts have been made to handle the encountered
imperfections, which are mainly occur in practice and pose a
great challenge to surface reconstruction algorithms. Despite
the recent development of scanning devices, these problems
are still remaining. In our paper, we present a set of novel
surface reconstruction algorithms to handle them.
2. SURFACE RECONSTRUCTION PHASES
Surface Reconstruction phases include:
Phase 1: Initial Surface Estimation
Phase 2: Mesh Optimization
Phase 3: Smooth Surface Optimization
Phase 1: Initial surface estimation: From an unorganized set of
points, the 1st phase constructs an initial dense mesh. The
Goal of this 1st phase is to determine the topological type of
the surface, and to produce an initial estimate of its geometry.
Phase 2: Mesh optimization: Starting with the dense mesh
created, the 2nd phase reduces the number of faces and
improves the fit to the given data points. We take this type of
problem as optimization of an energy function that explicitly
models the trade-off between the competing goals of accuracy
and conciseness. The available free variables in this
optimization are the number of vertices present in the mesh,
their connectivity, and also their positions. Phase 3: Smooth
surface optimization: In 3rd phase, the representation of
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surface is changed from a piecewise linear one to a piecewise
smooth one. Here we introduce a new piecewise smooth
representation based on subdivision. These surfaces are ideal
for surface reconstruction, as these are very simple to
implement and also these can model sharp features concisely,
these can fit by using an extension of the phase 2 optimization
.
Figure 1: The result of the Phase 1 a) original object, b) point cloud, c)
surface reconstruction.
3. RELATED STUDY
Min Wan, Yu Wang [1] proposed, a variational reconstruction
method for open surface is proposed based on graph
cuts.Integrating the variational model, Delaunay-based
tetrahedral mesh and multiphase technique,the proposed
method could robustly reconstruct not only open surfaces but
also more general surfaces such as the hybrids of open and
watertight ones. Surface reconstruction based on domain
decomposition, as an important application, is also presented.
Parallel implementation of this domain decomposition method
and investigation of its efficiency is one of our future research
interests further research has been done by Bharti Sood et.al
[2] presented the first kind of Crust Algorithm which is an
algorithm for the surface reconstruction from unorganized
cloud points in 3D. For a given point cloud from a smooth
surface, the output guarantees to be topologically correct and
as the sampling density increases it moves towards a common
point to the original surface. The algorithm is based on the
three-dimensional Voronoi diagrams. Increasing speed &
works properly in presence of sharp edges or non-uniform
sampling is our future research interest further research has
been done by Hui Li et.al [3] uses the Poisson surface
reconstruction algorithm based on power crust algo. To create
3D heart model because original data has a lot of noise and
without normal vector information. Power Crust is a surface
reconstruction algorithm based on Voronoi diagram in
computational geometry, which has a simple process and
accurate reconstructed results. For the scattered point cloud
data without normal vector, the speed is very quickly but the
effect is not very accurate enough. Normal vector information
has added after Poisson reconstruction, so the final
reconstructed results have accurate effect. The results not only
accurately display the heart, but also can display diseases
which can help doctors to detect and diagnose diseases
effectively, and improve the accuracy and security of medical
diagnosis. This algorithm has good robustness for noisy and
irregular point cloud data. Reducing noise and reconstruction
time is our future interest further research has been done by
Subhanga Kishore Das et.al [4] described a general method
for automatic reconstruction of accurate, concise, piecewise
smooth surfaces from unorganized 3D points. Instances of
surface reconstruction arise in numerous scientific and
engineering applications, including reverse engineering, the
automatic generation of CAD models from physical objects
etc. Previous surface reconstruction methods have typically
required additional knowledge, such as structure in the data,
known surface genus, or orientation information. In contrast,
the method outlined in this paper requires only the 3D
coordinates of the data points. From the data, the method is
able to automatically infer the topological type of the surface,
its geometry, and the presence and location of features such as
boundaries, creases, and corners. The surface reconstruction
method has three major phases: Initial surface estimation,
Mesh optimization, and piecewise smooth surface
optimization. In this paper emphasis has been given on the
initial surface estimation further research has been done by
Min Wan et.al [5] presented an energy functional based on a
weighted minimal surface model is proposed for surface
reconstruction, which is efficiently minimized by graph cut
methods. By solving the minimization problem on the graph
dual to a Delaunay based tetrahedral mesh; the advantages of
explicit and implicit methods for surface reconstruction are
well integrated. The Feature Swap method is proposed as a
post processing to recover all features described by some
critical points. The main idea of Feature Swap is to ensure the
presence of every critical point in the reconstructed surface.
Difficult cases involving under sampling, non-uniformity,
noises and topological complexities can be handled effectively
as well. Useful post processing method to recover features of
a surface ,surface smoothing and surface enhancement, this
method is still under investigation and an important aspect of

our future work further research has been done by De
Medeiros Brito et.al [6] proposed a strategy based on
Kohonen’s self-organizing map (SOM). It uses a set of mesh
operators and simple rules for selective mesh refinement.
Basically, a self-adaptive scheme is used for iteratively
moving vertices of an initial simple mesh in the direction of
the set of points, ideally the object boundary. Results show
generated meshes very close to object final shapes. Still there
are no rules defined for determination of the initial mesh size
and topology. The user must select the mesh according to his
needs. To be fully automated, the algorithm should work in
conjunction with some clustering algorithm that is able to
estimate both the minimum size geometry and the topology of
the input space. Finally, it may need larger data structures to
store the mesh and to run the SOM. As a future work, a
simplification procedure can be inserted in each intermediate
stage as well as in the final resulting mesh. With this, a good
adaptive scheme can be devised widening the application
areas further research has been done by Mincheol Yoona et.al
[7] proposed a surface and normal ensembles technique for
surface reconstruction. Their main advantages are the speed
and, given a reasonably good initial input, the high quality of
the reconstructed surfaces. The proposed method effectively
handling incomplete data with noise and outliers. An
ensemble is a statistical technique which can improve the
performance of deterministic algorithms by putting them into
a statistics based probabilistic setting. We experimented with
a widely used normal reconstruction technique and Multi-level
Partitions of Unity implicit for surface reconstruction
showing that normal and surface ensembles can successfully
be combined to handle noisy point sets further research has
been done by Andrei C. Jalba et.al [8] proposed a technique
for surface reconstruction based on generalized Coulomb
potentials that consider all data points at once, and thus they
convey global information which is crucial in the fitting
process. The author proposed a geometrically adaptive method
for surface reconstruction from noisy and sparse point clouds,
without orientation information. The method employs a fast
convection algorithm to attract the evolving surface towards
the data points Coulomb potentials offers a number of
advantages. Our method is highly resilient to shot noise and
can be used to disregard the presence of outliers due to noise.
Both the spatial and temporal complexities of our spatially-adaptive
method are proportional to the size of the
reconstructed object, which makes our method compare
favourably with respect to previous approaches in terms of
speed and flexibility. Experiments with sparse as well as noisy
data sets show that the method is capable of delivering crisp
and detailed yet smooth surfaces further research has been
done by Reuter et.al [9] proposed a technique Moving Least
Squares (MLS) projection that reconstructs continuous 3D
surfaces from scattered point data coming from laser range
scanners. One interesting property of the MLS projection is to
automatically filter out high frequency noise that is usually
present in raw data due to scanning errors. Unfortunately, the
MLS projection also smoothes out any high frequency feature,
such as creases or corners that may be present in the scanned
geometry, and does not offer any possibility to distinguish
between such feature and noise. The main contribution of this
paper is to present an alternative projection operator for
surface reconstruction, based on the Enriched Reproducing
Kernel Particle Approximation (ERKPA), which allows the
reconstruction process to account for high frequency features,
by letting the user explicitly tag the corresponding areas of the
scanned geometry. Improvement in MLS by some additional
technique is our future interest area further research has been
done by Hong-Wei et.al [10] presented an algorithm based on
minimum-weight triangulation for reconstructing a triangle
mesh surface from a given point cloud. Starting with a seed
triangle, the algorithm grows a partially reconstructed triangle
mesh by selecting a new point based on an intrinsic property
of the point cloud, namely, the sampling uniformity degree.
The reconstructed mesh is essentially an approximate
minimum-weight triangulation to the point cloud constrained
to be on a two-dimensional manifold. Thus, the reconstructed
surface has only small topological difference from the surface
of the sampled object. Topological correct reconstruction can
be guaranteed by adding a post-processing step. Improving
topological correctness is our future interest area further
research has been done by Nina Amenta et.al [11] proposed a
technique that is based on Power Crust. The paper described
the medial axis transform MAT is a representation of an
object as an infinite union of balls. We consider
approximating the MAT of a three-dimensional object, and its
complement, with a finite union of balls. Using this
approximate MAT we define a new piecewise-linear
approximation to the object surface, which we call the power
crust. Our results provide a new algorithm for surface
reconstruction from sample points. By construction, the power
crust is always the boundary of a polyhedral solid, so we
avoid the polygonization, hole-filling or manifold extraction
steps used in previous algorithms. The union of balls
representation and the power crust has corresponding
piecewise-linear dual representations, which in some sense
approximate the medial axis. We show a geometric
relationship between these duals and the medial axis by

proving that, as the sampling density goes to infinity, the set
of poles, the centers of the polar balls, converges to the medial
axis. The above technique gives some theoretical difficulties.
Removal of these theoretical difficulties is one of our future
interest further research has been done by Fausto Bernadini
et.al [12] described about the ball-Pivoting Algorithm (BPA)
which computes a triangle mesh interpolating a given point
cloud. The points on the surface samples acquired with
multiple range scans of an object. The principle of the BPA is
very simple. We applied the BPA to datasets of millions of
points representing actual scans of complex 3D objects. The
relatively small amount of memory required by the BPA, its
time efficiency, and the quality of the results obtained
compare favourably with existing techniques. It would be
interesting future work that weather BPA could be used to
triangulate surfaces sampled with practical system. Further
research has been done by Miguel Angel Garcia [13]
presented a new method based on weighted averages .It is to
reconstruct smooth surfaces from arbitrary triangulations of
scattered 3D points. These points are considered to be noisy as
a result of some sensory acquisition process. The
reconstruction problem is transformed into one of surface
approximation over irregular triangular meshes. The proposed
technique has been widely used in homogeneous data fusion.
Hence, the generated surfaces are the result of a geometric
fusion process that considers topological relationships among
control points. Moreover, an uncertainty factor can be
associated with every point. This factor affects the final shape
of the surface locally. The aforementioned characteristics of
this technique allow its utilization as an efficient surface
modelling tool in diverse disciplines, including robotics, GIS
and medical imaging. Reducing computational time &
improve output quality is our future interest area.
4. PROBLEMS IN SURFACE RECONSTRUCTION
The location of points may be perturbed by unknown levels of
noise. The points may not be equipped with point normal,
which indicate the orientation of the local shape. The surface
may not be well-sampled there is often holes, which are to be
filled via additional efforts. Holes resulting from the
insufficiently sampled regions might need to be filled. The
boundary of the surface might need to be preserved. A non-manifold
surface includes surface junctions or surface
boundaries, which cannot be reconstructed correctly by
traditional surface reconstruction algorithms. The triangles in
the resulting mesh should be well-shaped. It is required by
some follow-up operations on the mesh, such as Finite
Element Analysis. Sharp edges (creases) and corners should
be preserved, even though they break the assumption of
smoothness.
5. PROPOSED ALGORITHM AND WORK FOR
REDUCING THE SIZE OF FILE
Let’s consider a way to decrease the size of file of the surface
to be reconstructed. Let we have a cloud of N points and a
surface reconstruction algorithms (let’s denote them A). Let
algorithm A is able to reconstruct a correct CAD-model with
the specific size of file. We are reducing the size of file by
using redundant threshold at different value. Let we also have
an algorithm for filteration, that can remove all wrong edges
and triangles. The surface reconstruction can be made in the
way. First we apply algorithm A then we are using the
redundant threshold at different values and also we check that
at which redundant threshold value our algorithm removing
maximum number of duplicate points and we are also looking
for the quality of the surface then we apply the filtering
algorithm after this process we get that without any
compromise in the quality of the surface to be reconstructed
we are reducing the size of file.
5.1 CRUST ALGORITHM
Over the past decade, a number of algorithms have been
developed that impose different sampling density conditions
on the input points, but guarantee a good approximation of the
original curve once the conditions are met. One of these
algorithms is the crust algorithm which is a simple and
beautiful application of the Delaunay triangulation. The
algorithm not only gives a reconstruction of the original curve,
but it also produces a reconstruction of the medial axis of the
curve. The medial axis of a curve is the closure of the set of
points in the plane that have at least two closest points on the
curve and is useful in certain applications. The crust algorithm
guarantees a correct reconstruction only for smooth, closed
curves and for certain sampling density.
o The algorithm 1st computes the Vornoi Diagram of
the input point cloud S.
o For each sample point s :
· If s does not lie on the convex hull, let p + be the
farthest vornoi vertex of Vs from s. Let n + be the
vector of sp+.
· If s lies on the convex hull, let n + be the average of
the outer normals of the adjacent triangles.
· If p −be the vertex of Vs with negative projection on
n + that is farthest from s
· Let P be the set of poles p + and p −, compute the
Delaunay triangulation of S union P.
o And then keep only those triangles, which have all
the three vertices are sample point in S.
o After that filtration is applied which depends upon
the 3 factors
· Due to the number of vertices
· Due to number of edges

· Due to the orientation normal
o Then the output is produced which is the smooth
surface.
5.2 UMBRELLA FILTERING
Umbrella filtering is used to iterate over candidate triangles
and remove those not included in the umbrella. The structure
of the vertices in well-approximated surfaces resembles that a
topological disk is the so-called umbrella. A topological
structure resembling an umbrella is also used for detecting the
boundaries of the surface, i.e., holes in the under sampled
regions. The described method fills up the holes to make
surface watertight.
6. RESULTS
The result is implemented in C language and the software
used is ubuntu. The output is produced in geomview software
which is used for displaying 3 dimensional objects. In my
thesis initially calculate the number of bad poles by using
crust algorithm and after that applying the filtration to produce
the smooth surface as we are reducing the size of file and we
are saving the space.
Figure 2: Original snapshot of image bunny
The figure 2 shows the original snapshot of image bunny
without threshold The figure 3 (a)shows the snapshot of image
bunny when the value of redundant threshold is 0.6 and the
bad poles are 59.Here the size of file is 5.08 mb which is less
than the size of the snapshot of original image
Figure 3: Snapshot of image bunny a) Redundant threshold is
0.6, b) Redundant threshold 0.5 c) Redundant threshold is 0.4
The figure 3 (b) shows the snapshot of image bunny when the
value of redundant threshold is 0.5 and the bad poles are 214
when not using the redundant threshold value and here the
size of file is 5.07 mb. The figure 3 (c) shows the snapshot of
image bunny when the value of redundant threshold is 0.4 and
the bad poles are 557 and here the size of file is 5.03 mb The
figure 4(a) shows the snapshot of image bunny when the value
of redundant threshold is 0.3 and the bad poles are 1413.Here
the size of file is 4.97 mb. The figure 4(b) shows the snapshot
of image bunny when the value of redundant threshold is 0.2
and the bad poles are 4899.and here the size of file is 4.66 mb
The figure 4(c) shows the snapshot of image bunny when the

value of redundant threshold is 0.1 and the bad poles are
18936 and here the size of file is 3.37 mb
Figure 4: Snapshot of image bunny a) Redundant threshold is 0.3, b)
Redundant threshold 0.2 c) Redundant threshold is 0.1
Table 1: Computation of size of file using Crust Algorithm
Redund
ant
Thresho
ld
Number
of
Bad poles
Total Poles Size of file in
Mega byte
- 0 61015 5.09
0.6 59 60971 5.08
0.5 214 60826 5.07
0.4 557 60520 5.03
0.3 1413 59665 4.97
0.2 4899 56197 4.66
0.1 18936 42176 3.37
This table shows that on different redundant threshold value
the number of bad poles, total poles and size of file. We are
removing the duplicate points thus the space of the file is also
reducing the size of file 34% reduction is there and 1.72 MB
space is left here. The advantage of the left space is that we
can use this space for any other purpose. The figure 5 is a
graph plotted between redundant threshold and size of file.
We can easily see that at different threshold value how the
size of the file is reduced and hence the space is left. We see
that when the value of rt is 0.6 the size of file is not so much
affected but when we are reducing the rt values to 0.1 the size
of the file is reduced so much The main goal is to reconstruct
the shape of arbitrary topology objects with a controlled hole
filling strategy using implicit surface representation. All The
figures shows the effect of redundant threshold on the quality
and shape of image we see that when we are reducing the
redundant threshold value the quality of the image is not so
much affected.
6
5
4
3
2
1
0
0.60.50.40.30.20.1 -
Mega Byte
Redundent Threshold
size of file
in MB
Figure 5: Graph plotted between redundant threshold and size of file
7. CONCLUSIONS AND FUTURE WORK
Crust algorithm optimizes the mesh reconstruction system
from 3D point cloud and it presents the corresponding settings
and execution times. Crust algorithm plays an important role
due to its guaranteed quality of mesh generation. It proposes
optimization of mesh reconstruction system from 3D cloud
point. Crust algorithm computes the number of vertices,
number of edges and orientation of the image. After filtration
the number of bad poles can be calculated based on the
number of vertices and edges so that surface can be improved.
Smooth surface can be obtained when the number of bad poles
reaches to zero. In the previous work bad poles are reduced by
the noise threshold. Bad poles can also be reduced by

redundant threshold. In our work bad poles are reduced by
using redundant threshold using crust algorithm with umbrella
filtering and it is successfully implemented. In this thesis we
use geomview software which supports only .off extension
file format which is the main limitation. We can enhance the
algorithm by applying other image extensions used so that the
algorithm is reliable. In this we use geomview software for
displaying the output. Geomview is the software for
displaying the 3-dimensional images. An OFF file is good for
storing a description a 2D or 3D object constructed from
polygons. In the future we can improve the efficiency of the
algorithm so that it can support various other file format
extensions.
REFERENCES
[1] Min Wan et al.:’ Reconstructing Open Surfaces via Graph-Cuts’, IEEE
Transactions on visualization and computer graphics, 2013, pp
307-318.
[2] Bharti Sood et al.:’ Surface Reconstruction and Time Calculation using
Crust Algorithm’, International Journal of Computer Science & Engineering
Technology, 2012, pp 277-282.
[3] Hui Li et al.:’ Research on model correction based on scattered point
cloud data surface reconstruction’, IEEE International conference on Wireless
mobile and computing, 2011.
[4] Subhanga Kishore Das et al.:’Study On Applications and Techniques Of
Surface Reconstruction’, International Journal of Computer &
Communication Technology (IJCCT), 2011, 2, (6).
[5] Yu Wang et al.:’Variational surface reconstruction based on Delaunay
triangulation and graph cut’, International Journal for numerical methods in
Engineering’, July 2010.
[6] de Medeiros Brito et al.:’An Adaptive Learning Approach for 3-D Surface
Reconstruction From Point Clouds’,Neural Networks, IEEE Transactions on,
June 2008 ,19, (6), pp1130-1140.
[7] Reuter, P.:’Surface reconstruction with enriched reproducing kernel
particle approximation’, Point-Based Graphics, Eurographics/IEEE VGTC
Symposium Proceedings, June 2005, pp.79-87.
[8] Garcia, M.A.:’Efficient surface reconstruction from scattered points
through Geometric data fusion’, Multisensor Fusion and Integration for
Intelligent Systems, IEEE International Conference on MFI, 1994, pp 559-
566.
[9] Andrei C. Jalba et al.:’Efficient Surface Reconstruction using generalized
coulomb potentials’ IEEE transactions on visualization and computer
graphics, November/December 2007, 13, (6).
[10]Mincheol Yoona et al.:’Surface and normal ensembles for surface
reconstruction’, Computer-Aided Design 39, 2007.j
[11] Hong-Wei et al.:’ A mesh reconstruction algorithm driven by an intrinsic
property of a point cloud’, Computer-Aided Design, 2004.
[12] Nina Amenta et al.:’The power crust, unions of balls, and the medial axis
transform’, Computational Geometryss, 2001, pp 127–153.
[13] Patrick Reuter et al.:’Surface Reconstruction with Enriched Reproducing
Kernel Particle Approximation’, Eurographics Symposium on Point-Based
Graphics, 2005.
[14] Fausto Bernadini et al.:’The ball pivoting algorithm for surface
reconstruction’, IEEE transactions on visualization and computer graphics,
October/December 1999, 5, (6).
[15] Niloy J. et al.:’Estimating Surface Normals in Noisy Point Cloud Data’,
International Journal of computer geometry and applications, 2004.
[16] Tamal K et al.:’An Adaptive MLS Surface for Reconstruction with
Guarantees’, Eurographics Symposium on Geometry Processing, 2005.
[17] M. Samozino et al.:’ Reconstruction with Voronoi Centered Radial Basis
Functions’, Eurographics Symposium on Geometry Processing, 2006
[18] Anders Adamson et al.:’Ray Tracing Point Set Surfaces’, IEEE
International Conference on shape modeling, 2003

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