view-dependent hierarchical foliage simplification

View-Dependent Hierarchical FoliageSimplification

Qingqiong Deng1,2, Xiaopeng Zhang1,2, and Marc Jaeger3

1 Sino-French Laboratory LIAMA, CAS Institute of Automation, Beijing, China2 National Laboratory of Pattern Recognition, CAS Institute of Automation, Beijing,

Chinaqqdeng, [email protected]

3 INRIA-Rocquencourt,Project DigiPlante, CIRAD AMAP, Montpellier, [email protected]

Abstract. High compression of plant geometry is an important aspectin fast realistic visualization of plants. Hierarchical structuring plantmorphology is a key factor for real time plant rendering, especially whenpedestrian views, including both close-ups and far views, are requested.We present here a new geometric simplification method, called View-dependent Hierarchical Foliage Simplification (VHFS). It aims to con-struct efficient multi-resolution models, faithful to botanical knowledgefor sparse organs of trees, such as leaves, flowers and fruits. Both pre-processing and view-dependent rendering processes are consideredhereby. In the preprocessing phase, sparse organs are simplified hier-archically with respect to the topological structure of the plant, i.e. tothe plant branching order hierarchy and the phyllotaxy (or anthotaxy)groups. In the rendering phase, the simplification degrees for organs indifferent locations in the crown are defined from the current viewpoint.The selection of the different simplification levels is based on the dis-tance to the viewer and a visibility coefficient of the considered organs.This visibility coefficient is an approximate occlusion based on the rela-tionship between the viewing direction and direction of each first orderbranch. Compared with other foliage simplification methods, the mainadvantages of VHFS lay in the respect of consistent botanical structureat any stage of compression, ensuring realistic foliage appearance, higherefficiency in preprocessing stage and higher data compression.

1 Introduction

Vegetation is an important element in outdoor and indoor scenes. Fast and re-alistic plant rendering becomes a common request for numerous applicationsconcerning computer animation, flight simulation, urban visualization, virtualenvironment, and entertainment. But real-time rendering of such scenes is a chal-lenge since brute force geometry rendering far exceeds current CPU and GPUcapabilities. Software acceleration techniques of rendering have thus been widelydeveloped aiming to decimate the geometric complexity. A powerful way is thelevel of detail (LOD) technique. However, plants and trees are much different

K.-c. Hui et al. (Eds.): Edutainment 2007, LNCS 4469, pp. 44–55, 2007.c© Springer-Verlag Berlin Heidelberg 2007

View-Dependent Hierarchical Foliage Simplification 45

from classical continuous objects from topological structure point of view. Clas-sical model simplification approaches fail on sparse organs due to their primitivenumber, sizes and distributions.

Organs and more precisely leaves are of interest; foliage often determines theappearance of a tree. Various approaches have thus already been developed forfoliage simplification[1,2,3,4]. They can diminish the number of leaves in a crownwhile maintain its appearance.

But there are still many spaces for improvements. First, almost all of thesemethods represent leaves of one tree using a single unique choice of detail. Theonly exception is the approach of Remolar et al. View Dependent Multiresolu-tion Model for the Foliage (VDF)[4], where the selection of different resolutionsof foliage geometric models of a single tree follows a simple criterion, such asthe distance from the viewer or importance of the object in the scene. Second,methods do usually not take benefit of the plant topological structure; leaves areconsidered independent from each other, leading to high processing costs whenconsidering possible polygon fusion for instance. Finally leaf distribution andmore precisely occlusion are not considered either.

We aim to contribute to the definition of efficient LOD plant foliage modelsusing the underlying branch structure in order to render high realistic 3D naturalscenes. The proposed approach extends past contributions of VDF. Leaves arefirst clustered on a local level, then on hierarchical levels defined from branchstructures. Using a simple heuristic to evaluate foliage occlusion, we allow thenthe use of lower LOD models for occluded or partially occluded foliage parts.The implementation of the proposed approach is then illustrated on complexfoliage of stand-alone plants and on a natural scene.

2 Related Work

Plant modeling has been extensively explored. At present, there are many ma-ture systems. L-system[5], AMAP[6] and Xfrog[7] are the typical ones. In thesesystems, plants are usually designed on a strong topological base, mainly definedby the branching order. However, as the result of realistic plant modeling, thenumber of the polygons is often too big for a normal plant. So the representationof a small scene or forest with hundreds of plants is usually very huge. Thus, realtime rendering of outdoor trees with original full geometric models is impossible.

Acceleration techniques of rendering have been widely researched, and peoplehave proposed many methods. The methods can be classified into three generalcategories: image-based, point-based and polygon-based.

Image-based rendering is widely used due to its good property that its perfor-mance is independent of the geometric complexities of objects. There are variousapproaches in this field, such as billboard[8], billboard clouds[9,10], multi-layerZ-buffers[11], layered depth images[12], hierarchical bi-directional textures[13]and volumetric textures[14,10]. They are efficient for and can get fantastic re-sults when rendering plants and trees at a distance. However, the methods need

46 Q. Deng, X. Zhang, and M. Jaeger

a huge memory to store the texture images. The parallax effects are usually bad,and artifacts are obvious on close views.

Point-based rendering uses a point to represent a leaf when the projected sizeof the leaf on image space is smaller than a pixel[17,18]. It is efficient on plantsand trees that are far from viewer, but require costly sampling stages otherwise.

Polygon based rendering is the traditional and predominant rendering method.It has a well support of hardware acceleration and easy texture mapping. But thedata complexity through polygon model is usually too high for fast rendering.

There are many geometric simplification methods[15,16] dealing with polygonmodels. They usually work well on continuous manifold objects. However, whenapplied on trees, they may produce acceptable results for trunks, but will failon foliage. Some specific approaches have been proposed for the simplificationof foliage[1,2,3,4]. The Foliage Simplification Algorithm (FSA)[1] was proposedby Remolar et al. in 2002 for quadrilateral leaves, it diminishes the number ofleaves but maintain the appearance of the crown by leaves collapse; - two leavesare replaced by a new larger leaf with similar position and shape as the origi-nal ones. This method has been improved in Progressive Leaves Union (PLU)[2]using more reasonable measurements of similarity to select the best leaf pair toimplement leaves decimation. In addition, the PLU is view-dependent, all simpli-fication information is recorded on the hard disk, and appropriate approximationmodels will be chosen for different viewpoints automatically. Hierarchical Unionof Organs (HUO)[3] was recently developed on PLU to hierarchically and re-spectively simplify tree organs with respect to some basic botanical structure asphyllotaxy and anthotaxy. So that the botanical structure of the plant in theHUO algorithm is better kept for visualization than that of the FSA and thePLU, but all the topological structure is not fully applied.

However, the three algorithms, FSA, PLU and HUO, do not discriminatethe leaves that locate in different regions of the crown, thus their simplificationdegrees are uniform all around the crown. Remolar et al did propose a specificalgorithm VDF[4]. But it needs to maintain an active list of visible polygonsobtained by using a conservative visibility algorithm, and modify the active listtaking advantage of temporal coherence when the user’s viewing position shifts,so it is costly both in computation time and storage.

3 Hierarchical Foliage Simplification

The idea of View-dependent Hierarchical Foliage Simplification (VHFS) is tobuild LOD models for sparse organs on the base of the underlying plant topo-logical structure. This topological structure reflects the plant design process orgrowing process. It covers usually two levels: a local level and a global level. Thelocal level defines the organ topology itself and its insertion on a given point ona branch for its distribution in the crown. The global level corresponds to thetopology of all branches.

There are four steps in VHFS. The first step is to construct organ clusters cor-responding to the phyllotaxy structure, or the anthotaxy structure, for each plant.


Fig. 1. Progressive union of leaves in a leaf cluster

The second is to simplify complex mesh model of each organ in each cluster to aquadrangle by using Multiphase Surface Simplification algorithm [19]. The thirdstep recursively implements Progressive Union of Complex Organs [3] within eachleaf cluster, or phyllotaxy group, until all the quadrangles in the leaves cluster areunited as a single quadrangle, which is called as the representative quadrilateralof the leaves cluster (see Fig. 1). The forth step simplifies all representative quad-rangles hierarchically according to the topology information of branches and theposition of each leaf on a branch. VHFS is intuitive but very effective. In the fol-lowing sections, we will introduce step two and step four in detail.

3.1 Simplification of Complex Leaves

Multiphase Surface Simplification method[16] is used to simplify the complexmesh of each sparse organ to a quadrangle. A leaf mesh is often topologicallyequivalent to a patch, and it needs nice boundary preservation also. For eachleaf of the leaf class, or phyllotaxy group, we classify the vertices of a leaf meshinto three categories: inner, boundary and corner points. The definitions of innerpoints and boundary points are the same as that of ordinary mesh simplificationmethods, while a special attention is needed to pay only on the definition ofcorner points, which is fixed during the simplification. To get better preservedboundary, we determine two vertices as corner points for each leaf according toits feature. One is the vertex whose distance to the vertical-axis is the longest.Since the leaves of phyllotaxy group are arranged around the vertical-axis, it isthe tip of the leaf. The other is determined through the symmetry property ofthe leaf, and it is corresponding to the vertex that connects leafstalk althoughthe leafstalk is usually omitted in plant models. All the simplifications processand errors due to simplifications are recorded, where the error is defined as theone from a newly generated vertex to the old mesh.

Fig. 2. Leaf Simplification

Fig. 2 illuminates the simplification of a willow leaf to a quadrilateral withVHFS, where the red vertices are corner points. VHFS simplifies complex leavessmoothly.


3.2 Hierarchical Simplification According to Topology of Branches

As the last step of foliage simplification, all representative quadrangles are sim-plified hierarchically according to the topology of branches.

Each branch is evaluated with a level value at first. The level value of thetrunk is set as 0. The level value of each branch born on a level-k branch isk+1. We also define a subtree as the set of all successor branches and associatedleaves, and a k-subtree is a subtree located on a level-k branch.

After simplifying all leaf clusters, or all phyllotaxy groups, to a quadrilateral,Progressive Union of Complex Organs[3] is performed inside each different sub-tree. The order of this performance is the subtree levels with upper levels first.If the maximal level of branches of a tree is n, the progressive organs union isapplied first inside every n-subtree until only a single quadrilateral left, and thenwe move down to all (n-1)-subtrees. Such process will be recursively implementeduntil 0-subtree is reached and the whole foliage is united as one quadrilateral.The selection of the best leaf pair is usually the most time-consuming part inpre-processing. By simplifying organs hierarchically with respect to the botanicalconcept of phyllotaxy and topologic properties, VHFS is much more efficient inpreprocessing than other existing foliage simplification methods. The reason isthat in each step of decimation, the selection of the best organ pair is performedin a very limited scope, i.e., all organs grown on a branch.

Fig. 3 shows some simplification steps of a 15-year-old holly tree, whose max-imal branch level is 3. Fig. 3(a) is the original model; Fig. 3(b) is the result aftersimplifying each 3-subtrees to a single quadrangle; and the corresponding resultsof 2-subtrees and 1-subtrees are showed in Fig. 3(c) and Fig. 3(d) respectively.

Using VHFS, we can simplify very big trees with a great number of leafpolygons in a few second. In Fig. 7, less then 5 seconds are used to simplify of abig tree crown, with more then 412 thousand foliage polygons. This tree will makeall other existing foliage simplification methods, like HUO, much exhausted.

In the end of preprocessing, all the simplification data and simplificationprocess data are saved in the hard disk as a binary tree. In each step of organunion, the new generated organ is recorded as the father of the collapsed organs.

(a) Original (b) 3-subtree (c) 2-subtree (d) 1-subtree

Fig. 3. Foliage simplification according to branch topology


For each node of the binary tree, the corresponding error due to simplificationis recorded also.

4 View-Dependent Multi-resolution Model

While rendering, the selection of the appropriate LOD foliage model is definedfrom a spatial error threshold. The binary tree is traversed until the recordederror values are higher then the threshold or until lowest detail description isreached. The spatial error threshold value is computed from both the distanceand a foliage occlusion factor. In our implementation, distance from crown toviewer is defined as that between the tree bounding box center and the viewer.

Nevertheless, in order to increase the rendering efficiency when leaves are faraway from the viewer, lower details may be selected for leaves in different areason the crown, based on the fact that some leaves held by ”hidden branches”of the crown are often occluded by the front foliage. The idea is to mimic somehow the techniques used by traditional artists to paint trees. Painters use initiallylarge rough strokes to paint the leaves that are hidden, and then add detail usingfiner strokes over them to represent visible leaves.

The selection of the best leaf pair is usually the most time-consuming part ofpre-processing. By simplifying leaves hierarchically with respect to the botanicalconcept of phyllotaxy and topologic properties, VHFS is much more efficient inpreprocessing than other existing foliage simplification methods. The reason isthat in each step of decimation, the selection of the best leaf pair is performedin a very limited scope, i.e., all leaves grown on a specific branch.

The critical question is how to efficiently determine whether a leaf is visibleor not. Assuming that the visibility of leaves belonging to the same 1-subtreeare uniform, we do propose here a simple non-conservative method. It providesa fast approximation visibility factor for any leaf, avoiding the recording andtraversing of the active list.

This assumption makes sense since the main axis (the main branches, buildingthe skeleton of the tree) does generally keep the same direction. Leaves of a 1-subtree are rendered using a same LOD. It is also practicable, since the leavesof different 1-subtrees are simplified independently before the simplification ofthe 0-subtree. The proposed visibility value is therefore a simple dot productbetween the viewing direction and the 1-subtree direction, defined by its branchdirection.

To summarize, the leaves are rendered with models of different LODs con-trolled by the following special error threshold E(B), defined with equation(1)according to its branch direction:

E(B) ={

[(C − d)/(C − 1) + 1]ε; if d ≥ Cε; if d < C

(1)

where d = b ·v; b is the normalized direction of the branch B; v is the normalizedviewing direction; C is the constant used in our visibility criterion to classifyleaves into visible and invisible categories; and ε is the spatial error threshold


(a)Holly original (b)Holly simplified (c)Maple original (d)Maple simplified

Fig. 4. Branch improper visibility

(a) Front (b) Left (c) Top

d<0.50

0.50<d<0.65

0.65<d<0.75

0.75<d<0.875

0.875<d<1.00

(d) LOD levels

Fig. 5. Multiple levels foliage with false colors

corresponding to the basic LOD defined by the distance from tree to viewer. IfC is set to 0, silhouette cannot be properly kept for some branches orthogonalto the viewing direction. Fig.4 (b) and Fig.4 (c) show the improper visibilityfrom C = 0, and Fig.4 (a) and Fig.4 (d) are original models. In practice, we useC = 0.5 for all plants.

Fig. 5 shows a multi-resolution model with false colors of a 6-years-old hollymodel, where Fig.5(a) is the front view, Fig.5(b) is the left view of the samemodel, and Fig.5(c) is the top view. The definitions of the colors are shown onFig.5(d), where the green color means the finest LOD, and the red means thecoarsest one.

5 Implementation and Results

We did implement the proposed approach in C language, using OpenGL library,running on a PC with Pentium TM Xeon at 2.13GHz, 2GB RAM. Virtual treesused in this paper were generated with AMAP Genesis TM [6] software. We havedone experiments on many species of trees. The sparse parts of trees, such asleaves, flowers and fruits, are simplified using the proposed approach while thetrunk and branches have been simplified through a dynamic simplification ofcylinders.


In order to show the effect of multi-resolution on compression ratio, we test fourspecies of trees in Fig. 6: a 25-years-old boxwood, a 30-years-old erected black lo-cust, a 25-years-old Scots pine and a 40-years-old spruce. The criterions are basedon distance and a criterion based on distance and visibility. Fig. 6 (a1, b1, c1, d1)are original models. Fig. 6 (a2, b2, c2, d2) are the simplified models with a uni-form level of detail on the distance to the viewer. Fig. 6 (a3, b3, c3, d3) are thesimplified models with different levels of detail on the distance to the viewer andvisibility. The sub-title of each figure is the number of leaves. It can be seen thatthe visual qualities of each pair of associated simplified results are quite similar,but the compression ratios of the multi-resolution results are higher.

(a1)144276 (b1)187834 (c1)191940 (d1)454491

(a2)13180 (b2)11525 (c2)19194 (d2)28055

(a3)10152 (b3) 8676 (c3)13080 (d3)21129

Fig. 6. Original, distance LOD, and distance with visibility LOD models comparison


We did also compare our method with the HUO on pre-processing time withsome tree models. The details, including the names of trees, the number of leavesof the original model, the time spent for simplification of leaves with HUO, thecorresponding time of VHFS, and the times of acceleration, are shown on table 1.It turns out that our method is much more efficient.

Table 1. Comparison on pre-processing time in seconds

Tree name Holly White poplar Black poplar Scots pinePolygon Number of the model 23 K. 33 K. 282 K. 192 K.Preprocessing time of the HUO 484 7.48 1498 668Our VHFS preprocessing time 0.58 0.44 1.8 2.28

Gained time Ratio x 838 x 17 x 819 x 293

In order to show the similarity of visual effects of the same tree at differentresolutions, a 25-years-old Horse chestnut tree is shown at various distances (55,30, 19, and 11 meters) away from the viewer in Fig.7 (a). A zoomed view ofthese models is shown for comparison in Fig.7 (b, c, d, e).

Fig. 7. View-dependent LOD models with their respective organ polygon counts

Fig. 8 shows a virtual forest with 119 trees, using 4 instances: a 15-years-oldholly, a 25-years-old scots pine, a 20-years-old horse chestnut and a 30-years-olderected black locust. They are placed in different places in the virtual forest. Thetotal polygon number of sparse organs of the forest is over 16 million. The numberof polygons of sparse organs is 1.2 million for Fig.8 (a), so the compression is


(a) A Global View of the virtual forest

(b) A Close View to the middle part (c) A Close View to the right part

Fig. 8. Rendering of a virtual forest (119 trees, 4 species, 10-20 frames/second)

13.7. Foliage was generated in 36 ms. (shadow calculation is not included sinceimplemented as a post-process). Fig.8 (b, c) are close views with the same degreeof simplification.

6 Conclusion and Further Work

Foliage geometrical compression is a key feature for realistic fast rendering ofnatural scenes showing vegetation from pedestrian point of view.

We propose a new algorithm, VHSF, which hierarchically simplifies sparseorgans(leaves, flowers and fruits), respecting both botanical knowledge of phyl-lotaxy and topologic properties of trees, so that botanical structure of a plant iswell kept and the preprocessing time spent is much shorter. VHSF is thus a defin-ition of LOD models that hierarchically simplify organs of trees in preprocessingwith respect to the topological structure of leaves in the tree crown.


The approach includes a dynamical mechanism to determine simplificationdegrees of the foliage in different volumes of a crown according to posture ofbranches that bear these leaves during rendering. By using a very simple and effi-cient approach that exploits the direction information of the first order branches,we can build the model of a tree with non-uniform resolutions. As a result, thevisible leaves of a tree are represented with a finer level of detail, where thehidden leaves are represented with a low resolution. This way the compressionratio of results will be higher while the visual qualities are maintained.

The preprocessing and rendering are faster than non-topological structurebased existing approaches, and the generated LOD models keep better botanicalarchitecture of the original model at any simplification level.

There is still some work that deserves to improve in the future. At present,the visibility calculation uses only the branch direction information, and we canget good results for most kinds of trees. In the future, in addition to branchdirection, we could consider other properties of trees, such as the number ofleaves each branch bears, taking benefit of various foliage densities informationin the crown. We could also consider the visibility decay within the tree. Thiscould also be considered at the scene level later on. In experiment, we showthat the proposed approach is a very efficient method to compress the plantgeometric data. Nevertheless, in the case of real-time rendering, significant gainscould be achieved, combining advanced real-time visualization techniques suchas image-based methods on far plants, or deferred rendering on closer ones.

Acknowledgements

The authors would like to show thanks to Mr. Jean-Fran?ois BARCZI for hisassistance in understanding plant genesis models. All original plant models inthis paper are from the output of AMAP-GenesisTM . This work is supported byNational Natural Science Foundation of China projects No. 60073007, 60473110,30371157; by National High-Tech Research and Development Plan of China un-der Grant No. 2006AA01Z301; by the French National Research Agency withinproject NATSIM ANR- 05-MMSA-45; and by LIAMA funding with the projectGreenLab.

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