CN101847267A - Tree modeling method based on depth search - Google Patents

Abstract

The invention relates to a tree modeling method based on the depth search, and the method is to automatically build a tree model by taking a tree main branch and a tree crown outline drawn by hands as input. The method comprises the following main steps of: extracting two-dimension frameworks from drawn strokes through pixel analysis; directly converting the two two-dimension frameworks into a three-dimension main branch framework through the depth search; and building withes and leaves on the basis of restriction of the tree crown outline. The method can efficiently build the tree model which has the reality sense and accords with input restriction by simple algorithm. The modeling result obtained by the tree modeling method has the significant application value in fields of computer games, three-dimension movies, network roaming, city view design and the like.

Description

Tree modeling method based on depth search

Technical field

The invention belongs to computer graphics and technical field of computer vision, relate to a kind of method of carrying out the trees modeling according to sketch.

Background technology

Applications such as computer game design, three-dimensional movie making need have the plant model of visual effect true to nature or special visual effect in a large number.The plant modeling will satisfy requirement aspect two of modeling speed and the visual effects in these Application for Field.Therefore study easy to use, travelling speed fast, the plant modeling method that changes modelling effect of can following one's bent is significant to practical application.

Present plant modeling method is broadly divided into four big classes:

The first kind is based on botany knowledge is carried out modeling to phytomorph method.These class methods are mainly considered the plant growth rhythm, as the Lindenmayer system of Lindenmayer proposition;

Second class is based on the plant modeling method of image.These class methods as input information, make up plant model by various vision method for reconstructing with the plant picture, as the plant modeling method of Quan proposition in 2006;

The 3rd class is based on the plant modeling method of 3-D scanning.These class methods make up plant model with 3 d scan data as input, as the tree modeling method of Xu proposition in 2006;

The 4th class is based on the plant modeling method of manual interaction.The two-dimentional sketch that these class methods are delineated with the user is as input, or directly controls the three-dimensional model shape of output by three-dimension interaction, the plant modeling method that proposes as Okabe in 2005.

Method based on growth mechanism is applicable to growth simulation, agricultural analysis etc., but generally needs to adjust parameter, is not easy to control output, therefore is not suitable for the real plants modeling; Based on the method for 3-D scanning with the 3 d scan data of tree as input, geological information is abundant, the precision height, be applicable to the application that model accuracy is had relatively high expectations, but the expensive price of 3-D scanning equipment, the scanning process spended time is longer, the three-dimensional data amount is big, is unsuitable for rapid modeling; Method input information based on image obtains conveniently, and modeling method is flexible, and applicable to the application of various accuracy requirements, but it is lower than the modeling accuracy based on 3-D scanning; Method based on manual interaction is a kind of method more flexibly, can be used for the design of tree-model.

Summary of the invention

The objective of the invention is to, at the trees that exist in the real world, provide one based on image and sketch, can reflect the fast modeling method of the main form of trees, and make this method can be used for the design of various tree modelling.

For achieving the above object, the invention provides a kind of tree modeling method based on depth search, the step of this tree modeling method comprises:

Step 1: the user delineates out the trees sketch that has crown outline, has different major branch strokes by hand with single pixel paintbrush or paintbrush on two width of cloth trees pictures, two width of cloth sketches that will have different major branch strokes are input to image processing equipment;

Step 2: image processing equipment is analyzed neighbour's pixel of each major branch stroke pixel in the sketch, thereby extracts two-dimensional framework;

Step 3: two two-dimensional frameworks are carried out depth search, make up three-dimensional major branch skeleton, make this three-dimensional framework satisfy the two-dimensional framework constraint at the parallel projection of two input directions;

Step 4: the three-dimensional major branch skeleton with structure is a masterplate, in two-dimentional crown outline constraint, make up first order withe skeleton by the duplicating of major branch, translation, rotary manipulation, be that masterplate makes up second level withe skeleton by same procedure with first order withe skeleton then, the rest may be inferred, obtains specifying the withe skeleton of progression;

Step 5: create generalized cylinder according to estimation, obtain the geometric model of branch by the cylinder match to skeleton tangent vector, normal vector and secondary normal vector;

Step 6: interpolation leaf or fruit are finished whole tree modelling on the branch geometric model, each leaf or fruit are represented by the quadrilateral that has shone upon a four-way image texture, the leaf model of a sequence is placed on the withe skeleton point, then leaf position, leaf towards and the distance parameter of Ye Yuzhi in introduce enchancement factor.

Wherein, state the picture that the trees picture is a reflection trees side form.

Wherein, the stroke at single pixel adopts partial analysis to extract two-dimensional framework with the method that is connected.

Wherein, connect the extraction two-dimensional framework at paintbrush stroke by stroke picture element scan, central point differentiation, central point simplification and skeleton point with radius information.

Wherein, described two-dimensional framework has Zijia family feature, father family feature, largest extension altitude feature and father's family of path feature.

Wherein, described depth search method is to search the corresponding branch of two two-dimensional frameworks by characteristic matching, and of every pair of corresponding branch as depth information, is expanded to three dimensions with another branch.

Wherein, before three-dimensional branch of two corresponding branch structures, need carry out the prolongation of connectedness judgement and branch to two corresponding branches.

Wherein, every pair of corresponding point of two corresponding branches have identical ordinate, the process that makes up a three-dimensional point from two corresponding point is the X-axis of getting one of them point, Y-axis coordinate X-axis, the Y-axis coordinate as three-dimensional point, gets the Z axial coordinate of the X-axis coordinate of another point as three-dimensional point.

Wherein, by duplicating part father branch and in the certain included angle restriction range, the part father's branch that duplicates is connected to obtains corresponding son branch on father's minor matters point.

The invention has the beneficial effects as follows to have proposed a kind of rapid modeling new method that this method utilizes image information and intelligent interaction to make up three-dimensional configuration based on image and sketch.The coupling that the difference of the present invention and forefathers' method is mainly reflected in two-dimensional signal is not by image registration and camera calibration, but by the branch signature analysis and characteristic matching, therefore, computing time of the present invention and modelling effect are superior than previous methods, experiment shows, the tree modelling of structure has kept two-dimentional input information, and realistic.

This invention utilizes image information and manual interaction to create the two dimension input, extracts two-dimensional framework by pixel analysis, searches the corresponding branch of two two-dimensional frameworks by signature analysis and characteristic matching, obtains three-dimensional major branch by degree of depth setting, adds withe and leaf at last.The modeling result that the present invention obtained can be used for each application of computer graphics, comprises computer game, three-dimensional movie, netsurfing, city landscape design etc.Utilize the present invention can create various realistic tree modelling fast.

Description of drawings

Fig. 1 illustrates the inventive method process flow diagram.

Fig. 2 (a) illustrates by single pixel stroke to Fig. 2 (f) and makes up two-dimensional framework.

Fig. 3 (a) illustrates stroke pixel O place to Fig. 3 (f) partial analysis be connected.

Fig. 4 (a) illustrates by the paintbrush stroke to Fig. 4 (d) and makes up two-dimensional framework.

Fig. 5 illustrates central point and differentiates.

Fig. 6 (a) illustrates the pixel simplification at a H place to Fig. 6 (c).

Fig. 7 (a) illustrates skeleton to Fig. 7 (b) and connects.

Fig. 8 illustrates the reference frame of two width of cloth images and three-dimensional model.

Fig. 9 illustrates the architectural feature definition in the two-dimensional framework.

Figure 10 illustrates the branch through height V.Red branch a, b and c are the branch of process height V in the diagram two-dimensional framework.

Figure 11 illustrates the depth search method flow diagram.

Figure 12 illustrates by two corresponding branches of two dimension and makes up three-dimensional branch.

Figure 13 (a) illustrates the reverse extending process of corresponding branch to Figure 13 (f).

Figure 14 (a) illustrates the three-dimensional major branch skeleton and the projection of skeleton point on the input picture thereof of structure to Figure 14 (c).

Figure 15 illustrates the withe growth course.

Figure 16 illustrates the withe modeling principle.

Figure 17 (a) illustrates the contrast of two peach models that obtain as input based on two width of cloth pictures, with different strokes to Figure 17 (g).

Figure 18 (a) illustrates vine modeling based on a width of cloth picture to Figure 18 (h).

Figure 19 (a) illustrates the sketch of delineating from paintbrush to Figure 19 (g) and makes up tree modelling.

Figure 20 (a) illustrates the effect comparison of the inventive method and Neubert method to Figure 20 (c).

Figure 21 (a) illustrates the effect comparison of the inventive method and Tan method to Figure 21 (c).

Figure 22 (a) illustrates by two different peach models and the virtual tree forest farm scape that the apple tree model constitutes to Figure 22 (b).These woods comprise 100 trees, are distributed in 60 meters * 60 meters zones.

Embodiment

Describe each related detailed problem in the technical solution of the present invention in detail below in conjunction with accompanying drawing.Be to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any qualification effect.

1, method general introduction (overview of approach)

Fig. 1 has provided the flow process of entire method.The key step of the inventive method comprises:

1), the establishment of sketch;

2), the extraction of two-dimensional framework, in two kinds of situation: (a) two-dimensional framework based on single pixel stroke extracts, (b) extract based on the two-dimensional framework of paintbrush stroke;

3), the structure of three-dimensional major branch skeleton, comprise 5 sub-steps: the replenishing of reverse extending, (e) disappearance skeleton of (a) setting up characterizing definition, (c) depth search, (d) branch of three-dimensional system of coordinate, (b) skeleton;

4), withe modeling;

5), the branch geometric model is created;

6), leaf modeling;

7), the drafting of tree modelling output.

In instructions of the present invention, the complete plant that " trees " are made up of whole branches and leaf; " branch " refers to the part beyond the leaf in the trees, and branch is divided into two kinds of major branch and withes; " major branch " is meant the main branch of trees, is made up of thicker branch; " withe " refers to the part beyond the major branch in the branch; " trunk " refers to the stem set; " tree crown " refers to the top and the branches and leaves thereof of trunk in the trees.

2, the establishment of sketch

Fig. 2 (a) illustrates by single pixel stroke to Fig. 2 (f) and makes up two-dimensional framework; Fig. 2 (a) and Fig. 2 (d) are two photos of a peach; Fig. 2 (b) and Fig. 2 (e) are for delineating out the sketch of major branch and crown outline with single pixel pen on photo; Fig. 2 (c) and Fig. 2 (f) two-dimensional framework for making up.This modeling method with two sketches width of cloth same pixel size, that delineate different major branches and crown outline as input.A photo of two photos of two side of the reflection of one tree (being approximated to the right angle) or a reflection one side can be used to create sketch.Situation with two photos is an example, and the user ticks major branch and the crown outline of tree with single pixel pen or paintbrush on every photos.On blank image, also can delineate major branch and crown outline as sketch by the imagination.The sketch constructive process generally needs 2～3 minutes.

3, the extraction of two-dimensional framework

The present invention adopts two kinds of two-dimensional framework extracting method, is respectively applied for single pixel stroke from sketch and the paintbrush stroke and extracts two-dimensional framework.

3.1 the two-dimensional framework based on single pixel stroke extracts

The method of extracting two-dimensional framework from single pixel stroke is applicable to that all strokes all are situations about being communicated with.This method mainly obtains next tie point by analyzing each stroke pixel neighbour situation.Fig. 2 has provided an example that makes up two-dimensional framework.

Fig. 3 (a) illustrates the partial analysis and the connection procedure at stroke pixel O place to Fig. 3 (f).Known G, D and O are that this zone has been determined and has been connected to skeleton point when anterior branch, in order to obtain the new skeleton point of O back, carry out following partial analysis at the O place:

1), reads in stroke pixel O.

2), 8 neighbour's pixels and the 16 neighbour's pixels of search O, and should the fixed skeleton point in zone.For any one stroke pixel O, the stroke pixel that the present invention claims to be in its 8 positions of ground floor of next-door neighbour is O " 8 neighbour's pixel ", and the stroke pixel that is in its 16 continuous positions of second layer be O's " 16 neighbour's pixel ", shown in Fig. 3 (b), A, B, C and D are 8 neighbours of O, and E, F and G are 16 neighbours of O.Know that by known conditions G, D and O are fixed skeleton points, shown in Fig. 3 (a).

3), 16 neighbour's clusters of O.According to location of pixels, 16 adjacent neighbour's pixel clusters are one group, and 16 all like this neighbour's pixels can be clustered into some non-conterminous pixel groups.Shown in Fig. 3 (c), 16 all neighbour's pixels are clustered into three groups, and each group has only a pixel, and promptly E, F respectively become one group with G.

4), determine " outside is effectively organized " and " inner valid pixel ".For any one pixel groups that is clustered into by 16 neighbour's pixels, if wherein do not comprise fixed skeleton point, this group is called " outside is effectively organized " so; For all 8 neighbour's pixels, if it is not fixed skeleton point, it is called as " inner valid pixel " so.Shown in Fig. 3 (d), E and F are that two outsides are effectively organized, and A, B and C are three inner valid pixels.

5), determine new skeleton point.For each outside effectively group, choose any one adjacent inside valid pixel as new skeleton point, for example A and the C shown in Fig. 3 (e).So just obtained the new skeleton point of pixel O back.

After pixel O place carries out partial analysis, obtained new skeleton point P _i, i=1,2...N.Carry out connection processing in the following several ways:

1) if N=1, with this point P ₁Be connected to as a new skeleton point and work as anterior branch.Then at P ₁Carry out same partial analysis and find the skeleton point of back.

2) if N＞1, at P _i, i=1 selects a bit among the 2...N, for example P _x,, carry out same partial analysis in this point then as when the new skeleton point of anterior branch.The principle of choosing when the new skeleton point of anterior branch is: choose as far as possible and work as the less point of the tangential angle of anterior branch.Remaining point is saved as the Section Point (their bud node is O) of other shoot, waits for the processing of back.Shown in Fig. 3 (f), A is connected to as new skeleton point and works as anterior branch, and C remains (being defined in 4.2 of bud node and Section Point) as a new Section Point.

3) if N=0, when anterior branch finishes.If there is new Section Point, forwards this node so to and carry out partial analysis.If there is no such node, connection procedure finishes.

This method begins to carry out partial analysis from minimum stroke pixel, all passes through to handle connecting into a tree-shaped skeleton at last up to all pixels.

3.2 the two-dimensional framework based on the paintbrush stroke extracts

Fig. 4 (a) illustrates by the paintbrush stroke to Fig. 4 (d) and makes up two-dimensional framework.Fig. 4 (a) illustrates the paintbrush stroke; Fig. 4 (b) illustrates two-dimensional framework; Fig. 4 (c) illustrates the paintbrush stroke; Fig. 4 (d) illustrates two-dimensional framework.In the modeling based on depth search, the user can use paintbrush to delineate major branch, and represents different branch radiuses with the different stroke of thickness.This from the paintbrush stroke method of rapid extraction two-dimensional framework mainly obtain stroke pixel center point by horizontal and vertical scanning, then central point is coupled together the structure skeleton.This method does not require that all strokes all are communicated with.It can be used for having from the tree region rapid extraction two-dimensional framework of radius information.

3.2.1 central point is differentiated

At first on each image, search for the skeleton point of qualified stroke pixel center point as the candidate.Delineated at every width of cloth on the image of major branch, from left to right each row pixel of transversal scanning is searched all stroke pixels, and is write down two horizontal boundary points of each stroke, obtains their central point and corresponding diameter (being two horizontal boundary point distances).Central point differentiation process as shown in Figure 5 is: on a horizontal scanning line, some P is the central point of unicursal, and the diameter of the branch at this some place is d ₁On a vertical direction at P place, upwards search for two vertical frontier points of P point place stroke downwards, its distance is d ₂If d ₁＜d ₂, then P is a qualified central pixel point, otherwise P is just cast out.Then to same width of cloth image, each row pixel of longitudinal scanning of the present invention obtains a group switching centre pixel and differentiates with similar methods, if the vertical frontier distance of this place stroke is smaller or equal to its horizontal boundary distance, then this is qualified central pixel point, otherwise is cast out.Can obtain 2 combination center of a lattice points like this, it is merged into one group as candidate's skeleton point.

3.2.2 central point is simplified

According to the position relation, the qualified central pixel point that obtains can be clustered into pixel groups one by one.All pixel clusters that link to each other are one group.With H is example, and the simplification process at each pixel place is as follows in each group:

1. read in the pixel H of certain group;

2. 8 neighbour's pixels of inquiry H in this group if 8 neighbour's pixel counts, forwarded for the 3rd step to greater than 2, otherwise forwarded for the 1st step to;

3. 16 neighbour's pixels of in this group, inquiring about H.For each 16 neighbour's pixel of H, choose the 8 neighbour's pixels that are attached thereto arbitrarily.All 8 neighbour's pixel groups of choosing become pixel groups S.

4. simplify.For all 8 neighbour's pixels, if be included among the pixel groups S or have horizontal ordinate extreme value, so just be retained, all the other 8 neighbour's pixels all are removed as redundant points.Can guarantee that like this 8 minimum neighbour's pixels link to each other with 16 neighbour's pixels.

Fig. 6 (a) illustrates the pixel simplification at a H place to Fig. 6 (c).As Fig. 6 (a) initial pixel is shown and distributes, pixel A～H, i, j are the parts of a pixel groups obtaining of cluster; As Fig. 6 (b) the simplification back being shown and distributing (a kind of possibility situation), after the simplification that H is ordered is finished, removed five pixels, kept two pixels---A (perhaps G) and C (perhaps D, E) link to each other with H with j because these two pixels are put 16 neighbours i respectively; Fig. 6 (c) illustrates a pixel simplified example.

3.2.3 skeleton connects

After the simplification at each pixel place was finished, remaining pixel can be regarded two-dimensional points as.In each pixel groups, need find a starting point, the point sequence that connects into a little in will organizing from this point, the i.e. initial configuration of branch.

In order to determine the starting point of a group, to give a mark for it according to position and neighbour's situation of each point in the group, the highest point of score is as the starting point of this group.The initial score of each point is 0, and the fractional computation process is as follows:

If the abscissa value of this point of the first step has the maximal value or the minimum value of an abscissa value for this group, then this fractional value adds 3, otherwise bonus point not;

If the ordinate value of second this point of step has the maximal value or the minimum value of an ordinate value for this group, then this fractional value adds 3, otherwise bonus point not;

If the 3rd this point of step has only one 8 neighbour's point, then this fractional value adds 2, otherwise bonus point not.

Judge that the point that score is the highest is exactly starting point (if has two or more point to obtain identical best result, so just optional one as starting point) through top three steps.From starting point, the sequence that is in turn connected into a little will guarantee that in this process each point links to each other with two points at most.

In each sequence, to have a few all be to link to each other successively from the starting point to the distal point.The inceptive direction that we are provided with for each sequence is to the distal point direction from its starting point.The connection procedure of skeleton is: since a sequence with minimum end points, constantly search for and connect all the other sequences along sequence of points, finally form a complete skeleton.The starting point of " sequence with minimum end points " or distal point have minimum ordinate in all sequences end points.

From minimum end points, move a circle along this place sequence to its another end points, this circle is the center of circle with the sequence of points, is radius with 2 times of the skeleton radius of every bit.In moving process, the besieged end points that advances other sequence of this circle just is connected.Shown in Fig. 7 (a), the sequence of three different colours connects as yet, and A, B, C are respectively the starting point of three sequences, from minimum terminal A, moves a circle along the sequence of redness; Yellow sequence and green sequence all are connected into respectively in this process, and the direction of each sequence obtained rectification, shown in Fig. 7 (b).In this way, all sequences can be connected, and form the tree-shaped two-dimensional framework with hierarchy.

4, the structure of three-dimensional major branch skeleton

The present invention adopts the depth search algorithm to make up three-dimensional major branch according to two-dimensional framework A on two planes of delineation and B.The main flow process of this algorithm is: for any one branch, for example λ of two-dimensional framework A ⁱ, at first in two-dimensional framework B, search a corresponding μ ^j, λ then ⁱFrom corresponding branch μ ^jObtain depth information, be converted into a three-dimensional branch.Three-dimensional building process connection rank according to branch in skeleton A is carried out successively, needs in this process to guarantee that all three-dimensional branches that make up all are communicated with.

4.1 set up three-dimensional system of coordinate

Fig. 8 illustrates the reference frame of two width of cloth images and three-dimensional model.Image A is with X _A, Y _ABe coordinate axis; Image B is with X _B, Y _BBe coordinate axis; Three-dimensional model is at X _A, Y _A, Z _AIn the coordinate system of determining.Two width of cloth input sketch A and B can regard rectangular two sides of the major branch of one tree as.Position by two sketches concerns as can be known: sketch B is the depth information of sketch A.

4.2 skeleton characterizing definition

The branch skeleton is a branched structure, and each branch is made up of a series of skeleton point (from the bud node to endpoint node).Two-dimensional framework can be by following denotational description:

A={ λ ⁱI=1,2...I _A, wherein two-dimentional branch λ ⁱForm by two-dimensional framework point, promptly

With

Be respectively horizontal stroke, the ordinate of skeleton point,

Radius for this some place branch.

For any one three-dimensional framework C, C={ η is arranged ^kK=1,2...K _C, wherein ${\mathrm{\η}}^k=\{(x_{k,\mathrm{\γ}}^3,y_{k,\mathrm{\γ}}^3,r_{k,\mathrm{\γ}}^3);\mathrm{\γ}=\mathrm{1,2}...l_k\}.$

Below with branch

The architectural feature of introducing in the two-dimensional framework for example defines, as shown in Figure 9.

● bud node P ₁: first skeleton point of branch λ, it links to each other with father's branch of λ;

● Section Point P ₂: second skeleton point of branch λ, after the bud node;

● endpoint node P _m: last skeleton point, i.e. Zhi end of branch λ;

● starting altitude b (λ): the bud node P of branch λ ₁Ordinate value, promptly

● finish height e (λ): the endpoint node P of tree λ _mOrdinate value, promptly

● minimum constructive height h (λ): the minimum value in the ordinate value of all skeleton points of branch λ;

● maximum height H (λ): the maximal value in the ordinate value of all skeleton points of branch λ;

● the u of Zijia family (λ): branch λ and all filial generations thereof;

● the d of father family (λ): branch λ and all parents thereof;

● largest extension height M (λ): the maximum ordinate value of skeleton point among the u of Zijia family (λ) of branch λ;

● father's family of path p (λ): the whole communication path of root point from branch λ end to tree among the d of father family (λ) of branch λ.

● the root point of tree: the starting point of whole skeleton, i.e. Shu root node.

" the Zijia family " of a branch of definition comprises this branch itself, its all son branches, all filial generation branches such as son branch of son branch." the father family " of a branch comprises this branch itself, its father's branch, father's branch of father's branch or the like until the root point of tree.For example, for the trunk of one tree, its Zijia family is exactly all branches of this tree, and its father family only comprises itself." the largest extension height " of a branch can obtain by the skeleton point of search ordinate maximum in its Zijia family.In addition, for assigned altitute V, " through the branch of height V " refers to those and comprises the branch that one or more ordinates are the skeleton point of V in a two-dimensional framework, and as shown in figure 10, a, b and c be the process branch of V highly in this skeleton.

4.3 depth search

The process flow diagram of depth search method as shown in figure 11.Suppose that in two-dimensional framework A three-dimensional building process has proceeded to branch λ ⁱThe bud node, the height that proceeds to (being current height V) is λ ⁱThe bud node ordinate (promptly the branch λ ⁱStarting altitude b (λ ⁱ), so current height V=b (λ ⁱ).In two-dimensional framework B, search for all " branch of the current height V ' of process, branch group G of these branch compositions _iBecause skeleton A and B are the tree structures that are communicated with and highly similar, therefore G in most of the cases _iAt least comprise a branch.By characteristic matching, can be at branch group G _iIn retrieve λ ⁱCorresponding branch μ ^jThen by two dimension branch λ ⁱAnd μ ^jMake up a new three-dimensional branch η ^kIntroduce characteristic matching and three-dimensional branch building process below in detail.

The largest extension height M (x) of branch x is the architectural feature of x arbitrarily.For the two-dimensional framework that extracts from single pixel stroke, in formula 1, the present invention has defined a linear discriminant equation F _i(x); For the two-dimensional framework that has radius information that extracts from the paintbrush stroke, formula 1 is rewritten as 2, has wherein increased branch x and branch λ ⁱThe radius ratio at height V place (radius of two branches at the V place be respectively r (x, V) and r (λ ⁱ, V), k ₁, k ₂All be constant coefficient).At branch group G _iIn, can make F _i(x) obtain the branch of minimum value, i.e. μ in the formula 3 ^j, be exactly branch λ ⁱCorresponding branch.

F _i(x)＝|M(x)-M(λ ⁱ)| (1)

F _i(x)＝k _l·|M(x)-M(λ ⁱ)|+k ₂·|r(x，V)-r(λ ⁱ，V)| (2)

μ ^j＝arg{min{F _i(x)，x∈G _i}} (3)

By two dimension branch λ ⁱAnd μ ^jThe three-dimensional branch of structure η ^kProcess can be summarized as: locate at equal height (ordinate), each two dimension branch is respectively got a bit and is constructed a three-dimensional point as corresponding point, and all three-dimensional point constitute a three-dimensional branch.Two two dimension branch height superposed part, promptly each part that is used to construct three-dimensional branch is defined as " live part " of this two dimension branch.The three-dimensional structure process is followed following rule:

1), supposes branch λ ⁱOn two-dimensional points

With branch μ ^jOn two-dimensional points

Has identical ordinate, promptly

Then they can construct η ^kA three-dimensional point Its coordinate satisfies:

$x_{k,\mathrm{\γ}}^3=x_{i,\mathrm{\α}}^1---\left(4\right)$

$y_{k,\mathrm{\γ}}^3=y_{i,\mathrm{\α}}^1=y_{j,\mathrm{\β}}^2---\left(5\right)$

$z_{k,\mathrm{\γ}}^3=x_{j,\mathrm{\β}}^2---\left(6\right)$

$r_{k,\mathrm{\γ}}^3=(r_{i,\mathrm{\α}}^1+r_{j,\mathrm{\β}}^2)/2---\left(7\right)$

2), as fruit branch λ ⁱMaximum height smaller or equal to μ ^jMaximum height, i.e. H(λ ⁱ)≤H (μ ^j), λ so ⁱAll two-dimensional framework points can be converted into three-dimensional point.Next can handle the next branch of skeleton A λ ^I+1

3), as fruit branch λ ⁱThe big μ of maximum height ^jMaximum height, i.e. H (λ ⁱ)＞H (μ ^j), so three-dimensional building process can be parked in λ ⁱAn intermediate point At current height V=H (μ j)+1 place, be λ by characteristic matching ⁱRemainder (by The part that the skeleton point of back is formed) finds a corresponding branch, and then carry out the three-dimensional structure.

Figure 12 has provided an example that is made up three-dimensional branch by the two dimension branch.Skeleton A is made up of branch a, b, c among the figure, and skeleton B is made up of branch d, e, f, g, and wherein branch a and d are corresponding branch.Go up two points at any equal height place, for example the two-dimensional points P of a by two corresponding branches ₀(x ₀, y ₀, z ₀, r ₀) and the two-dimensional points P ' of d ₀(x ' ₀, y ' ₀, z ' ₀, r ' ₀) (these two somes y that satisfies condition ₀=y ' ₀) can construct three-dimensional branch a some P (x, y, z, r), some P satisfies: x=x ₀, y=y ₀=y ' ₀, z=x ' ₀, r=(r ₀+ r ' ₀)/2.Because the maximum height of branch a is greater than the maximum height of branch d, three-dimensional building process can be parked in the P of an a ₁The point.In skeleton B, search through P ₁The branch of some height obtains two branches---e and f.Obvious F _a(f)≤F _a(e), therefore branch f is the corresponding branch of branch a remainder, can proceed three-dimensional the structure.

For the three-dimensional framework that guarantees to obtain at last is communicated with, after obtaining a pair of corresponding branch, branch λ for example ⁱAnd μ ^j, need judge at first whether the three-dimensional branch of directly being constructed by them links to each other with the three-dimensional framework that forms before.If do not link to each other, so just need earlier their live part (can be used for making up the part of three-dimensional branch) along separately father's family of path reverse extending to certain position, and then make up three-dimensional branch by the three-dimensional structure method of front.Just go through the problem of reverse extending of branch below.

4.4 the reverse extending of branch

According to the connection rank order of branch, three-dimensional building process can travel through all branches of A successively.Yet in skeleton B, the corresponding branch of those of A may be disconnected, and this three-dimensional framework that will cause constructing is disconnected.For three-dimensional framework and the assurance three-dimensional framework that obtains a connection meets the constraint that two dimension is imported in the projection of both direction, when obtain a pair of corresponding branch by characteristic matching after, carry out connective differentiation, if do not satisfy condition, just the live part (being used to make up the part of three-dimensional branch) of two branches need be arrived certain position along its father's family of path reverse extending separately, and then make up three-dimensional branch with the new live part of these two branches.Being depicted as example with Figure 13 (a) to Figure 13 (f) below introduces concrete differentiation in detail and prolongs processing procedure.In order to have more ubiquity, get that any one intermediateness describes in the three-dimensional constructive process.

Two-dimensional framework A and B are two two-dimensional frameworks (Figure 13 (a)) that extracted the one tree that obtains by stroke.Be depicted as current state as Figure 13 (b): in skeleton A, suppose that the three-dimensional building process of current time has proceeded to the bud node P of branch a _a, branch a is " A work as anterior branch " so, P _aBe " the current point of a ", P among a _aAbove part is " live part of a ".By characteristic matching, the branch b among the skeleton B is chosen as the corresponding branch of a, and the P of known a _aThe P of point and b _bPoint has identical ordinate, P so _bBe " the current point of b ", P among the b _bThe above part of point is " live part of b ".Green branches among skeleton A and the B is the corresponding branch that forms in the three-dimensional building process before the current time.The corresponding branch of supposing these greens has all carried out connective differentiation and has prolonged handling, and all is communicated with in each skeleton.For the corresponding branch a and the b that have just obtained, connective differentiation and prolongation processing procedure are as follows:

1), determine branch a and b father's family of path separately, the blue path shown in Figure 13 (c) is father's family of path.

2), determine branch a and b " having used the path " separately." having used the path " of definition a as father's family of path of a at current some P _aFollowing part.And b " having used the path " is defined as the path that the corresponding branch of " having used the path " all in skeleton B of a is formed.Yellow path shown in Figure 13 (d) is for using the path.

3), determine branch a and b " effectively father's family of path " separately." having used the path " of definition a is its " effectively father's family of path ".For branch b, its " father's family of path " and its total part of " having used the path " are " the effectively father's family of path " of b.Blue path shown in Figure 13 (e) is effective father's family of path.

4), differentiation and prolongation.If current some P _bOn " the effectively father's family of path " of branch b, so corresponding branch a and b just do not need to handle and can directly construct a three-dimensional branch with their live part.If P _bPoint not on " effectively father's family of path " of branch b, so will elongated shoot a and the live part of b (Figure 13 (f) makes up three-dimensional with new live part then, and step is as follows:

The first step, current with branch b from P _bMove in the other direction along branch b " father's family of path ", till " the effectively father's family of path " that move to b gone up, i.e. P _cThe point.Point P _cAnd the path between the branch b end is exactly the new live part of a b.

Second step, current with branch a from P _a" father's family of path " along branch a oppositely moves to and P _cIdentical height place, i.e. P _dPoint, current new P _dAnd the path between the branch a end is exactly the new live part of an a.

5), in three-dimensional building process based on depth search, whenever obtain a pair of corresponding branch, just carry out above-mentioned judgment processing, so just can guarantee that the three-dimensional framework that forms is communicated with, and satisfy two-dimensional constrains.

4.5 replenishing of disappearance skeleton

After all branches of skeleton A all pass through 3D processing, in skeleton B, can remain some branches usually, they part or all also is not used as the corresponding branch of branch among the A.Search obtains these residue branches, for the corresponding branch of their search, constructs three-dimensional framework with same procedure then in skeleton A.Through above-mentioned steps, finally can obtain a complete three-dimensional major branch skeleton, this skeleton satisfies stroke constraint in the sketch in the two-dimensional projection of two input picture directions.The three-dimensional major branch skeleton and the projection of skeleton point on the input picture thereof of structure are shown to Figure 14 (c) as Figure 14 (a).Figure 14 (a) is a three-dimensional major branch skeleton that obtains by said method, and it is projected to two input pictures respectively, can see that the three-dimensional framework point is distributed on all sketch strokes, shown in Figure 14 (b) and Figure 14 (c).

5, withe modeling

After finishing the structure of major branch skeleton, need add that withe and leaf finish whole tree-model.In this process, guarantee that the shape of tree-crown of model meets two-dimentional crown outline constraint.Based on the self similarity principle, to derive the withe shape from the major branch shape, and they reasonably are connected on the major branch, so newborn withe has kept the architectural feature of major branch.

Complete branch skeleton is from the major branch structure, and what withe growth of process forms, as shown in figure 15.Each grade branch all is by duplicating the part of his father's branch, then with this a part of translation, rotate, be connected to that father's branch skeleton point obtains.

${\mathrm{\η}}^k=\{S_{\mathrm{\γ}}^k;\mathrm{\γ}=\mathrm{1,2}...,l_k\}---\left(8\right)$

The modeling principle of withe as shown in figure 16, η ^kRepresent a three-dimensional major branch, by formula 8 expressions.Its son branch η ^{K, i}(i=1 2...N) obtains by following step:

1), duplicates a η ^kA part---from its bud node

To a middle skeleton point

This part of duplicating is called son branch masterplate η ^k[σ] is by formula 9 expression, wherein coefficient 0＜σ≤1;

${\mathrm{\η}}^k\left[\mathrm{\σ}\right]=\{S_{\mathrm{\γ}}^k;\mathrm{\γ}=\mathrm{1,2}...,m\},m=\mathrm{\σ}\·l_k---\left(9\right)$

2), with η ^kThe bud node of [σ] is connected to η ^kThe skeleton point

And rotate a certain angle.

Be called as sprouting.

In the formula 10,

Be a η ^kWith its son branch η ^{K, i}Between angle, this angle need satisfy

While two son branches η ^{K, i}And η ^{K, i-1}Between angle Need to satisfy

Parameter N, σ, θ ₁, θ ₂, And the sprouting position that grows the son branch on father's branch

Can adjust according to different floristics.

The withe density that the present invention can distribute and control generation by the sprouting on the control father branch.Specific operation process is to calculate the local density of branch in each sprouting position, if this areal concentration is excessive, then gives up this sprouting.The control of the shape of tree-crown of model is mainly by being provided with the total progression of withe, and retrains withe with the crown outline stroke in the input sketch and grow and realize.In the withe growth course, the withe skeleton is projected to two input sketch planes of delineation differentiate, if skeleton point in crown outline then keep, otherwise is just cast out, the tree crown that the three-dimensional branch model that obtains so just can satisfy on the both direction retrains.

Because the withe shape is by the decision of major branch shape, therefore different types of plant modeling is insensitive to the parameter information in the withe growth.Easy to use for domestic consumer, the present invention adopts one group of typical withe growth parameter(s) value to create the tree modelling of multiple class, as the vine of rattan shape branch, the pine tree of pagoda tree hat etc.Carried out parameter adjustment for general application with regard to not needing like this.The present invention has also provided other 2～3 groups of standby parameter values, to adapt to the adjustment needs of different user to branch density.

6, the establishment of branch geometric model

The major branch sketch that sketches the contours with single pixel pen is during as input, the rule that the radius of branch is found by Da Vinci

Determine.This rule description all son branch radius r of father's branch radius r and its _iBetween relation.Under the situation of the major branch sketch that sketches the contours with paintbrush as input, the radius of three-dimensional major branch can be obtained by the radius of two-dimensional framework, also can be calculated by rule.In order to obtain the grid model of branch, we calculate a local Frenet frame according to the estimation to skeleton tangent vector, normal vector and secondary normal vector to each skeleton point of choosing, create generalized cylinder according to Frenet frame and radius information then.The geometric model that has been connected to form branch of these cylinders.

7, leaf modeling

Each leaf and fruit are represented by the quadrilateral that has shone upon a four-way image texture (being made up of red, green and blue colour and transparency (alpha) passage).At first the leaf model of a sequence is placed on the withe skeleton point, then leaf position, leaf towards and the parameters such as distance of Ye Yuzhi in introduce enchancement factor.The average angle of Ye Yuzhi can be adjusted according to priori or measurement data.Finally can obtain the tree modelling of a band texture, this model satisfies the constraint of two pictures in the projection that input sketch counterparty makes progress.

8, the drafting of tree modelling output

For the result of modeling, the present invention stores the gridding information of tree modelling with document form, shown by professional software again.

9, experimental result and conclusion

We apply the present invention to the trees modeling of various forms and tree modelling design, compare with before two kinds of main tree modeling methods.Prove that by experiment modeling speed of the present invention tree modelling faster, that make up has kept two-dimentional input information better, robustness is also stronger.

9.1 various trees modeling results

The user can be based on two side photos of the approximate rectangular one tree of shooting angle, by delineating major branch and the crown outline sketch constructs the three-dimensional tree model as input.Figure 17 (a) illustrates the contrast of two peach models that obtain as input based on two width of cloth pictures, with different strokes to Figure 17 (g).Two photos of a peach of Figure 17 (a); First group of input of Figure 17 (b): the sketch of two less strokes; Second group of input of Figure 17 (c): the sketch of two more strokes; Figure 17 (d) is by first group of view of importing the branch model of structure in two input picture directions; Figure 17 (e) is by second group of view of importing the branch model of structure in two input picture directions; Figure 17 (f) is by the views of first group of tree modelling of obtaining of input in two input picture directions; Figure 17 (g) is by the views of second group of tree modelling of obtaining of input in two input picture directions.In this example, based on two photos of a peach, the user as input, can obtain two similar peach models with the stroke of varying number.This example illustrates that modeling effect of the present invention is not subjected to the influence of the stroke quantity that the user delineates.

Modeling also can utilize a pictures to carry out modeling.Just can reconstruct a three-dimensional tree model true to nature easily based on the picture of downloading on any internet, Figure 18 (a) is depicted as one to Figure 18 (h) and rebuilds example viny, and Figure 18 (a) is depicted as vine picture (www.huaxia.com); Figure 18 (b) is depicted as the sketch A based on picture; Figure 18 (c) is depicted as the sketch B that arbitrarily delineates; The three-dimensional branch model of Figure 18 (d) front elevation; The three-dimensional branch model of Figure 18 (e) side view; Figure 18 (f) is depicted as three-dimensional branch model vertical view; Figure 18 (g) is depicted as the band leaf of reconstruction and the vine of fruit; Figure 18 (h) is depicted as the part enlarged drawing of vine model.

The simple drawing that the user has imagination can create multiple interesting tree-model.Figure 19 (a) makes up the example of tree-model for the sketch of delineating from paintbrush to Figure 19 (g).Figure 19 (a) illustrates input sketch A and the B that delineates with paintbrush; Figure 19 (b) illustrates the front elevation of three-dimensional branch; Figure 19 (c) illustrates the side view of three-dimensional branch; Figure 19 (d) illustrates the vertical view of three-dimensional branch; Figure 19 (e) illustrates the front elevation of tree modelling; Figure 19 (f) illustrates the side view of tree modelling; Figure 19 (g) illustrates the vertical view of tree modelling.

The constraint of input stroke is all satisfied in the projection that these tree modelling that modeling obtains make progress input picture counterparty, and is realistic.

This modeling operational efficiency height.After the user delineated major branch and crown outline with interactive mode, two-dimensional framework extracted and three-dimensional major branch building process needs several seconds; The growth efficiency of withe is 2000 withes of growing about 10 seconds.On the computing machine of a double-core 2G processor, the working time of branch modeling process is usually less than one minute.Modeling process does not generally need parameter regulation, and the modeled example shown in the instructions of the present invention has all been used identical parameter.Comprise that the user delineates the process of sketch, the time of using a tree modelling of this modeling establishment generally is no more than 5 minutes.

9.2 trees modeling contrast experiment

To shown in Figure 20 (c), the present invention adopts the input picture identical with the Neubert method to make up tree-model as Figure 20 (a), compares with the modeling result of Neubert method, and the major branch structure of the three-dimensional branch model that method of the present invention obtains is more identical with the input picture.Figure 20 (a) illustrates the input picture; Figure 20 (b) illustrates the view of the branch model of Neubert method structure in input picture direction; Figure 20 (c) illustrates branch model that the inventive method the obtains view in input picture direction.

Compare with the Tan method, the trees kind that this method is suitable for is more extensive.To the modeled example shown in Figure 21 (c), Figure 21 (a) illustrates the input picture for Figure 21 (a); Figure 21 (b) illustrates the view of the branch model of Tan method structure in input picture direction; Figure 21 (c) illustrates model that the inventive method the obtains view in input picture direction.Method of the present invention need be ticked more major branches with stroke, but system modelling speed is faster---the branch modeling process needs about 40 seconds, and the branch modeling needs 20 minutes (2.4G CPU) in the Tan method, and method of the present invention can guarantee that the major branch shape that human eye can be discerned in three-dimensional model and the picture, be hidden in the leaf matches.

9.3 the application of the present invention in complex scene is drawn

The tree modelling that the present invention obtains can be used for making up virtual tree forest farm scape.Choose some models that obtain above, can make up the woods.Figure 22 (a) illustrates by two different peach models and the virtual tree forest farm scape that the apple tree model constitutes to Figure 21 (b).These woods comprise 10 * 10 trees, are distributed in 60 meters * 60 meters zones, and wherein Figure 22 (a) is a woods close shot, and Figure 22 (b) is a woods distant view.

The tree modeling method that the present invention proposes is characterised in that the sketch that utilizes two width of cloth to have major branch shape and crown outline makes up realistic tree modelling fast.

Above-mentioned experimental result and based on the tree modeling method of depth search can be used for each application of computer graphics, has characteristics simple to operate, that modeling speed is fast, model is true to nature, application prospect is wide.

The above; only be the embodiment among the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprising within the scope, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (9)

1. the tree modeling method based on depth search is characterized in that, the step of this tree modeling method comprises:

Step 1: the user delineates out the trees sketch that has crown outline, has different major branch strokes by hand with single pixel paintbrush or paintbrush on two width of cloth trees pictures, two width of cloth sketches that will have different major branch strokes are input to image processing equipment;

Step 2: image processing equipment is analyzed neighbour's pixel of each major branch stroke pixel in the sketch, thereby extracts two-dimensional framework;

Step 3: two two-dimensional frameworks are carried out depth search, make up three-dimensional major branch skeleton, make this three-dimensional framework satisfy the two-dimensional framework constraint at the parallel projection of two input directions;

Step 4: the three-dimensional major branch skeleton with structure is a masterplate, in two-dimentional crown outline constraint, make up first order withe skeleton by the duplicating of major branch, translation, rotary manipulation, be that masterplate makes up second level withe skeleton by same procedure with first order withe skeleton then, the rest may be inferred, obtains specifying the withe skeleton of progression;

Step 5: create generalized cylinder according to estimation, obtain the geometric model of branch by the cylinder match to skeleton tangent vector, normal vector and secondary normal vector;

Step 6: interpolation leaf or fruit are finished whole tree modelling on the branch geometric model, each leaf or fruit are represented by the quadrilateral that has shone upon a four-way image texture, the leaf model of a sequence is placed on the withe skeleton point, then leaf position, leaf towards and the distance parameter of Ye Yuzhi in introduce enchancement factor.

2. by the described method of claim 1, it is characterized in that described trees picture is the picture of reflection trees side form.

3. by the described method of claim 1, it is characterized in that, extract two-dimensional framework at the stroke employing partial analysis of single pixel and the method that is connected.

4. by the described method of claim 1, it is characterized in that, connect by stroke picture element scan, central point differentiation, central point simplification and skeleton point at paintbrush stroke and extract two-dimensional framework with radius information.

5. by the described method of claim 1, it is characterized in that described two-dimensional framework has Zijia family feature, father family feature, largest extension altitude feature and father's family of path feature.

6. by the described method of claim 1, it is characterized in that described depth search method is to search the corresponding branch of two two-dimensional frameworks by characteristic matching, of every pair of corresponding branch as depth information, is expanded to three dimensions with another branch.

7. by the described method of claim 6, it is characterized in that, before three-dimensional branch of two corresponding branch structures, need carry out the prolongation of connectedness judgement and branch two corresponding branches.

8. by the described method of claim 6, it is characterized in that, every pair of corresponding point of two corresponding branches have identical ordinate, the process that makes up a three-dimensional point from two corresponding point is the X-axis of getting one of them point, Y-axis coordinate X-axis, the Y-axis coordinate as three-dimensional point, gets the Z axial coordinate of the X-axis coordinate of another point as three-dimensional point.

9. by the described method of claim 1, it is characterized in that, by duplicating part father branch and in the certain included angle restriction range, the part father's branch that duplicates is connected to obtains corresponding son on father's minor matters point.

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