Reconstruction of Tree Crown Shape from Scanned Data.
ABSTRACT Reconstruction of a real tree from scattered scanned points is a new challenge in virtual reality. Although many progresses
are made on main branch structures and overall shape of a tree, reconstructions are still not satisfactory in terms of silhouette
and details. We do think that D reconstruction of the tree crown shapes may help to constrain accurate reconstruction of
complete real tree geometry. We propose here a novel approach for tree crown reconstruction based on an improvement of alpha
shape modeling, where the data are points unevenly distributed in a volume rather than on a surface only. The result is an
extracted silhouette mesh model, a concave closure of the input data. We suggest an appropriate scope of proper alpha values,
so that the reconstruction of the silhouette mesh is a valid manifold surface. Experimental results show that our technique
works well in extracting the crown shapes of real trees.

Conference Paper: ClusterBased Construction of Tree Crown from Scanned Data
[Show abstract] [Hide abstract]
ABSTRACT: It is a challenge task to reconstruct a real tree from scattered scanned points in virtual reality. Although many progresses have been made on main branch structures and overall tree shape, reconstructions are still not faithful in terms of silhouette and details. We push the idea that D reconstruction of the tree crown shapes may help to constrain reconstruction of complete real tree geometry. We propose here a new approach to reconstruct tree crown based on clusters of points, where the data are unevenly distributed points in a volume rather than lying on a surface. From this approach several extracted silhouette mesh models can be generated; every mesh model represents a crown section of the reconstructed tree crown. Experimental result shows that our technique works well on crown shape of real trees.Plant Growth Modeling, Simulation, Visualization and Applications (PMA), 2009 Third International Symposium on; 01/2009  SourceAvailable from: Jari Vauhkonen[Show abstract] [Hide abstract]
ABSTRACT: Airborne laser scanning (ALS) has become a very common forest inventory data source during the 2000’s. Previous research on singletree interpretation of such data suggests limitations due to both undetected trees and inaccuracies in species recognition and allometric estimation of stem dimensions. This work examined reconstruction of tree crowns by means of computational geometry of the point data and techniques for turning the obtained crown shape and structure information into improved estimates of tree attributes. Alpha shape metrics, i.e. a collection of various volume, complexity and area features derived from 3D alpha shapes based on the point data, were found to have potential for describing speciesspecific allometric differences in the trees, while combining these metrics with features based on the height and intensity distributions in the data was beneficial with respect to the final accuracies. Nearest neighbor estimation proved efficient for making use of the high number of predictors available, but also for the simultaneous estimation of the attributes of interest, thus avoiding error propagation of an estimation chain. Random Forest, in particular, proved to be a flexible method with an ability to handle all available predictors with no need for their reduction. The classification of dominant to intermediate Scots pine, Norway spruce and deciduous trees showed an accuracy of 78%, and the estimates of diameter at breast height, tree height, and stem volume had root mean square errors of 13%, 3%, and 31%, respectively, when evaluated against separate validation data. Less supervised tree detection and estimation resulted in unreliable treelevel descriptions of the test stands, being hindered by both inaccuracy in the tree attributes, especially in species identification, and errors in tree delineation. The need to acquire field reference data and a potential need for an auxiliary information source both place constraints on the applicability of the developed approach. On the other hand, it was shown that crown base height, which is an important measure of external quality of mature Scots pine trees, could be estimated with an RMSE of 20–30% solely by ALS data with a pulse density of 4 m2. The results suggest focusing singletree interpretation specifically towards detailed measurements on the dominant tree layer, thus presenting a further need to assess the treelevel production line with respect to obtainable information, alternative methods and their costs.Dissertationes Forestales. 05/2010; 104.
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Z. Pan et al. (Eds.): Edutainment 2008, LNCS 5093, pp. 745–756, 2008.
© SpringerVerlag Berlin Heidelberg 2008
Reconstruction of Tree Crown Shape from Scanned Data
Chao Zhu1,2, Xiaopeng Zhang1,2,*, Baogang Hu1,2, and Marc Jaeger3
1 SinoFrench Laboratory LIAMA, CAS Institute of Automation, Beijing, China
2 National Laboratory of Pattern Recognition, CAS Institute of Automation, Beijing, China
3 INRIASaclay, Project DigiPlante, CIRAD AMAP, Montpellier, France
{czhu, xpzhang, hubg}@nlpr.ia.ac.cn, jaeger@cirad.fr
Abstract. Reconstruction of a real tree from scattered scanned points is a new
challenge in virtual reality. Although many progresses are made on main branch
structures and overall shape of a tree, reconstructions are still not satisfactory in
terms of silhouette and details. We do think that 3D reconstruction of the tree
crown shapes may help to constrain accurate reconstruction of complete real tree
geometry. We propose here a novel approach for tree crown reconstruction based
on an improvement of alpha shape modeling, where the data are points unevenly
distributed in a volume rather than on a surface only. The result is an extracted
silhouette mesh model, a concave closure of the input data. We suggest an ap
propriate scope of proper alpha values, so that the reconstruction of the silhouette
mesh is a valid manifold surface. Experimental results show that our technique
works well in extracting the crown shapes of real trees.
Keywords: tree crowns, reconstruction, Delaunay triangulation, alpha shape.
1 Introduction
With the current development of virtual environment establishment, product design,
digital entertainment, antique protection, and city programming 3D geometry model
construction and processing is now an active development area. 3D geometry modeling
is regarded as the fourth digital multimedia in addition to digital audio, digital image,
and digital video. 3D geometry models are normally used to represent object surface to
identify extendedly shape and appearance attributes.
With the advancement of 3D scanning technology, more and more 3D digital
scanners are popularly used for different applications. Rich details of the object shape
can be acquired from scanned data with dense sampling points (point cloud), where no
topological connection relations are included. It becomes important to develop new
processing methods to represent, to process, to reconstruct and to render these highly
complex geometric bodies. Reconstruction of geometry model is one of the important
research topics in modern virtual reality.
Trees are typical objects in virtual reality, so it is very important to reconstruct and to
represent the real trees. Tree reconstruction can be used in many applications, including
digitization of vegetation scenes, design of a new scene, digital entertainment, and so on.
* Corresponding author.
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Reconstruction of the tree crown shape is useful to model a real tree and in various
research fields interested by growth simulation of virtual trees for light interception,
biomass evaluation, and so on. Many researches have been carried on surface recon
structions, but the shape of a tree crown is more difficult than that of a usual solid object
in its heavy occlusions and its high complexity in geometry and topology.
Reconstruction of a real tree crown from scattered scanned points is a new challenge
in virtual reality. The points are unstructured, unevenly distributed, and sampled from
nonmanifold shapes; it is very difficult to define typical boundary points in a tree
crown in accordance with the visual perception. Rich concavity is another feature of the
crown shape of a real tree. Classical surface reconstruction techniques do not work for
such tree crown data. Other difficulties are that the data have no topological informa
tion among points, their 3D distribution is not even at all, and they are not complete; so
it becomes rather difficult to reconstruct it with sufficient details.
Alpha shape is a new technique [1] in the classification of all the simplexes from 3D
Delaunay triangulation of a 3D point set, and the result of this classification is three
categories: the internal simplexes of the shape, the regular one and the external one.
With a proper heuristic alpha value specified by the user [1], a concave silhouette shape
of a point set sampled from a regular manifold surface can be constructed.
We will improve this approach to the point cloud data acquired from the scan on a
real tree. Because of the limitations of alpha shape technique and complexity of
scanned tree data, it is not possible to have all details of the tree crown reconstructed to
a regular mesh through a direct application of the alpha shape technique [1]. In this
paper we solve this problem using a range of alpha values and testing the close property
of the constructed mesh, so that the mesh model is a concave closure of the point data.
The structure of this paper is as follows. Related work in shape information analysis
and plant modeling is introduced in section 2. Fundamental knowledge of our method is
described in section 3. Technical details of this new approach are described in section 4.
Experiments of this technique to reconstruct tree crown shapes are shown in section 5.
Conclusions about this technique and further investigation are described in section 6.
2 Related Work
In the past decades, many methods have been developed on point shape processing and
shape modeling of complex objects including plants, but with unequal results.
2.1 Point Geometry Processing
Jarvis [2] was the first to consider the problem of computing the shape as a generali
zation of the convex hull of a planar point set. A mathematically definition of the shape
was developed by Edelsbrunner in [3]. For 3D points, Boissonnat [4] suggested to use
Delaunay triangulation to “sculpture” a single connected shape of a point set.
In the frame of projects such as the digital Michelangelo project [5] at Stanford
Computer Graphics Lab in the 2000’s, and with the improvement of computer hard
ware, a numerous number of research papers have been published on point cloud
processing and rendering. Point geometry processing and analysis became an active
research topic.
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Reconstruction of Tree Crown Shape from Scanned Data 747
2.2 Plant Modeling on Knowledge and Rules
The different approaches of 3D tree model construction can be roughly classified into
three categories: botanical models, geometrical models, and digitized models from real
plants.
There are a numerous methods to simulate real plant appearance. Many early
methods were based on rule iterations (botanical, physical, geometrical, mathematical),
or simply based on strong user control with advanced dedicated patterns. In the 1980s,
modeling by botanical rules appeared, and produced nice findings, researchers tried to
simulate the growth of natural plants, plants could be constructed by some botanical
rules or grammars. AMAP [6] modeling method is based on bud life cycles of botanical
knowledge with real measurement data (on plant topology). This modeling method
clear reflects the growth mechanism of plants, including space occupation and the
location of leaves, fruits, and flowers. Lsystems presented by a Lindenmayer and
Prusinkiewicz were broadly applied to describe the growth process of plant organs,
which were based on fractal pattern [7, 12].
GreenLab [13] modeling approach is put forward as a mathematical model, which
simulates interactions of plant structure, leaves, trunk, branch and function. This model
can exactly engender the dynamics of plant, architecture and geometry of woody plants,
because of internal competition for resources, leaves sizes are different, and growth of
pruning can also be simulated.
These methods, used mainly in biology research fields are not dedicated to control
the 3D plant shape, and cannot easily do it, but aim to understand plant shape as the
result of a dynamic. It as be cited that this kind of model is not suitable to construct a 3D
models of real tree by using botanical methods [10].
Geometrically interactive modeling is another way to model virtual plants. Although
this method does not strictly follow the botanical rules, but visually realistic trees can
be produced [14]. In general, given 3D skeleton points of real plant, 3D model of each
branch can be generated with generalized circular cylinders [15]. Prism model is a
simplified application of this method. This approach is widely applied in some plant
software such as Xfrog, if combining rulebased method with traditional geometric
modeling approach. Nice 3D plant model could be produced, such as flowers, bushes,
and trees [8, 14].
To summarize, these rule based or pattern based methods used to build the real plant
faithful to botanic knowledge or appearance, can produce visually very realistic plants,
although they could not be used to model a specific existing real plant.
2.3 Digitalization of Real Plants
New modeling methods have been developed to digitalize real plants in very recent
years [911]. These methods can be used to reconstruct the trunk, the branches, and the
leaves, but the realism of the reconstructed model is still different from the real shape
due to the lack of crown silhouette shape information.
Plant digitization aims to reconstruct the shape of real plants from the information
digital instruments. The most popular techniques are the use of 3D laser scanner [9] or
the use of digital photos [10].
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748 C. Zhu et al.
When scanning a real plant from a single viewpoint many occlusions occur. In par
ticular, many leaves do usually hide branches and other organs from the view. One way
to make reconstruction efficient is to work both on plant branching structure recon
struction and on plant crown reconstruction. The idea of the proposed approach is to
consider that when processing the branch reconstruction of a real plant, we must con
strain the silhouette of branches from the crown shape.
By scanning a real tree, we have a point cloud data set, from which we could re
construct the shape of the real tree crown by combining existing methods.
Considering the branch structure, we may underline several interesting works.
Cheng [16] reconstructs a real tree from a range image, using generalized circular
cylinders to fit incomplete data and compute the skeleton based on axis direction.
Pfeifer [17] introduces a set of algorithms for automatically fitting and tracking cyl
inders along branches and reconstructing the entire tree.
With the appearance of advanced precise digital camera and laser scanner, the de
velopment of digital plant is accelerated. Imagebased and laserscanning based
methods have come up to produce 3D model of real trees in nature. Shlyakhter [18]
builds a 3D model of tree from a set of photographs. His method constructs the visual
hull of tree first, then a plausible skeleton is built up from medial axis of visual hull, and
finally Lsystem is applied to construct branches and leaves. Teng [19] reconstruct 3D
trunk of plant only from two images, this method only estimates skeleton and radius of
branches roughly. Quan [10] also models a plant from digital image. Their work focus
on reconstruction of big leaves, branches are reconstructed by interaction.
These imagebased approaches can build 3D plant from images of different view
points, but because of inevitable noise of images and error of camera parameters, the
accuracy of those methods is limited.
The approaches of Xu [9, 11] are based on some prior knowledge. A skeleton is first
constructed by connection of the centroids of points, which have an analogous length of
the shortest path to a root point. Then the corresponding radius of skeleton nodes could
be computed by the allometric theory. Leaves are constructed in the end, so that the
reconstructed tree is visually impressive.
However during the reconstruction, the methods of imagedbased or 3D laser
scanning data based first construct the skeleton, and then construct leaves, but because
of much occlusion, the reconstructed skeleton is incomplete. 3D laser scanner could not
scan the thin branches because of its limited precision.
But we have to reconstruct these thin branches for the architecture shape of real
plants in botany and digital forestry and for high visual impression in virtual reality.
We must thus construct the shape of tree crown to constrain the reconstruction of
thin branches.
3 Algorithm Bases: Alpha Shape
Alpha shape was proposed in 2D by Edelsbrunner [3], and was then extended to 3D in
[1]. This method can be used to reconstruct object surface from an unorganized point
cloud. Our reconstruction of concave tree crown is based on this technique.
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Reconstruction of Tree Crown Shape from Scanned Data 749
3.1 Delaunay Triangulation
A set P of points can be used to construct a complex if the points do not lay in a plane.
Delaunay triangulation is a natural choice to do it. In literature, different Delaunay
triangulation techniques are proposed [2022], where Lawson flip method is a typical
one. in Lawson’s method, the tetrahedron bounding the point set P is constructed at
first, and the other points are inserted into the triangulation one by one then. Each time,
the triangulation is optimized to satisfy the Delaunay property: the circumsphere of
every tetrahedron does not contain any other points. Those tetrahedrons, which do not
satisfy a local Delaunay property, are flipped.
The flip process in 3D can be described as follows. The triangulation in 3D is a set of
tetrahedrons constructing a simplical complex. We will explain the case of two tetra
hedrons incident to a triangle ace (Figure 1). If the circumsphere of tetrahedron
aecd does not contain band circumsphere of tetrahedron aecb does not contain d , it
can be said that (the triangle) aec
?
is local Delaunay. Otherwise, this situation can be
modified inserting a new edge bd inserted. Therefore the complex is a Delaunay tri
angulation.
The result of Delaunay triangulation of the point set is its convex hull composing
several tetrahedrons.
Fig. 1. Flipping in three dimensions
3.2 Alpha Shape
The concept of alphashapes formalizes the intuitive notion of shape for spatial point
sets on user’s selection. Alphashape is a mathematically welldefined generalization of
the convex hull. Its result is a series of subgraphs of the Delaunay triangulation, de
pending on different alpha values. Given a finite point set, a family of simplexes can be
computed from the Delaunay triangulation of the point set, a real parameter alpha
controls the desired level of detail. All real alpha values lead to a whole family of
shapes. The alphashape of a point set is made up of the set of points, edges, triangles
and tetrahedrons, which satisfy the constraint condition: the alpha test [1]. This test
applies for each a triangle t of the triangulation. If t is not on the boundary of the
convex hull, there must be two tetrahedrons , p q , which are incident to t . Tetrahedrons
p and q are tested to be in the circumsphere of t or not. If they both are not in that
circumsphere, and the radius of the circumsphere is less than the alpha value, t is said
to satisfy alpha test, and it is regarded as one member of the alpha shape. So al
phashape is a subset of the triangulation.
If we let alpha be large enough, the shape is the convex hull of the points set. If alpha
approaches 0, no tetrahedral, triangles and edges could pass the alpha test, so the alpha
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750 C. Zhu et al.
shape is the points set. With the adjustment of the alpha values, this subset can follow
the topology of the points set. So, if we choose a proper value for alpha, we will find a
reasonable surface for a tree crown.
The alpha shape is a subcomplex of the Delaunay triangulation of the points set P .
This can be explained in the following. There is a ball eraser with alpha as its radius,
and it could move to all possible positions in the 3D space and with no point of P in
cluded. This eraser will delete all simplexes whose size is bigger than alpha and it can
pass through. So the remaining simplexes construct the alpha shape.
4 Shape Construction of Tree Crown
The most impressive aspect of a tree is the silhouette of its crown, so the shape of the
crown surface is one important aspect for tree reconstruction for the virtual environ
ments. We can only acquire discrete points of the crown with the most recent sensors in
nowadays. Normally the data with 3D laser scanner are range images, each of which is
obtained from the scan at single viewpoint.
Point cloud from leaves determines the shape of tree crown. Since branches support
leaves in the architecture, branch reconstruction is important also. If we do not have the
branch model, we do not know how to locate the leaves. Reconstruction of branches
consistent to tree crown should be the main target of the reconstruction of a real tree. It
is very hard to reconstruct tree branches directly since shape information of the point
data is rather weak. The data for branches are incomplete due to the occlusion of leaves
and other branches. On the other hand, some little twigs cannot be scanned because of
precision limit laser spots.
If we build up the surface of a tree crown from the scanned data, the reconstruction
of tree branches will be easier under the control of tree crown surface. Otherwise, the
reconstruction result might be different from the real tree, so not faithful to be applied
to tree measurement.
4.1 Analysis of Scanned Data of a Real Tree
It is an ordinary technique to sample the surface of real object using 3D laser scanner,
and then to reconstruct the shape from the sample data with limited precision. This
point cloud data describe the geometry and the appearance attribute of objects surface.
The normal point cloud is densely sampled from continuous or smooth surface, al
though the data is unorganized and irregular. A number of successful methods have
been presented to deal with these data and to reconstruct appearance of object.
Plants, such as trees, have too many organs and its structure is too complex. A tree is
made up of trunk, branches, and a huge number leaves. The point cloud data of tree is
not sampled from a manifold surface, so it is more irregular than those from other data
from the manifold surface. The points from leaves are even more irregular. The density
variation of point cloud from leaves may be very large. Thus, traditional technique does
not work for these objects. Special methods should be developed to reconstruct real
plants. In order to keep the shape of plants, branch skeleton extraction and construction
of plant crown should be included. One difficulty of this work is that the points from
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Reconstruction of Tree Crown Shape from Scanned Data 751
branches and those from leaves are mixed together, so that it is hard to initialize the
work of shape analysis.
4.2 Building the Mesh Model of Tree Crown
From the above analysis and the range image data acquired from a single scan in Figure
3(a) and Figure 4(a), we can recognize the dense region and the sparse region of the
data by observation, but this recognition process is very difficulty to be performed in a
computer. The points from the tree side facing the scanner and the region with dense
leaves (the side of a tree facing the sun, for example) are denser. There may be some
interstices among dense leaves. When we scan a tree, laser lights will pass the interstice
and meet the branch or leaves at another side of tree, or pass through the tree. So there
should be holes in the data. Although we can distinguish the dense region, the sparse
region, the convex region and concave region, the algorithms processing very dense
point set will make mistakes in topological reconstruction. Therefore, we must con
struct topological structure of points at first, where Delaunay triangulation is an ideal
choice.
Our algorithm contains four steps:
The first step is to triangulate point set
a set of connected tetrahedrons
adopted to correct irregular triangulation in
constitute a convex solid, the shell of this solid is a convex hull.
The second step is to compute all radii, ( )
after triangulation. This value will be one attribute of a tetrahedron
of the circumcircle of each face of a tetrahedron arecomputed also, and they are thought
of as an attribute of each face.
The third step is to classify tetrahedrons { }
all
j
R T . This classification is performed by the relation of ( )
threshold α and, where α is specified by users. The scope of α should be proper.
Then all tetrahedrons are classified into two categories according to a real value α :
interior tetrahedrons and exterior tetrahedrons. If ( )
terior tetrahedron. Otherwise, it is classified as an interior tetrahedron. All faces { }
from each tetrahedron
faces and boundary faces. The classification role is as follows. If a face on the convex
hull belongs to an exterior tetrahedron, it is an exterior faces; otherwise, if it belongs to
an interior tetrahedron, it is a boundary faces. For each face not on the hull, if it is an
intersection face of two exterior tetrahedrons, it is an exterior face. If it is an intersec
tion face of two interior tetrahedrons, it is an interior face. If it is an intersection face of
one interior tetrahedron and one exterior tetrahedron, it is a boundary face. All
boundary faces will construct a mesh, and this mesh M will be an concave approxi
mation of the crown.
Let rmax be the largest radius of all
R T and all (
smallest radius of all
( )
j
R T
and all ()
k
r F
min
Ar
λ=
,
max
Br
μ=
,
0.9
λ =
, and
1.1
μ =
{ }
p
i
P
are obtained. Flipping method in [23] is
{ }
i
Pp
=
. All tetrahedrons
=
with Delaunay triangulation, so that
{ }
T
j
T
=
{ }
T
j
T
=
will
j
R T , of circumsphere of every tetrahedron
j T . The radii, ()
k
r F ,
j T and their all faces. The rule to classify
j T is the size of ( )
j
R T with
j
R T
α>
,
j T is classified as an ex
k F
j T are classified into three categories also: interior faces, exterior
( )
. We acquire an interval [ , ]
. The α value should be confined to the
j
)
k
r F , and Let rmin be the
A B , where
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752 C. Zhu et al.
Fig. 2. Pipeline of this algorithm
interval[ , ]
mesh M will not be a solid.
The fourth step is to test the validity of specific alpha values, so that the mesh
M builds a boundary surface of a manifold. If the alpha value is set larger than B ,
boundary points are on the convex hull, so the mesh cannot be concave. If the alpha
value is set smaller than A, some sample points are isolated from in the solid, so the
reconstructed shape is not complete. Those both extreme cases are not interesting for
tree crowns. Therefore, α must lay in interval [ , ]
iterative process. We initialize α as the average value of A and B . In each iteration
step, we check if the boundary triangles constitute a manifold surface; if so, the alpha
value can be reduced, if not, it is increased.
Figure 2 shows the pipeline of this approach.
A B ; otherwise, if
B
α >
, the mesh M will be a convex hull, and if
A
α <
, the
A B . Finding the proper α value is an
5 Experiments and Discussion
Our algorithm is written with C Language with the support of OpenGL for graphics.
Tests were held on a PC with P4, 3.0GHz processor and 1G RAM. CGAL library is
used to perform Delaunay triangulation [24]. Our experimental results of concave tree
crowns are shown with local illumination.
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Reconstruction of Tree Crown Shape from Scanned Data 753
(a) (b) (c)
Fig. 3. Extraction of the Crown shape of a Maple tree; (a) is the source point cloud data; (b) is the
boundary point cloud data; (c) is the extracted boundary mesh model
(a) (b) (c)
Fig. 4. Extraction of the crown shape of a Candlenut tree; (a) is the source point cloud data
displayed with a cube for each point; (b) is a comparison of the extracted boundary mesh with the
source point cloud date; (c) is a close view of (b)
We reconstruct the shape of tree crowns with two data sets of two trees. The first
one is a single scan of a 20meter high maple tree with leaves. Figure 3 (a) shows the
original point model of the maple tree of 114997 points displayed with a cube for each
point. When the alpha value is set as 4.2354, we acquire 2810 points on the boundary
(Figure 3 (b)). Figure 3 (c) shows the reconstructed tree crown mesh model.
The second example is a candlenut tree without leaves shown in Figure 4. The
original data of the candlenut tree has 86675 points (Figure 4 (a), and when the alpha
value is set as 0. 41399, 4291 points are left on the boundary. The implementation of
our algorithm is shown in Table 1, where the last column is the time spent from data
input, to Delaunay triangulation, and to the list of all triangular faces on the boundary.
To show the properness of this approach, the original point model of the candlenut
tree is combined to its reconstructed crown mesh model. Figure 4 (b) shows this
comparison, and Figure 4 (c) shows a close view of Figure 4 (b). It can be seen in
Table 1. Experimental details on two data sets
Tree
Maple
Candlenut
Point set
114997
86675
Alpha value
4.2354
0.41399
Points on boundary
2810
4291
Time in secs
1814.16
2131.03
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754 C. Zhu et al.
Figure 4 (b) and Figure 4 (c) that the reconstructed crown mesh model includes the
original point model well.
These two examples show that the shape concavity is well reconstructed. The ap
proach is illustrated here on both dense crown and spare (unfoliaged) one.
6 Conclusion
Current 3D acquisition systems lead to model more and more 3D shapes of real life
objects. However, nowadays reconstruction approaches classically fail on high com
plexity objects, such as trees. Even if nice progresses have been noticed on the main
branch structure on unfoliaged trees, the overall reconstruction is not satisfactory,
especially on small structures and leaves.
We proposed hereby a method to reconstruct in 3D the scanned tree crown, in order
to constrain the definition of the branch structures, especially the thinner ones, and
contribute to define local geometrical constraints for leaf area reconstruction.
The principle of our approach is based on the use of the alphashape on the range
point data set, a generalization of the convex hull and subgraph of the Delaunay tri
angulation. In the Delaunay triangulation process, we choose the triangle candidates on
the boundary according to the alpha value, and constrain the surface mesh to stay a
manifold. Therefore, our constructed boundary mesh builds in fact the silhouette of the
crown. This shape of the tree crown is much more convincing than the convex hull of
the tree crown in keeping the major concave features of the crown. This shape can be
used to constrain faithfully the reconstruction of branches and foliage.
The proposed approach was successfully implemented and tested on two data sets.
Of course, the reconstructed crown shape mesh is rough, thus fast to render, and thus
not strongly concave, so that higher branching structures are not recreated. In future,
progress can be achieved by dividing the data into several subsets according to point
density, with different alpha values applied to each subset. Concave silhouette surfaces
can then be reconstructed independently, and then merged to a more detailed shape.
It is also interesting to note that such crown shapes do find applications in various
domains. Such tree crown can contribute to define intermediate LOD plant models,
from real plants or simulated ones. It contributes to define low weighted geometrical
models. Of course, appropriate color and transparency value computations can increase
the appearance while rendering such shapes.
Finally, the proposed technique may be of interest on a wide range of complex object,
showing high topological complexity, where simplified representation, based on in
ternal complex structure is useful. Such could be the case of human organs represen
tation build from their internal vessels.
Acknowledgments
The authors would like to show thanks to Dr. Baoquan CHEN and Ms. Wei Ma for
providing scanned data of trees. CGAL library was used for Delaunay triangulation
[24]. This work is supported in part by National Natural Science Foundation of China
with projects No. 60073007, 60672148, 60473110; in part by the National High
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Reconstruction of Tree Crown Shape from Scanned Data 755
Technology Development 863 Program of China under Grant No.2006AA01Z301; by
the French National Research Agency within project NATSIM ANR05MMSA45;
and in part by the MOST International collaboration project No. 2007DFC10740.
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