CN103559705A - Computer method for comparing similarity of different plant forms - Google Patents

Abstract

The invention discloses a computer method for comparing similarity of different plant forms. The plant topological structure features, peripheral contour features and organ geometry structure information are utilized, and the method comprises the steps of firstly adopting the simplified topological structure of a tree graph describing plant, then computing the similarity of the topological structure based on a tree graph editing distance method, then computing the similarity of three-dimensional convex hulls comprising plants among projections of a plurality of planes based on the two-dimensional graph similarity algorithm, on the basis of the similarity, integrating two-dimensional similarity values in all the projections so as to compute the similarity of peripheral contours of the plants, then, comprehensively considering the geometric attribute of subtrees of all levels, computing the similarity of geometric details of the plants, finally, fusing multi-feature information of the plants, and calculating the similarity among different plant structures. According to the method, form similarity of the different plants can be quantized, and the aim of distinguishing varieties or subjects of the different plants through the similarity can be achieved.

Description

A kind of computer approach of more different phytomorph similarities

Technical field

Content of the present invention relates to plant classification, area of pattern recognition, has invented the computer approach of similarity between more different phytomorphs especially for the diversity of taxonomic features.

Background technology

The formalness of plant is the foundation that natural classification method is carried out plant classification.Between different floristics, the similarity degree of the aspect such as form, structure and habit, can describe their close and distant degree in sibship.Differentiating the similarity between different plants, is a committed step of carrying out plant classification retrieval.Traditional method of discrimination mainly relies on manual operation, and subjective, efficiency is compared with low and workload is large, therefore be more and more not suitable with the needs of plant Fast Classification retrieval.In addition, accurately describe the plant structure analogy model of plant space rule, in the scientific research of the quantification such as field evapotranspiration, the design of crop plant type, cultivation step optimization, there is actual directive significance.Yet, whether accurately judging a model, key issue is the 3D model of judgement reconstruction and the similarity degree between real plants.Relatively etc. compare with the similarity calculating of three-dimensional model and the structural similarity comparison of retrieval, DNA and protein sequence, malicious code similarity, the research that plant structure similarity is calculated is at present also weaker.Mainly comprise with tree construction similarity calculating method: overall relative method, analytical comparison and the relative method based on tree graph.The plant height of overall situation relative method comparison plant, the parameters such as size of tree crown are calculated the similarity degree between plant.This method can compare the similarity of plant roughly, but can not compare subtly the spatial similarity of plant topological structure and organ.First analytical comparison carries out statistical study to the space distribution situation of the topological structure of plant and organ, after obtaining the distribution characteristics parameter of these entities, recycles these features and carrys out the similarity between comparison plant.Relative method based on tree graph adopts editing distance to describe two strain plants to be compared.Owing to relating to comparatively complicated mathematical operation and replacing frequently, delete, insert nodal operation, some complexity of the comparison procedure of this method.In addition, the similarity based on blade can be distinguished the kind of seeds to a certain extent, but this class research for be only the blade of plant, and the similarity that does not relate to plant topological structure and contour feature is calculated.The similarity of tree construction data estimates, its research also only for be the tree construction in data structure, there is obviously difference with real tree structure.In sum, also lack at present the effective method in order to similarity between more different plant structures both at home and abroad.

Summary of the invention

The invention provides a kind of computer approach that carries out the comparison of phytomorph similarity, to differentiate the similarity between different plants, thereby provide a kind of brand-new technological means for fields such as Plant Taxonomy and pattern-recognitions.

The technical solution adopted for the present invention to solve the technical problems is:

A computer approach for more different phytomorph similarities, described computing method comprise the following steps:

1) from the viewpoint of three of the topological structures of plant, peripheral contour shape, inside plants minutia, computing formula and the calculation process of definition phytomorph similarity

Suppose to calculate plant n (n is positive integer) individual aspect the similarity value of (as topological similarity, appearance profile similarity, multiple interior details characteristic similarity), be designated as proper vector s=(s ₀, s ₁..., s _n-1) ^t, and be assigned to every kind of corresponding weight of feature (span (0,1]), be designated as row vector w=(w ₀, w ₁..., w _n-1), weighted mean calculating formula of similarity is:

$\stackrel{\‾}{S}=\frac{w_i{s}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i}---\left(1\right)$

And ask for final similarity by formula (2):

$S=\stackrel{\‾}{S}+(S_m-\stackrel{\‾}{S})(1-a^n)---\left(2\right)$

(1), in (2) two formulas, s _i∈ [0,1], w _i>0, and a ∈ [0,1), i is 1 to n integer, a is empirical constant, S _m=max{s ₀, s ₁..., s _n-1.

The present invention has considered the characteristic similarity of seven aspects of plant, respectively: topological structure similarity S _t, peripheral wide shape similarity S _3g, the average axial angle similarity S of branch on trunk _a, one-level side shoot with the diameter of trunk than similarity S _d, whole the ratio of width to height similarity S _wh, the axial angle average similarity S between secondary side shoot and one-level side shoot _a1, one-level side shoot and trunk sectional area ratio similarity S _s1.The characteristic similarity of these seven aspects is composed respectively with weights: w _t, w _3g, w _a, w _d, w _wh, w _a1, w _s1, the value scope of getting of weights is (0,1).Note S _m=max{S _t, S _3g, S _a, S _d, S _wh, S _a1, S _s1,

for attaching the weighted mean value of seven characteristic similarities of weight.According to formula (2), can obtain phytomorph calculating formula of similarity is:

$S=S_m-(S_m-\stackrel{\‾}{S})a^7---\left(3\right)$

2) use respectively tree graph to represent abstract in computing machine of target plant to be compared and source plant

Tree graph G is defined as the set of summit V and limit E, is designated as G={V, E}.Wherein, summit only represents internode (not comprising other organs such as leaf, flower, fruit).If not otherwise specified, below node also represents tree graph summit.The geometric element of node comprises diameter d, the long l of internode, axial angle θ, rotationangleφ.Limit represents the connected mode between node, with ordered pair (v ₁, v ₂) represent (v wherein ₁and v ₂represent summit).Internodal connected mode has two kinds: forerunner's relation (representing with ' < ') and branch's relation (representing with '+').For being related to v ₁<v ₂, can claim v ₂v ₁axial child node or descendant node; For being related to v ₁+ v ₂, can claim v ₂v ₁branch's child node or adnation node.In addition, with T[v] represent to take the complete subtree (node set comprises v and all descendants's nodes thereof) that node v is root, use | T| represents the node number of tree graph T.

3) based on tree graph edit distance approach, calculate the similarity between two plant topological structures

The axial degeneration of 3.1 tree graphs

The similarity comparison of plant topological structure, only considers the otherness of bifurcation approach and does not consider the otherness of geometric configuration.For expand the impact of bifurcation approach on Topology Similarity comparison algorithm as far as possible, tree graph is carried out to axial degeneration.Axially degeneration is defined as: for arbitrary node v in tree graph T, if v has and only have a follow-up child node, have again father node, v is rejected from tree graph simultaneously.The tree graph obtaining is in this way called axial regression tree.Axially degeneration can be rejected each subtree on tree graph and be set unnecessary node on direction of principal axis.

3.2 tree graph editor mappings and mapping constraint

By source tree graph T _sthrough editor's sequence, S is converted into target tree graph T _drequired minimum cost, is defined as the distance between these two trees.Editor's sequence S forms (as Fig. 4) by some insertions, deletion and replacement operation, and it can be described intuitively by editor's mapping.The available tlv triple of editor's mapping (M, T _s, Td) represent, wherein M={ (v _i, w _j) | 1≤i≤| T _s|, 1≤j≤| T _d|.

For guaranteeing that the operation of tree graph editing distance follows the self-sow rule of plant, the present invention to editor's mapping settings three kinds of constraints, set axle mapping constraint, subtree nodes alignment mapping constraint and subtree depth match mapping constraint.Suppose node v ∈ T _d, w ∈ T _s, (v, w) ∈ M, v and w have respectively child node { v ₀, v ₁, v ₂..., v _nand { w ₀, w ₁, w ₂..., w _m, and meet relation { v<v ₀, v+v ₁, v+v ₂..., v+v _n, w<w ₀, w+w ₁, w+w ₂..., w+w _m, have:

Tree axle mapping constraint: if node v ₀in the axle direction of growth of father node v, meet and be related to v<v ₀, claim subtree T[v ₀] be the axial subtree of node v.For (v, w) ∈ M, the axial subtree T[v of tree axle mapping constraint requirements node v ₀] and the axial subtree T[w of w ₀] between set up independent subtree mapping.

Subtree nodes alignment mapping constraint: when carrying out subtree mapping, this constraint requirements is respectively to T[v ₁], T[v ₂] ..., T[v _n] and T[w ₁], T[w ₂] ..., T[w _m] by their nodes, in descending mode, sort, then at T[v _i] and T[w _i] between by the nodes of subtree, set up independent subtree mapping.

Subtree depth match mapping constraint: when carrying out subtree mapping, this constraint requirements is respectively to T[v ₁], T[v ₂] ..., T[v _n] and T[w ₁], T[w ₂] ..., T[w _m] by their the subtree degree of depth, in descending mode, sort, then at T[v _i] and T[w _i] between by the degree of depth of subtree, set up independent subtree mapping.

The calculating of 3.3 topological similarities

One that arranges in two tree graphs to be compared is goal tree T _d, another is source tree T _s.Ask respectively T _dand T _saxial degeneration tree graph, then by T _dnode according to node mapping M, carry out being transformed to T after several times insertion, deletion and replacement operation _srequired total cost D _t(T _d, T _s) be defined as:

$D_t(T_d,T_s)=D_t\left(T\right[p\left(T_d\right)],T[p\left(T_s\right)\left]\right)+\underset{i=1}{\overset{\max \left\{\right|b\left(T_d\right)|,|b\left(T_s\right)\left|\right\}}{\mathrm{\&Sigma;}}}{D}_t\left(T\right[b(T_d,i)],T[b(T_s,i)\left]\right)---\left(4\right)$

In formula, p (T) represents the descendant node (non-branch node) of tree graph T root node; B (T) represents the branch node set of tree graph T root node, and the element of b (T) is by nodes or the degree of depth descending sort of its corresponding subtree.I the element that represents this set with b (T, i); As i>|b (T) | time, get

and

wherein,

represent that empty tree becomes the cost of (deletion of node) T,

represent that T becomes the cost of (insertion node) empty tree, | T| represents the node number of tree graph T, i>|b (T) | subscript out of bounds while representing access set b (T).

According to formula (4), by linear transformation, real-valued distance map is arrived to interval [0,1], thereby obtain the similarity value (similarity between numerical value from 0 to 1 expression plant topological structure increases gradually) of topological structure.Conversion formula is defined as:

$S_t(T_d,T_s)=1-\frac{D_t(T_d,T_s)}{\left|T_d\right|+\left|T_s\right|}---\left(5\right)$

So far, the topological similarity S of plant tree graph _tcalculating completes.

4) calculate the similarity of two plants on peripheral profile

4.1 two-dimensional silhouette shape similarities calculate

Leave the apex coordinate of figure to be compared in proper vector V=((x ₀, y ₀), (x ₁, y ₁) ..., (x _n, y _n)) in.Consider translation, rotation and the flexible unchangeability of figure, need carry out standardized operation to targeted graphical to be compared and source figure.Concrete grammar is: in rectangular coordinate system O-XY, obtain the minimum circle-cover of two profile vertex sets, again these two vertex sets are carried out to translation, make the center of circle of their minimum circle-cover be positioned at initial point place, then vertex set is carried out to convergent-divergent, making minimum circle-cover is separately unit circle (radius is 1).

To describing the summit of figure, carry out unification operation.Method is: above-mentioned least unit circumscribed circle is divided into the sector that several areas are identical (as Fig. 6).So, every radian 2 π/K (K is integer constant), just can obtain a ray sending from the center of circle.The crossing situation of this ray and graph outline may have: without intersection point, there are one or more intersection points.If without intersection point, get that on this ray reverse extending line, nearest intersection point is mark intersection point from the center of circle.When if the intersection point of ray and profile only has one, will get this intersection point is mark intersection point; If while having a plurality of intersection point, the intersection point of getting from the center of circle is farthest designated as mark intersection point.Obtain respectively K mark intersection point (x of targeted graphical and source figure _di, y _di), (x _si, y _si), and connect successively mark intersection point separately, can obtain respectively the approximate contours G of targeted graphical _dwith the approximate contours G with source figure _s.Consider the symmetry of figure, by G _dby 180 ° of figures that obtain of x axle upset, be designated as G _d', then adopt Euclidean distance method to ask the similarity of two X-Y schemes, as shown in the formula.

$S_g(G_d,G_s)=1-\frac{\min \{\sqrt{\underset{i=0}{\overset{K-1}{\mathrm{\&Sigma;}}}[{(x_{\mathrm{di}}-x_{\mathrm{si}})}^2+{(y_{\mathrm{di}}-y_{\mathrm{si}})}^2]},\sqrt{\underset{i=0}{\overset{K-1}{\mathrm{\&Sigma;}}}[{(x_{\mathrm{di}}^{\&prime;}-x_{\mathrm{si}})}^2+{(y_{\mathrm{di}}^{\&prime;}-y_{\mathrm{si}})}^2]}\}}{\sqrt{K}}---\left(6\right)$

In formula, (x _di, y _di) expression G _di apex coordinate, (x _si, y _si) expression G _si apex coordinate, (x _di', y _di') expression G _d' i apex coordinate.

4.2 three-D profile figure similarities are calculated

The 3-D out that comprises whole plant is wrapped on X, Y, tri-faces of Z and carries out projection, based on X-Y scheme similarity algorithm, calculate one by one the similarity of target plant and the projection of source plant on same projection face, then integrate the two-dimentional similarity value of all projections, thereby calculate the similarity of two plants on peripheral profile.Concrete steps are as follows:

Step1 extracts respectively figure G _3dand G _3sproper vector V=((x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁) ..., (x _n-1, y _n-1, z _n-1)).

Step2 carries out translation to the vertex set of above-mentioned two three-dimensional picture, and the centre of sphere of their minimum ball covering on soils and initial point are overlapped, and then vertex set is carried out to convergent-divergent, makes minimum ball covering on soil separately become unit ball (radius is 1).

Step3 first rotates 2 π i/K (K gets even number) radians around x axle respectively by the three-dimensional picture point set after conversion, then rotates 2 π j/K radians around y axle, then from z axle negative direction respectively to they projections, to obtain the projection P of targeted graphical _dijprojection P with source figure _sij.

Step4 utilizes X-Y scheme similarity calculating method to calculate corresponding P _dijand P _sijsimilarity, in the similarity value of all projections, get maximal value as targeted graphical G _3dwith source figure G _3ssimilarity, its computing formula is as follows:

$S_{3g}(G_{3d},G_{3s})=\max \left\{S_g(P_{\mathrm{dij}},P_{\mathrm{sij}})\right\},(i,j=\mathrm{0,1},...,\frac{K}{2}-1)---\left(7\right)$

4.3 calculate plant appearance profile similarity

The contour feature of plant is described with the convex closure that can comprise the convex closure of whole tree graph point set and comprise subtree point set.The three-D profile point set of convex closure can calculate by the geological information on the summit on traversal tree graph.In the similarity of the whole point set convex closure of tree graph is calculated, for improving operation efficiency, formula (7) is carried out to dimension-reduction treatment: 1) for targeted graphical (tree graph T _d) and source figure (tree graph T _s), only around y axle, rotate and from z axle negative direction, it carried out to projection; 2) suppose that locus, root node place is P, the center of circle of tree graph minimum circle-cover is O, and the direction that should retrain PO line overlaps with y axle.Make T _dconvex closure figure around y axle rotate 2 π i/K and from z axle negative direction, its projection is obtained be projected as P _d0i, T _sconvex closure figure around y axle rotate 2 π j/K and from z axle negative direction, its projection is obtained be projected as P _s0j, the similarity of the whole point set convex closure of tree graph can be calculated with following formula:

$S_{3g}^{\&prime;}(T_d,T_s)=\max \left\{S_g(P_{d0i},P_{s0j})\right\},(i,j=\mathrm{0,1},...,\frac{K}{2}-1)---\left(8\right)$

The present invention has also further considered the similarity between the non degenerate complete subtree at different levels of tree graph.For a node v of certain tree graph T, with T[v] represent to take the complete subtree (node set comprises v and all descendants's nodes thereof) that node v is root.If T[v] in data structure, be not degenerated to chained list, and nodes is greater than 2, and v has the brotgher of node, a T[v at least] be a non degenerate complete subtree.As shown in Figure 7,0 of this tree graph grade of non degenerate complete subtree is self T[v ₁]=T, 1 grade of non degenerate complete subtree has T[v ₂], T[v ₃] and T[v ₄], 2 grades of non degenerate complete subtree have T[v ₅], T[v ₆] and T[v ₇].

Suppose T _dhave 0～m level non degenerate complete subtree, T _shave 0～i level non degenerate complete subtree.For certain tree graph T, get that element the most similar to T in its i level non degenerate complete subtree set and be designated as MS (T, i), T _dand T _sfinal geometric profile similarity value computing formula is:

$S_{3g}(T_d,T_s)=\left\{\begin{array}{cc}\frac{\underset{i=0}{\overset{\min (m,n)}{\mathrm{\&Sigma;}}}{S}_{3g}^{\&prime;}(\mathrm{MS}(T_d,i),\mathrm{MS}(T_s,i))}{\min (m,n)},& \min (m,n)\&NotEqual;0\\ 0,& \min (m,n)=0\end{array}\right.---\left(9\right)$

5) calculate the similarity of inside plants minutia

The present invention considers the geometric attribute of subtrees at different levels, as the average axial angle S of branch on trunk _a, one-level side shoot compares S with the diameter of trunk _d, whole the ratio of width to height S _wh, secondary side shoot and one-level side shoot average axial angle S _a1, one-level side shoot compares S with the cross-sectional area of trunk _s1thereby, calculate the similarity of plant geometric detail.Above-mentioned parameter is all real-valued parameter, and the present invention provides the similarity calculating method to two positive number x and y.Might as well establish x >=y, the similarity calculating method of parameter x and y is defined as:

$s(x,y)=\left\{\begin{array}{cc}1-\frac{|x^2-y^2|}{2\mathrm{xy}},& 1\&le;\frac{x}{y}<\sqrt{2}+1\\ 0,& \frac{x}{y}\&GreaterEqual;\sqrt{2}+1\end{array}\right.---\left(10\right)$

For example two set T _dand T _saxial angle average be respectively θ _dand θ _s, according to formula (10), can draw axial angle similarity S _afor:

S _a(T _d,T _s)=s(θ _d,θ _s) (11)

The scope of above formula acquired results is [0,1].When similarity value is 0, represent that these two parameter factors are completely dissimilar, be to represent that they are identical at 1 o'clock.So similarity value is larger, represent that two parameters to be compared are more similar.

Adopt similar method to obtain the similarity S of other interior details feature in formula (3) _d, S _wh, S _a1, S _s1.

6) calculate final phytomorph similarity

Merge above-mentioned plant multicharacteristic information, as the topological structure of plant, peripheral contour shape, inside plants minutia, utilize the similarity value of the various details of obtaining, in conjunction with formula (5), (9) and weight, formula (3) according to step (1) definition, finally calculates the overall similarity between different plant structures.

Technical conceive of the present invention

Along with the raising of computing machine soft and hardware performance, and the development of pattern-recognition, image processing techniques, traditional plant classification and search method can not meet people's requirement, need to explore easy, quick, effective brand-new technical method.Profit in this way, not only can be differentiated the similarity degree of the aspects such as form, structure and habit between different floristics, also can judge the 3D model of reconstruction and the similarity degree between real plants, thereby provides effective technical support for plant classification retrieval.

Therefore, the present invention, according to plant topological structure feature, peripheral contour feature and organ geometry information, has invented a kind of method of calculating plesiomorphism degree between different plants.The method adopts simplifies the topological structure that tree graph is described plant, then based on tree graph edit distance approach, calculates the similarity of topological structure.Based on X-Y scheme similarity algorithm, calculate the 3-D out that comprises plant and wrap in the similarity between the projection on a plurality of, and the two-dimentional similarity value of integrating all projections is to calculate the similarity of the peripheral profile of plant.Consider the geometric attribute of subtrees at different levels, calculate the similarity of plant geometric detail.On this basis, according to the definition of phytomorph similarity, calculate the similarity between different plant structures.

Beneficial effect of the present invention is mainly manifested in: the computer approach of the more different phytomorph similarities of application the present invention invention, plesiomorphism between more different plants effectively, reach by similarity and distinguish the object that different floristics or section belong to, thereby provide a kind of brand-new pattern classification means for fields such as Plant Taxonomy and pattern-recognitions.

Accompanying drawing explanation

Fig. 1 is the overall procedure of phytomorph similarity calculating method.

Fig. 2 is the example of a tree graph.

Fig. 3 is the example that a tree graph carries out axial degeneration.

Fig. 4 has described a tree graph and how to have edited and become another tree graph.

Fig. 5 has shown three kinds of editor's mapping constraints.

How Fig. 6 is for representing approx X-Y scheme with profile point set.

Fig. 7 is the example of a non degenerate complete subtree.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1, a kind of computer approach of more different phytomorph similarities, comprises the following steps:

1) from the viewpoint of three of the topological structures of plant, peripheral contour shape, inside plants minutia, computing formula and the calculation process of definition phytomorph similarity

Suppose to calculate plant n (n is positive integer) individual aspect the similarity value of (as topological similarity, appearance profile similarity, multiple interior details characteristic similarity), be designated as proper vector s=(s ₀, s ₁..., s _n-1) ^t, and be assigned to every kind of corresponding weight of feature (span (0,1]), be designated as row vector w=(w ₀, w ₁..., w _n-1), weighted mean calculating formula of similarity is:

$\stackrel{\&OverBar;}{S}=\frac{w_i{s}_i}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i}---\left(1\right)$

And ask for final similarity by formula (2):

$S=\stackrel{\&OverBar;}{S}+(S_m-\stackrel{\&OverBar;}{S})(1-a^n)---\left(2\right)$

(1), in (2) two formulas, s _i∈ [0,1], w _i>0, and a ∈ [0,1), i is 1 to n integer, a is empirical constant, S _m=max{s ₀, s ₁..., s _n-1.

The present invention has considered the characteristic similarity of seven aspects of plant, respectively: topological structure similarity S _t, peripheral wide shape similarity S _3g, the average axial angle similarity S of branch on trunk _a, one-level side shoot with the diameter of trunk than similarity S _d, whole the ratio of width to height similarity S _wh, the axial angle average similarity S between secondary side shoot and one-level side shoot _a1, one-level side shoot and trunk sectional area ratio similarity S _s1.The characteristic similarity of these seven aspects is composed respectively with weights: w _t, w _3g, w _a, w _d, w _wh, w _a1, w _s1, the value scope of getting of weights is (0,1).Note S _m=max{S _t, S _3g, S _a, S _d, S _wh, S _a1, S _s1,

for attaching the weighted mean value of seven characteristic similarities of weight.According to formula (2), can obtain phytomorph calculating formula of similarity is:

$S=S_m-(S_m-\stackrel{\&OverBar;}{S})a^7---\left(3\right)$

The comparison flow process of phytomorph similarity as shown in Figure 1.First, use respectively tree graph to represent abstract in computing machine of target plant to be compared and source plant.For they tree graphs separately, use respectively topological similarity algorithm and geometric configuration similarity algorithm to carry out computing, and add weight, finally calculate two strain phytomorph similarities.

2) use respectively tree graph to represent abstract in computing machine of target plant to be compared and source plant

Tree graph G is defined as the set of summit V and limit E, is designated as G={V, E}.Wherein, summit only represents internode (not comprising other organs such as leaf, flower, fruit).If not otherwise specified, below node also represents tree graph summit.The geometric element of node comprises diameter d, the long l of internode, axial angle θ, rotationangleφ.Limit represents the connected mode between node, with ordered pair (v ₁, v ₂) represent (v wherein ₁and v ₂represent summit).Internodal connected mode has two kinds: forerunner's relation (representing with ' < ') and branch's relation (representing with '+').For being related to v ₁<v ₂, can claim v ₂v ₁axial child node or descendant node; For being related to v ₁+ v ₂, can claim v ₂v ₁branch's child node or adnation node.In addition, with T[v] represent to take the complete subtree (node set comprises v and all descendants's nodes thereof) that node v is root, use | T| represents the node number of tree graph T.Tree graph example is as Fig. 2.

3) based on tree graph edit distance approach, calculate the similarity between two plant topological structures

The axial degeneration of 3.1 tree graphs

The similarity comparison of plant topological structure, only considers the otherness of bifurcation approach and does not consider the otherness of geometric configuration.For expand the impact of bifurcation approach on Topology Similarity comparison algorithm as far as possible, tree graph is carried out to axial degeneration.Axially degeneration is defined as: for arbitrary node v in tree graph T, if v has and only have a follow-up child node, have again father node, v is rejected from tree graph simultaneously.The tree graph obtaining is in this way called axial regression tree.Axially degeneration can be rejected each subtree on tree graph and be set unnecessary node on direction of principal axis.For example, the node v of tree graph T in Fig. 3 ₁, v ₂, v ₃, v ₄, v ₅meet above-mentioned condition, therefore they can be rejected one by one, thereby obtain axial regression tree T '.

3.2 tree graph editor mappings and mapping constraint

By source tree graph T _sthrough editor's sequence, S is converted into target tree graph T _drequired minimum cost, is defined as the distance between these two trees.Editor's sequence S forms (as Fig. 4) by some insertions, deletion and replacement operation, and it can be described intuitively by editor's mapping.The available tlv triple of editor's mapping (M, T _s, T _d) represent M={ (v wherein _i, w _j) | 1≤i≤| Ts|, 1≤j≤| Td|}.

For guaranteeing that the operation of tree graph editing distance follows the self-sow rule of plant, the present invention to editor's mapping settings three kinds of constraints, set axle mapping constraint, subtree nodes alignment mapping constraint and subtree depth match mapping constraint.Suppose node v ∈ T _d, w ∈ T _s, (v, w) ∈ M, v and w have respectively child node { v ₀, v ₁, v ₂..., v _nand { w ₀, w ₁, w ₂..., w _m, and meet relation { v<v ₀, v+v ₁, v+v ₂..., v+v _n, w<w ₀, w+w ₁, w+w ₂..., w+w _m, have:

Tree axle mapping constraint: if node v ₀in the axle direction of growth of father node v, meet and be related to v<v ₀, claim subtree T[v ₀] be the axial subtree of node v.For (v, w) ∈ M, the axial subtree T[v of tree axle mapping constraint requirements node v ₀] and the axial subtree T[w of w ₀] between set up independent subtree mapping.

Subtree nodes alignment mapping constraint: when carrying out subtree mapping, this constraint requirements is respectively to T[v ₁], T[v ₂] ..., T[v _n] and T[w ₁], T[w ₂] ..., T[w _m] by their nodes, in descending mode, sort, then at T[v _i] and T[w _i] between by the nodes of subtree, set up independent subtree mapping.

Subtree depth match mapping constraint: when carrying out subtree mapping, this constraint requirements is respectively to T[v ₁], T[v ₂] ..., T[v _n] and T[w ₁], T[w ₂] ..., T[w _m] by their the subtree degree of depth, in descending mode, sort, then at T[v _i] and T[w _i] between by the degree of depth of subtree, set up independent subtree mapping.

In Fig. 5, if set up independent subtree mapping between the axial subtree A of v and the axial subtree A ' of w, A and A ' meet tree axle mapping constraint.If set up independent subtree mapping between C and B ', between B and C ', set up independent subtree mapping, between them, met respectively subtree nodes alignment mapping constraint.If set up independent subtree mapping between B and B ', between C and C ', set up independent subtree mapping, between them, meet respectively subtree depth match mapping constraint.

The calculating of 3.3 topological similarities

One that arranges in two tree graphs to be compared is goal tree T _d, another is source tree T _s.Ask respectively T _dand T _saxial degeneration tree graph, then by T _dnode according to node mapping M, carry out being transformed to T after several times insertion, deletion and replacement operation _srequired total cost D _t(T _d, T _s) be defined as:

$D_t(T_d,T_s)=D_t\left(T\right[p\left(T_d\right)],T[p\left(T_s\right)\left]\right)+\underset{i=1}{\overset{\max \left\{\right|b\left(T_d\right)|,|b\left(T_s\right)\left|\right\}}{\mathrm{\&Sigma;}}}{D}_t\left(T\right[b(T_d,i)],T[b(T_s,i)\left]\right)---\left(4\right)$

In formula, p (T) represents the descendant node (non-branch node) of tree graph T root node; B (T) represents the branch node set of tree graph T root node, and the element of b (T) is by nodes or the degree of depth descending sort of its corresponding subtree.I the element that represents this set with b (T, i); As i>|b (T) | time, get

and

wherein,

represent that empty tree becomes the cost of (deletion of node) T,

represent that T becomes the cost of (insertion node) empty tree, | T| represents the node number of tree graph T, i>|b (T) | subscript out of bounds while representing access set b (T).

According to formula (4), by linear transformation, real-valued distance map is arrived to interval [0,1], thereby obtain the similarity value (similarity between numerical value from 0 to 1 expression plant topological structure increases gradually) of topological structure.Conversion formula is defined as:

$S_t(T_d,T_s)=1-\frac{D_t(T_d,T_s)}{\left|T_d\right|+\left|T_s\right|}---\left(5\right)$

So far, the topological similarity S of plant tree graph _tcalculating completes.

4) calculate the similarity of two plants on peripheral profile

4.1 two-dimensional silhouette shape similarities calculate

Leave the apex coordinate of figure to be compared in proper vector V=((x ₀, y ₀), (x ₁, y ₁) ..., (x _n, y _n)) in.Consider translation, rotation and the flexible unchangeability of figure, need carry out standardized operation to targeted graphical to be compared and source figure.Concrete grammar is: in rectangular coordinate system O-XY, obtain the minimum circle-cover of two profile vertex sets, again these two vertex sets are carried out to translation, make the center of circle of their minimum circle-cover be positioned at initial point place, then vertex set is carried out to convergent-divergent, making minimum circle-cover is separately unit circle (radius is 1).

To describing the summit of figure, carry out unification operation (make number of vertices identical).Unification method is: above-mentioned least unit circumscribed circle is divided into the sector that several areas are identical (as Fig. 6).So, every radian 2 π/K (K is integer constant), just can obtain a ray sending from the center of circle.The crossing situation of this ray and graph outline may have: without intersection point, there are one or more intersection points.If without intersection point, get that on this ray reverse extending line, nearest intersection point is mark intersection point from the center of circle.When if the intersection point of ray and profile only has one, will get this intersection point is mark intersection point; If while having a plurality of intersection point, the intersection point of getting from the center of circle is farthest designated as mark intersection point.Obtain respectively K mark intersection point (x of targeted graphical and source figure _di, y _di), (x _si, y _si), and connect successively mark intersection point separately, can obtain respectively the approximate contours G of targeted graphical _dwith the approximate contours G with source figure _s.Consider the symmetry of figure, by G _dby 180 ° of figures that obtain of x axle upset, be designated as G _d', then adopt Euclidean distance method to ask the similarity of two X-Y schemes, as shown in the formula.

$S_g(G_d,G_s)=1-\frac{\min \{\sqrt{\underset{i=0}{\overset{K-1}{\mathrm{\&Sigma;}}}[{(x_{\mathrm{di}}-x_{\mathrm{si}})}^2+{(y_{\mathrm{di}}-y_{\mathrm{si}})}^2]},\sqrt{\underset{i=0}{\overset{K-1}{\mathrm{\&Sigma;}}}[{(x_{\mathrm{di}}^{\&prime;}-x_{\mathrm{si}})}^2+{(y_{\mathrm{di}}^{\&prime;}-y_{\mathrm{si}})}^2]}\}}{\sqrt{K}}---\left(6\right)$

In formula, (x _di, y _di) expression G _di apex coordinate, (x _si, y _si) expression G _si apex coordinate, (x _di', y _di') expression G _d' i apex coordinate.

4.2 three-D profile figure similarities are calculated

The 3-D out that comprises whole plant is wrapped on X, Y, tri-faces of Z and carries out projection, based on X-Y scheme similarity algorithm, calculate one by one the similarity of target plant and the projection of source plant on same projection face, then integrate the two-dimentional similarity value of all projections, thereby calculate the similarity of two plants on peripheral profile.Concrete steps are as follows:

Step1 extracts respectively figure G _3dand G _3sproper vector V=((x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁) ..., (x _n-1, y _n-1, z _n-1)).

Step2 carries out translation to the vertex set of above-mentioned two three-dimensional picture, and the centre of sphere of their minimum ball covering on soils and initial point are overlapped, and then vertex set is carried out to convergent-divergent, makes minimum ball covering on soil separately become unit ball (radius is 1).

Step3 first rotates 2 π i/K (K gets even number) radians around x axle respectively by the three-dimensional picture point set after conversion, then rotates 2 π j/K radians around y axle, then from z axle negative direction respectively to they projections, to obtain the projection P of targeted graphical _dijprojection P with source figure _sij.

Step4 utilizes X-Y scheme similarity calculating method to calculate corresponding P _dijand P _sijsimilarity, in the similarity value of all projections, get maximal value as targeted graphical G _3dwith source figure G _3ssimilarity, its computing formula is as follows:

$S_{3g}(G_{3d},G_{3s})=\max \left\{S_g(P_{\mathrm{dij}},P_{\mathrm{sij}})\right\},(i,j=\mathrm{0,1},...,\frac{K}{2}-1)---\left(7\right)$

4.3 calculate plant appearance profile similarity

The contour feature of plant is described with the convex closure that can comprise the convex closure of whole tree graph point set and comprise subtree point set.The three-D profile point set of convex closure can calculate by the geological information on the summit on traversal tree graph.In the similarity of the whole point set convex closure of tree graph is calculated, for improving operation efficiency, formula (7) is carried out to dimension-reduction treatment: 1) for targeted graphical (tree graph T _d) and source figure (tree graph T _s), only around y axle, rotate and from z axle negative direction, it carried out to projection; 2) suppose that locus, root node place is P, the center of circle of tree graph minimum circle-cover is O, and the direction that should retrain PO line overlaps with y axle.Make T _dconvex closure figure around y axle rotate 2 π i/K and from z axle negative direction, its projection is obtained be projected as P _d0i, T _sconvex closure figure around y axle rotate 2 π j/K and from z axle negative direction, its projection is obtained be projected as P _s0j, the similarity of the whole point set convex closure of tree graph can be calculated with following formula:

$S_{3g}^{\&prime;}(T_d,T_s)=\max \left\{S_g(P_{d0i},P_{s0j})\right\},(i,j=\mathrm{0,1},...,\frac{K}{2}-1)---\left(8\right)$

The present invention has also further considered the similarity between the non degenerate complete subtree at different levels of tree graph.For a node v of certain tree graph T, with T[v] represent to take the complete subtree (node set comprises v and all descendants's nodes thereof) that node v is root.If T[v] in data structure, be not degenerated to chained list, and nodes is greater than 2, and v has the brotgher of node, a T[v at least] be a non degenerate complete subtree.As shown in Figure 7,0 of this tree graph grade of non degenerate complete subtree is self T[v ₁]=T, 1 grade of non degenerate complete subtree has T[v ₂], T[v ₃] and T[v ₄], 2 grades of non degenerate complete subtree have T[v ₅], T[v ₆] and T[v ₇].

Suppose T _dhave 0～m level non degenerate complete subtree, T _shave 0～i level non degenerate complete subtree.For certain tree graph T, get that element the most similar to T in its i level non degenerate complete subtree set and be designated as MS (T, i), T _dand T _sfinal geometric profile similarity value computing formula is:

$S_{3g}(T_d,T_s)=\left\{\begin{array}{cc}\frac{\underset{i=0}{\overset{\min (m,n)}{\mathrm{\&Sigma;}}}{S}_{3g}^{\&prime;}(\mathrm{MS}(T_d,i),\mathrm{MS}(T_s,i))}{\min (m,n)},& \min (m,n)\&NotEqual;0\\ 0,& \min (m,n)=0\end{array}\right.---\left(9\right)$

5) calculate the similarity of inside plants minutia

The present invention considers the geometric attribute of subtrees at different levels, as the average axial angle S of branch on trunk _a, one-level side shoot compares S with the diameter of trunk _d, whole the ratio of width to height S _wh, secondary side shoot and one-level side shoot average axial angle S _a1, one-level side shoot compares S with the cross-sectional area of trunk _s1thereby, calculate the similarity of plant geometric detail.Above-mentioned parameter is all real-valued parameter, and the present invention provides the similarity calculating method to two positive number parameter x and y.Might as well establish x >=y, the similarity calculating method of parameter x and y is defined as:

$s(x,y)=\left\{\begin{array}{cc}1-\frac{|x^2-y^2|}{2\mathrm{xy}},& 1\&le;\frac{x}{y}<\sqrt{2}+1\\ 0,& \frac{x}{y}\&GreaterEqual;\sqrt{2}+1\end{array}\right.---\left(10\right)$

For example two set T _dand T _saxial angle average be respectively θ _dand θ _s, according to formula (10), can draw axial angle similarity S _afor:

S _a(T _d,T _s)=s(θ _d,θ _s) (11)

The scope of above formula acquired results is [0,1].When similarity value is 0, represent that these two parameter factors are completely dissimilar, be to represent that they are identical at 1 o'clock.So similarity value is larger, represent that two parameters to be compared are more similar.

Adopt similar method to obtain the similarity S of other interior details feature in formula (3) _d, S _wh, S _a1, S _s1.

6) calculate final phytomorph similarity

Merge above-mentioned plant multicharacteristic information, as the topological structure of plant, peripheral contour shape, inside plants minutia, utilize the similarity value of the various details of obtaining, in conjunction with formula (5), (9) and weight, formula (3) according to step (1) definition, finally calculates the overall similarity between different plant structures.

Claims (1)

1. a computer approach for more different phytomorph similarities, is characterized in that: described computing method comprise the following steps:

1) from the viewpoint of three of the topological structures of plant, peripheral contour shape, inside plants minutia, computing formula and the calculation process of definition phytomorph similarity

Suppose to calculate plant n (n is positive integer) individual aspect the similarity value of (as topological similarity, appearance profile similarity, multiple interior details characteristic similarity), be designated as proper vector s=(s ₀, s ₁..., s _n-1) ^t, and be assigned to every kind of corresponding weight of feature (span (0,1]), be designated as row vector w=(w ₀, w ₁..., w _n-1), weighted mean calculating formula of similarity is:

$\stackrel{\&OverBar;}{S}=\frac{w_i{s}_i}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i}---\left(1\right)$

And ask for final similarity by formula (2):

$S=\stackrel{\&OverBar;}{S}+(S_m-\stackrel{\&OverBar;}{S})(1-a^n)---\left(2\right)$

(1), in (2) two formulas, s _i∈ [0,1], w _i>0, and a ∈ [0,1), i is 1 to n integer, a is empirical constant, S _m=max{s ₀, s ₁..., s _n-1.

The present invention has considered the characteristic similarity of seven aspects of plant, respectively: topological structure similarity S _t, peripheral wide shape similarity S _3g, the average axial angle similarity S of branch on trunk _a, one-level side shoot with the diameter of trunk than similarity S _d, whole the ratio of width to height similarity S _wh, the axial angle average similarity S between secondary side shoot and one-level side shoot _a1, one-level side shoot and trunk sectional area ratio similarity S _s1.The characteristic similarity of these seven aspects is composed respectively with weights: w _t, w _3g, w _a, w _d, w _wh, w _a1, w _s1, the value scope of getting of weights is (0,1).Note S _m=max{S _t, S _3g, S _a, S _d, S _wh, S _a1, S _s1,

for attaching the weighted mean value of seven characteristic similarities of weight.According to formula (2), can obtain phytomorph calculating formula of similarity is:

$S=S_m-(S_m-\stackrel{\&OverBar;}{S})a^7---\left(3\right)$

2) use respectively tree graph to represent abstract in computing machine of target plant to be compared and source plant

Tree graph G is defined as the set of summit V and limit E, is designated as G={V, E}.Wherein, summit only represents internode (not comprising other organs such as leaf, flower, fruit).If not otherwise specified, below node also represents tree graph summit.The geometric element of node comprises diameter d, the long l of internode, axial angle θ, rotationangleφ.Limit represents the connected mode between node, with ordered pair (v ₁, v ₂) represent (v wherein ₁and v ₂represent summit).Internodal connected mode has two kinds: forerunner's relation (representing with ' < ') and branch's relation (representing with '+').For being related to v ₁<v ₂, can claim v ₂v ₁axial child node or descendant node; For being related to v ₁+ v ₂, can claim v ₂v ₁branch's child node or adnation node.In addition, with T[v] represent to take the complete subtree (node set comprises v and all descendants's nodes thereof) that node v is root, use | T| represents the node number of tree graph T.

3) based on tree graph edit distance approach, calculate the similarity between two plant topological structures

The axial degeneration of 3.1 tree graphs

The similarity comparison of plant topological structure, only considers the otherness of bifurcation approach and does not consider the otherness of geometric configuration.For expand the impact of bifurcation approach on Topology Similarity comparison algorithm as far as possible, tree graph is carried out to axial degeneration.Axially degeneration is defined as: for arbitrary node v in tree graph T, if v has and only have a follow-up child node, have again father node, v is rejected from tree graph simultaneously.The tree graph obtaining is in this way called axial regression tree.Axially degeneration can be rejected each subtree on tree graph and be set unnecessary node on direction of principal axis.

3.2 tree graph editor mappings and mapping constraint

By source tree graph T _sthrough editor's sequence, S is converted into target tree graph T _drequired minimum cost, is defined as the distance between these two trees.Editor's sequence S forms (as Fig. 4) by some insertions, deletion and replacement operation, and it can be described intuitively by editor's mapping.The available tlv triple of editor's mapping (M, T _s, T _d) represent M={ (v wherein _i, w _j) | 1≤i≤| T _s|, 1≤j≤| T _d|.

For guaranteeing that the operation of tree graph editing distance follows the self-sow rule of plant, the present invention to editor's mapping settings three kinds of constraints, set axle mapping constraint, subtree nodes alignment mapping constraint and subtree depth match mapping constraint.Suppose node v ∈ T _d, w ∈ T _s, (v, w) ∈ M, v and w have respectively child node { v ₀, v ₁, v ₂..., v _nand { w ₀, w ₁, w ₂..., w _m, and meet relation { v<v ₀, v+v ₁, v+v ₂..., v+v _n, w<w ₀, w+w ₁, w+w ₂..., w+w _m, have:

Tree axle mapping constraint: if node v ₀in the axle direction of growth of father node v, meet and be related to v<v ₀, claim subtree T[v ₀] be the axial subtree of node v.For (v, w) ∈ M, the axial subtree T[v of tree axle mapping constraint requirements node v ₀] and the axial subtree T[w of w ₀] between set up independent subtree mapping.

Subtree nodes alignment mapping constraint: when carrying out subtree mapping, this constraint requirements is respectively to T[v ₁], T[v ₂] ..., T[v _n] and T[w ₁], T[w ₂] ..., T[w _m] by their nodes, in descending mode, sort, then at T[v _i] and T[w _i] between by the nodes of subtree, set up independent subtree mapping.

Subtree depth match mapping constraint: when carrying out subtree mapping, this constraint requirements is respectively to T[v ₁], T[v ₂] ..., T[v _n] and T[w ₁], T[w ₂] ..., T[w _m] by their the subtree degree of depth, in descending mode, sort, then at T[v _i] and T[w _i] between by the degree of depth of subtree, set up independent subtree mapping.

The calculating of 3.3 topological similarities

One that arranges in two tree graphs to be compared is goal tree T _d, another is source tree T _s.Ask respectively T _dand T _saxial degeneration tree graph, then by T _dnode according to node mapping M, carry out being transformed to T after several times insertion, deletion and replacement operation _srequired total cost D _t(T _d, T _s) be defined as:

$D_t(T_d,T_s)=D_t\left(T\right[p\left(T_d\right)],T[p\left(T_s\right)\left]\right)+\underset{i=1}{\overset{\max \left\{\right|b\left(T_d\right)|,|b\left(T_s\right)\left|\right\}}{\mathrm{\&Sigma;}}}{D}_t\left(T\right[b(T_d,i)],T[b(T_s,i)\left]\right)---\left(4\right)$ In formula, p (T) represents the descendant node (non-branch node) of tree graph T root node; B (T) represents the branch node set of tree graph T root node, and the element of b (T) is by the nodes of its corresponding subtree.I the element that represents this set with b (T, i); As i>|b (T) | time, get

and

wherein,

represent that empty tree becomes the cost of (deletion of node) T,

represent that T becomes the cost of (insertion node) empty tree, | T| represents the node number of tree graph T, i>|b (T) | subscript out of bounds while representing access set b (T).

According to formula (4), by linear transformation, real-valued distance map is arrived to interval [0,1], thereby obtain the similarity value (similarity between numerical value from 0 to 1 expression plant topological structure increases gradually) of topological structure.Conversion formula is defined as:

$S_t(T_d,T_s)=1-\frac{D_t(T_d,T_s)}{\left|T_d\right|+\left|T_s\right|}---\left(5\right)$

So far, the topological similarity S of plant tree graph _tcalculating completes.

4) calculate the similarity of two plants on peripheral profile

4.1 two-dimensional silhouette shape similarities calculate

Leave the apex coordinate of figure to be compared in proper vector V=((x ₀, y ₀), (x ₁, y ₁) ..., (x _n, y _n)) in.Consider translation, rotation and the flexible unchangeability of figure, need carry out standardized operation to targeted graphical to be compared and source figure.Concrete grammar is: in rectangular coordinate system O-XY, obtain the minimum circle-cover of two profile vertex sets, again these two vertex sets are carried out to translation, make the center of circle of their minimum circle-cover be positioned at initial point place, then vertex set is carried out to convergent-divergent, making minimum circle-cover is separately unit circle (radius is 1).

To describing the summit of figure, carry out unification operation.Method is: above-mentioned least unit circumscribed circle is divided into the sector that several areas are identical (as Fig. 6).So, every radian 2 π/K (K is integer constant), just can obtain a ray sending from the center of circle.The crossing situation of this ray and graph outline may have: without intersection point, there are one or more intersection points.If without intersection point, get that on this ray reverse extending line, nearest intersection point is mark intersection point from the center of circle.When if the intersection point of ray and profile only has one, will get this intersection point is mark intersection point; If while having a plurality of intersection point, the intersection point of getting from the center of circle is farthest designated as mark intersection point.Obtain respectively K mark intersection point (x of targeted graphical and source figure _di, y _di), (x _si, y _si), and connect successively mark intersection point separately, can obtain respectively the approximate contours G of targeted graphical _dwith the approximate contours G with source figure _s.Consider the symmetry of figure, by G _dby 180 ° of figures that obtain of x axle upset, be designated as G _d', then adopt Euclidean distance method to ask the similarity of two X-Y schemes, as shown in the formula.

$S_g(G_d,G_s)=1-\frac{\min \{\sqrt{\underset{i=0}{\overset{K-1}{\mathrm{\&Sigma;}}}[{(x_{\mathrm{di}}-x_{\mathrm{si}})}^2+{(y_{\mathrm{di}}-y_{\mathrm{si}})}^2]},\sqrt{\underset{i=0}{\overset{K-1}{\mathrm{\&Sigma;}}}[{(x_{\mathrm{di}}^{\&prime;}-x_{\mathrm{si}})}^2+{(y_{\mathrm{di}}^{\&prime;}-y_{\mathrm{si}})}^2]}\}}{\sqrt{K}}---\left(6\right)$

In formula, (x _di, y _di) expression G _di apex coordinate, (x _si, y _si) expression G _si apex coordinate, (x _di', y _di') expression G _d' i apex coordinate.

4.2 three-D profile figure similarities are calculated

The 3-D out that comprises whole plant is wrapped on X, Y, tri-faces of Z and carries out projection, based on X-Y scheme similarity algorithm, calculate one by one the similarity of target plant and the projection of source plant on same projection face, then integrate the two-dimentional similarity value of all projections, thereby calculate the similarity of two plants on peripheral profile.Concrete steps are as follows:

Step1 extracts respectively figure G _3dand G _3sproper vector V=((x ₀, y ₀, z ₀), (x ₁, y ₁, z ₁) ..., (x _n-1, y _n-1, z _n-1)).

Step2 carries out translation to the vertex set of above-mentioned two three-dimensional picture, and the centre of sphere of their minimum ball covering on soils and initial point are overlapped, and then vertex set is carried out to convergent-divergent, makes minimum ball covering on soil separately become unit ball (radius is 1).

Step3 first rotates 2 π i/K (K gets even number) radians around x axle respectively by the three-dimensional picture point set after conversion, then rotates 2 π j/K radians around y axle, then from z axle negative direction respectively to they projections, to obtain the projection P of targeted graphical _dijprojection P with source figure _sij.

Step4 utilizes X-Y scheme similarity calculating method to calculate corresponding P _dijand P _sijsimilarity, in the similarity value of all projections, get maximal value as targeted graphical G _3dwith source figure G _3ssimilarity, its computing formula is as follows:

$S_{3g}(G_{3d},G_{3s})=\max \left\{S_g(P_{\mathrm{dij}},P_{\mathrm{sij}})\right\},(i,j=\mathrm{0,1},...,\frac{K}{2}-1)---\left(7\right)$

4.3 calculate plant appearance profile similarity

The contour feature of plant is described with the convex closure that can comprise the convex closure of whole tree graph point set and comprise subtree point set.The three-D profile point set of convex closure can calculate by the geological information on the summit on traversal tree graph.In the similarity of the whole point set convex closure of tree graph is calculated, for improving operation efficiency, formula (7) is carried out to dimension-reduction treatment: 1) for targeted graphical (tree graph T _d) and source figure (tree graph T _s), only around y axle, rotate and from z axle negative direction, it carried out to projection; 2) suppose that locus, root node place is P, the center of circle of tree graph minimum circle-cover is O, and the direction that should retrain PO line overlaps with y axle.Make T _dconvex closure figure around y axle rotate 2 π i/K and from z axle negative direction, its projection is obtained be projected as P _d0i, T _sconvex closure figure around y axle rotate 2 π j/K and from z axle negative direction, its projection is obtained be projected as P _s0j, the similarity of the whole point set convex closure of tree graph can be calculated with following formula:

$S_{3g}^{\&prime;}(T_d,T_s)=\max \left\{S_g(P_{d0i},P_{s0j})\right\},(i,j=\mathrm{0,1},...,\frac{K}{2}-1)---\left(8\right)$

The present invention has also further considered the similarity between the non degenerate complete subtree at different levels of tree graph.For a node v of certain tree graph T, with T[v] represent to take the complete subtree (node set comprises v and all descendants's nodes thereof) that node v is root.If T[v] in data structure, be not degenerated to chained list, and nodes is greater than 2, and v has the brotgher of node, a T[v at least] be a non degenerate complete subtree.As shown in Figure 7,0 of this tree graph grade of non degenerate complete subtree is self T[v ₁]=T, 1 grade of non degenerate complete subtree has T[v ₂], T[v ₃] and T[v ₄], 2 grades of non degenerate complete subtree have T[v ₅], T[v ₆] and T[v ₇].

Suppose T _dhave 0～m level non degenerate complete subtree, T _shave 0～i level non degenerate complete subtree.For certain tree graph T, get that element the most similar to T in its i level non degenerate complete subtree set and be designated as MS (T, i), T _dand T _sfinal geometric profile similarity value computing formula is:

$S_{3g}(T_d,T_s)=\left\{\begin{array}{cc}\frac{\underset{i=0}{\overset{\min (m,n)}{\mathrm{\&Sigma;}}}{S}_{3g}^{\&prime;}(\mathrm{MS}(T_d,i),\mathrm{MS}(T_s,i))}{\min (m,n)},& \min (m,n)\&NotEqual;0\\ 0,& \min (m,n)=0\end{array}\right.---\left(9\right)$

5) calculate the similarity of inside plants minutia

The present invention considers the geometric attribute of subtrees at different levels, as the average axial angle S of branch on trunk _a, one-level side shoot compares S with the diameter of trunk _d, whole the ratio of width to height S _wh, secondary side shoot and one-level side shoot average axial angle S _a1, one-level side shoot compares S with the cross-sectional area of trunk _s1thereby, calculate the similarity of plant geometric detail.Above-mentioned parameter is all real-valued parameter, and the present invention provides the similarity calculating method to two positive number parameter x and y.Might as well establish x >=y, the similarity calculating method of parameter x and y is defined as:

$s(x,y)=\left\{\begin{array}{cc}1-\frac{|x^2-y^2|}{2\mathrm{xy}},& 1\&le;\frac{x}{y}<\sqrt{2}+1\\ 0,& \frac{x}{y}\&GreaterEqual;\sqrt{2}+1\end{array}\right.---\left(10\right)$

For example two set T _dand T _saxial angle average be respectively θ _dand θ _s, according to formula (10), can draw axial angle similarity S _afor:

S _a(T _d,T _s)=s(θ _d,θ _s) (11)

The scope of above formula acquired results is [0,1].When similarity value is 0, represent that these two parameter factors are completely dissimilar, be to represent that they are identical at 1 o'clock.So similarity value is larger, represent that two parameters to be compared are more similar.

Adopt similar method to obtain the similarity S of other interior details feature in formula (3) _d, S _wh, S _a1, S _s1.

6) calculate final phytomorph similarity

Merge above-mentioned plant multicharacteristic information, as the topological structure of plant, peripheral contour shape, inside plants minutia, utilize the similarity value of the various details of obtaining, in conjunction with formula (5), (9) and weight, formula (3) according to step (1) definition, finally calculates the overall similarity between different plant structures.

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