CN103914690A - Shape matching method based on projective invariant - Google Patents

Abstract

The invention belongs to the field of computer vision, and relates to a constructing and matching method of projective invariant contexts. According to the method, the hierarchical projective invariant contexts are constructed and used for achieving the shape recognition under the projective changes. According to the method, all sampling points are selected from coarseness to fineness to form the contexts of the sampling points, and therefore the overall geometrical information is ensured, and the contextual information of a contour is reserved. Five contexts based on the traditional projective invariant cross ratio and the newly found projective invariant features are further provided on the framework. The stability and noise immunity of the contexts are improved by introducing exterior points and the ratio in. Experiments show that the method not only has higher recognition rate on the shapes with severe projective deformation, but also has a very good distinguishing effect on the shapes with high similarity.

Description

A kind of shape matching method based on projective invariant

Technical field

The invention belongs to computer vision field, relate to shape description, specially refer to structure and the matching process of the constant shape feature descriptor of a kind of projection.

Background technology

Shape is an important way of portraying object and image, and therefore the structure of shape description symbols and coupling play vital effect in image recognition and retrieving.Shape description symbols need to have certain differentiation, because a lot of shape has certain similarity in part.And the identification of shape under various variations is also a large difficult point, because a lot of images that obtain are due to shooting angle problem, there is problem on deformation to a certain degree in actual life.

Classical shape facility descriptor is mainly to describe shape with the position relationship between profile up-sampling point, and for example Shape Contex (SC) is exactly histogram distance and the directional information adopting under polar coordinate system, has obtained good effect.There is successively afterwards certain methods to carry out effective improvement to SC.Propose histogram direction contextual algorithms, the upset situation of image has been had to good treatment effect.The feature of this class descriptor is the variation that can obtain shape details, therefore has very strong differentiation effect.But this class descriptor cannot be processed the various conversion including affined transformation and projective transformation, and this conversion is more common in actual conditions.

In order to make shape description symbols adapt to various Geometrical changes, the method that part Study is mated by figure is found the transformation relation of image and then is completed the identification of shape, also have by geometric senses such as distance, areas and design relevant descriptor, but all cannot solve the identification problem of shape under affine or projective transformation.In addition, also have the methods such as fourier descriptor, covariance order curve method and local geometrical invariants by corresponding affine invariant structure form descriptor.These descriptors can be processed the shape recognition under affine variation, still poor effect under projective transformation.

The patent of invention " form fit based on PCA-SC algorithm and target identification method " of University Of Suzhou, application number 201310096658.2, utilize PCA-SC algorithm to carry out extraction and the coupling of shape facility, but the method only has yardstick unchangeability, rotational invariance and translation invariance, state the shape under common in actual applications affine and projective transformation without identification.

A kind of face shape matching method application number 200710046676.4 based on Shape Context of patent of invention of Donghua University.Propose a kind of face shape matching method based on Shape Context, mainly utilized positional information between face shape profile up-sampling point as feature, cannot process the situation of the projective transformations such as ubiquitous side face in actual monitoring application.

Summary of the invention

Change in order to make shape descriptor can adapt to projection, this patent has been constructed a kind of constant shape feature descriptor of projection (hierarchical projective invariant contexts)-HPIC of stratification, by by the thick sampled point of choosing to essence, and reach the object of shape under description projective transformation in conjunction with corresponding projective invariant.The describing method of this stratification can be described shape from entirety to local information, thereby when assurance projection is constant, similar shape is also had to good differentiation effect.Technical scheme of the present invention comprises the steps:

Step 1. utilizes the method for rim detection to extract profile to original image;

Step 2. is carried out uniform sampling to shape profile, and sampling number is N; N configuration sampling point is expressed as P={P ₁, P ₂..., P _n;

Step 3. is to each sampled point P _i(i=1 ..., N), take by slightly choosing other 4 sampled points and P to mode smart, that draw near around it _iform a series of projective invariants;

Step 3-1 is with P _ifor axle, choose two point (P in its left side _i-k, P _i-2k), in like manner also choose two point (P at same interval on right side _i+k, P _i+2k), k is sampling interval.Such 5 points utilize the method for step 5 or step 6 together to form a projective invariant

Step 3-2 is by adjusting sampling interval k, the value of k from L (L=N/5) to 1, as shown in Figure 1.Can obtain about a P _il dimensional feature vector, as shown in formula (1);

${\mathrm{HPIC}}_i={(f_i^L,f_i^{L-1},...,f_i^1)}^T---\left(1\right)$

Step 3-3 will by normalized mode value be limited between-1 to 1.If the value of being set to 1, the value of being set to-1.

Step 4. is adopted and can be obtained in the same way N HPIC vector as shown in formula (2) N sampled point.

HPIC(P)＝(HPIC ₁,HPIC ₂,...,HPIC _N) (2)

The dimension of this matrix H PIC (P) is L × N, and i row are P _iproper vector.

Step 5. is utilized 5 double ratio structure projective invariants

First step 5-1 chooses 5 coplanar sampled point (P on shape profile ₁, P ₂, P ₃, P ₄, P ₅), these 5 points interconnect and can obtain two groups of 4 collinear point according to the mode of Fig. 2 (a), are respectively (P ₁, P ₂, X, Y) and (P ₅, P ₄, X, Z);

Step 5-2 calculates two groups of double ratio values, is obtained by formula (3) (4)

${\mathrm{CR}}_1(P_1,P_2,X,Y)=\frac{{|m}_{145}\left|\right|m_{234}|}{{|m}_{245}\left|\right|m_{134}|}---\left(3\right)$

${\mathrm{CR}}_2(P_5,P_4,X,Z)=\frac{{|m}_{125}\left|\right|m_{234}|}{{|m}_{235}\left|\right|m_{124}|}---\left(4\right)$

Step 5-3 utilizes exterior point R to replace P1 and other 4 formation double ratios; Its constructive method is wherein l _ijrepresent the straight line that some i and some j form, symbol × be expressed as the intersection point of two straight lines or connect the straight line of 2, as Fig. 2 (b)

Shown in;

Step 5-4 replaces P with R point ₁point, adopts as the connection mode of Fig. 2 (c), and on two line segments, the value of double ratio is compared to last eigenwert; The last form of Definition of projective invariant based on double ratio as shown in Equation 5

$\mathrm{CR}(R,P_2,P_3,P_4,P_5)=\frac{{\mathrm{CR}}_1}{{\mathrm{CR}}_2}---\left(5\right)$

Step 6. is utilized 5 characteristic number structure projective invariants

Step 6-1 gets three points on profile form triangle;

Step 6-2, by the method for step 5, utilizes the line of other 2 points and these three points, obtains two other point on every limit of triangle, 5 somes called after respectively as shown in Fig. 3 (a);

Point of step 6-3 can be by two corresponding summit Pi and Pi+1 linear expression as shown in Equation 6, i=1 here, 2,3, j=1,2.

$Q_i^{\left(j\right)}=a_i^{\left(i\right)}{P}_i+b_i^{\left(j\right)}{p}_{i+1}---\left(6\right)$

And then 5 characteristic numbers can be expressed as:

Step 6-4 is the stability that strengthens descriptor, with exterior point R replacement P ₁, as shown in Fig. 3 (b).Use (R, P ₂, P ₃, P ₄, P ₅) these 5 form the fundamental point of triangle character numbers, the point on all the other limits is all connected and produces by these 5.Similar with the exterior point of double ratio, be provided with two exterior point M, N.M point and N point can pass through with obtain respectively;

Step 6-5 is by point the triangle Δ RXP forming ₅and point set on three limits is respectively characteristic number can pass through

Step 6-6 is by exchanging P ₁and P ₅order, can obtain a new exterior point R' and new triangle Δ R ' X ' P ₅, as shown in Fig. 3 (c).Can obtain thus the description of the characteristic number new about of 5 here and then utilize the ratio of two characteristic numbers of successively trying to achieve as last eigenwert.

$\mathrm{CN}(R,P_2,P_3,P_4,P_5)=\frac{{\mathrm{CR}}_1}{{\mathrm{CR}}_2}---\left(8\right)$

The similarity of step 7. shape compares and coupling

Given two the shape X of step 7-1 and Y, the sampled point on two shape profiles is respectively X _i∈ X (i=1,2 ..., M), Y _j∈ Y (j=1,2 ..., N).Two sampled point X _iand Y _jbetween similarity can obtain by the HPIC feature of two points relatively.

$C(X_i,Y_j)=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}|f_i^k-f_j^k|---\left(9\right)$

Wherein f _iand f _jbe respectively sampled point X _iand Y _jproper vector, therefore the difference between two shapes can be calculated with the similar matrix of a M × N dimension.

Step 7-2 finds optimum coupling path by dynamic programming algorithm; By finding the corresponding relation H (X of sampled point optimum of two shapes _i): X → Y, makes minimum.Difference between latter two shape can represent by the cumulative sum of the difference of each corresponding point descriptor.The similarity that is worth two shapes of less expression is higher.

$S(X,Y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}C(X_i,H\left(X_i\right))---\left(10\right)$

Accompanying drawing explanation

Fig. 1 (a) sampled point P _iexemplary plot.

Fig. 1 (b) obtains 5 sampled point exemplary plot with interval L.

Fig. 1 (c) adjusts interval k and obtains 5 different sampled point exemplary plot.

Fig. 1 (d) k gets the sampled point exemplary plot of 5 o'clock.

Fig. 1 (e) k gets the sampled point exemplary plot of 1 o'clock.

In Fig. 1 (a), with P _ipoint is for example, and the sampled point of shape profile represents with solid black point, and the sampled point small circle of choosing for calculating 5 double ratios or characteristic number is irised out.Initial sampling interval is L, and 5 sampled points that obtain are evenly distributed on shape profile, as shown in Fig. 1 (b).By adjusting sampling interval k, the value of k is from L (L=N/5) to 1 sampled point obtaining different interval, as shown in Fig. 1 (c).Fig. 1 (d), Fig. 1 (e) are respectively k and get 5 and the sampled point chosen at 1 o'clock.

5 sampled point exemplary plot of Fig. 2 (a) shape profile.

Fig. 2 (b) is by interconnecting the exemplary plot that obtains two groups of 4 collinear point;

Fig. 2 (c) replaces P with R point _ithe exemplary plot of the mode connection result of Fig. 2 (a) for point.

(P in Fig. 2 (a) ₁, P ₂, P ₃, P ₄, P ₅) be 5 sampled points on shape profile, can obtain two groups of 4 collinear point by interconnecting, be respectively (P ₁, P ₂, X, Y) and (P ₅, P ₄, X, Z); For strengthening the stability of descriptor, use mode obtain 1 R in profile.Wherein l _ijrepresent the straight line that some i and some j form, symbol × be expressed as the intersection point of two straight lines or connect the straight line of 2.Fig. 2 (b) is the schematic diagram that obtains R in order to upper method.With R point replacement P ₁point connects the result that can obtain Fig. 2 (c) by the mode of Fig. 2 (a).

The sampled point schematic diagram of Fig. 3 (a) calculated characteristics number.

Fig. 3 (b) exterior point R replaces original P ₁the schematic diagram of point.

Fig. 3 (c) exchanges P ₁and P ₅the order new exterior point and the feature triangle that obtain.

Fig. 3 (a) is the explanation take triangle as basic constitutive characteristic number, wherein represent 3 basic sampled points on shape profile. represent respectively the sampled point in different edge ^.obtain exterior point R by the method identical with Fig. 2 and replace original P ₁point, as shown in Fig. 3 (b).Use (R, P ₂, P ₃, P ₄, P ₅) these 5 form the fundamental point of triangle character numbers, the point on all the other limits is all connected and produces by these 5.Similar with the exterior point of double ratio, be provided with two exterior point M, N.M point and N point can pass through with obtain respectively.Triangle Δ RXP ₅be the fundamental triangle of constitutive characteristic number.All the other points are the sampled point in triangle edges.Fig. 3 (b) is for exchanging P ₁and P ₅the order new exterior point R' and the new triangle Δ R ' X ' P that obtain ₅.

Embodiment

For making object of the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing and instantiation, the present invention is described in further details.These examples are only illustrative, and are not limitation of the present invention.

1. read in a symbol picture, as the symbol in Fig. 1 (a).Use canny edge detection algorithm to extract symbol profile, then extract on this basis the convex closure of symbol.Adopt uniform sampling method, on convex closure, extract N sampled point, be labeled as P={P ₁, P ₂..., P _n, as shown in Fig. 1 (a), black point is the sampled point on convex closure.

2. couple each sampled point P _i(i=1 ..., N), with P _ifor axle, choose two point (P in its left side _i-k, P _i-2k), in like manner also choose two point (P at same interval on right side _i+k, P _i+2k), such 5 points can form a projective invariant according to step 5 or any one mode of step 6 this value can represent to be spaced apart the constant geological information of projection between 5 sampled points of k.

3. by adjusting sampling interval k, the value of k is from L (L=N/5) to 1.Can obtain about a P _il dimensional feature vector ${\mathrm{HPIC}}_i={(f_i^L,f_i^{L-1},...,f_i^1)}^T,$ As Fig. 1 (b), (c), (d) shown in.

4. a couple N sampled point is adopted and can be obtained in the same way N HPIC vector, forms a HPIC matrix H PIC (P)=(HPIC ₁, HPIC ₂..., HPIC _n), the dimension of this matrix H PIC (P) is L × N, i row are P _iproper vector.Here suppose sampling number N=100, L=20, k=(20,19 ..., 1).Will by normalized mode value be limited between-1 to 1.If the value of being set to 1, the value of being set to-1.

5. the input feature descriptor of shape and the feature descriptor of shape of template are compared respectively.Here need to utilize the relatively similarity between two each sampled points of shape of formula (9).

6. utilize dynamic programming algorithm to find optimum coupling path; If X is shape of template Y is shape to be matched.By finding the corresponding relation H (Xi) of sampled point optimum of two shapes: X → Y, makes minimum.Difference between latter two shape can represent by the cumulative sum of the difference of each corresponding point descriptor.The similarity that is worth two shapes of less expression is higher.Select the highest shape of template of similarity to be the matching result of input shape.

Claims (1)

1. the shape matching method based on projective invariant, its feature comprises the following steps:

Step 1. utilizes the method for rim detection to extract profile to original image;

Step 2. is carried out uniform sampling to shape profile, and sampling number is N; N configuration sampling point is expressed as P={P ₁, P ₂..., P _n;

Step 3. is to each sampled point P _i(i=1 ..., N), take by slightly choosing other 4 sampled points and P to mode smart, that draw near around it _iform a series of projective invariants:

Step 3-1 is with P _ifor axle, choose two point (P in its left side _i-k, P _i-2k), in like manner also choose two point (P at same interval on right side _i+k, P _i+2k), k is sampling interval; These 5 points utilize the method for step 5 or step 6 together to form a projective invariant ;

Step 3-2 is by adjusting sampling interval k, and the value of k is from L to 1, L=N/5; Obtain about a P _il dimensional feature vector, as shown in formula (1);

${\mathrm{HPIC}}_i={(f_i^L,f_i^{L-1},...,f_i^1)}^T---\left(1\right)$

Step 3-3 will by normalized mode value be limited between-1 to 1; If the value of being set to 1, the value of being set to-1;

Step 4. is adopted and is obtained in the same way N HPIC vector as shown in formula (2) N sampled point:

HPIC(P)＝(HPIC ₁HPIC ₂，...，HPIC _N (2)

The dimension of this matrix H PIC (P) is L × N, and i row are P _iproper vector;

Step 5. is utilized 5 double ratio structure projective invariants :

First step 5-1 chooses 5 coplanar sampled point (P on shape profile ₁, P ₂, P ₃, P ₄, P ₅), these 5 points interconnect and obtain two groups of 4 collinear point, are respectively (P ₁, P ₂, X, Y) and (P ₅, P ₄, X, Z);

Step 5-2 calculates two groups of double ratio values, is obtained by formula (3) (4)

${\mathrm{CR}}_1(P_1,P_2,X,Y)=\frac{{|m}_{145}\left|\right|m_{234}|}{{|m}_{245}\left|\right|m_{134}|}---\left(3\right)$

${\mathrm{CR}}_2(P_5,P_4,X,Z)=\frac{{|m}_{125}\left|\right|m_{234}|}{{|m}_{235}\left|\right|m_{124}|}---\left(4\right)$

Step 5-3 utilizes exterior point R to replace P ₁with other 4 formation double ratios; Its constructive method is wherein l _ijrepresent the straight line that some i and some j form, symbol × be expressed as the intersection point of two straight lines or connect the straight line of 2;

Step 5-4 replaces P with R point ₁point, on two line segments, the value of double ratio is compared to last eigenwert; The last form of Definition of projective invariant based on double ratio as shown in Equation 5

$\mathrm{CR}(R,P_2,P_3,P_4,P_5)=\frac{{\mathrm{CR}}_1}{{\mathrm{CR}}_2}---\left(5\right)$

Step 6. is utilized 5 characteristic number structure projective invariants

Step 6-1 gets three points on profile form triangle;

Step 6-2, by the method for step 5, utilizes the line of other 2 points and these three points, obtains two other point on every limit of triangle, 5 somes called after respectively

Point of step 6-3 by two corresponding summit P _iand P _i+1linear expression as shown in Equation 6, i=1 here, 2,3, j=1,2;

$Q_i^{\left(j\right)}=a_i^{\left(i\right)}{P}_i+b_i^{\left(j\right)}{p}_{i+1}---\left(6\right)$

And then 5 characteristic numbers are expressed as:

Step 6-4 is the stability that strengthens descriptor, with exterior point R replacement P ₁, use (R, P ₂, P ₃, P ₄, P ₅) these 5 form the fundamental point of triangle character numbers, the point on all the other limits is all connected and produces by these 5; Similar with the exterior point of double ratio, be provided with two exterior point M, N; M point and N point pass through $M=(X\×(l_{{\mathrm{RP}}_4}\×L_{P_2{P}_5}))\×L_{{\mathrm{RP}}_5}$ With $N=l_{{\mathrm{XP}}_3}\×l_{{\mathrm{RP}}_5}$ Obtain respectively;

Step 6-5 is by point point set on triangle Δ RXP5 and three limits that form is respectively characteristic number can be passed through

Step 6-6 is by exchanging P ₁and P ₅order, obtain a new exterior point R' and new triangle Δ R'X'P ₅; Obtain thus the description of the characteristic number new about of 5 here and then utilize the ratio of two characteristic numbers of successively trying to achieve as last eigenwert;

$\mathrm{CN}(R,P_2,P_3,P_4,P_5)=\frac{{\mathrm{CR}}_1}{{\mathrm{CR}}_2}---\left(8\right)$

The similarity of step 7. shape compares and coupling

Given two the shape X of step 7-1 and Y, the sampled point on two shape profiles is respectively X _i∈ X (i=1,2 ..., M), Y _j∈ Y (j=1,2 ..., N); Two sampled point X _iand Y _jbetween similarity obtain by the HPIC feature of two points relatively;

$C(X_i,Y_j)=\underset{k=1}{\overset{L}{\mathrm{\Σ}}}|f_i^k-f_j^k|---\left(9\right)$

Wherein f _iand f _jbe respectively sampled point X _iand Y _jproper vector, the similar matrix of a therefore M for the difference between two shapes × N dimension calculates;

Step 7-2 finds optimum coupling path by dynamic programming algorithm; By finding the corresponding relation H (X of sampled point optimum of two shapes _i): X → Y, makes minimum; Difference between latter two shape represents by the cumulative sum of the difference of each corresponding point descriptor, and the similarity that is worth two shapes of less expression is higher.