CN102279979A - Method for calculating scale factor in perspective projection imaging model by utilizing bone constraints - Google Patents

Abstract

The preset invention discloses a method for calculating a scale factor in a perspective projection imaging model by utilizing bone constraints A scale factor corresponding to the root joint in a human body bone model and calculated through the method can be used for extracting human body 3D motion attitudes based on monocular video. According to the method, a nonlinear equation group is constructed by utilizing the constraint of the invariance of human body bone length and the constraint condition that two connected symmetrical bones have equal bone lengths, and the scale factor corresponding to the root joint is obtained by solving the nonlinear equation group. The invention also provides an algebraic approach for solving the nonlinear equation group, and the solving of the nonlinear equation group is devided into several processes for solving quadratic equations, according to the two theorems proven in the invention. The invention has the advantages of simplicity, accuracy of the obtained scale factor, and being capable of widely used in fields such as man-machine interaction, interactive entertainment, intelligent monitoring and medical diagnosis.

Description

Utilize the bone constraint to calculate the method for scale factor in the perspective projection imaging model

[technical field]

The present invention relates to computer vision and field of video processing, particularly the computing method of scale factor in the perspective projection imaging model.

[background technology]

Be extracted in fields such as man-machine interaction, interaction entertainment, intelligent monitoring, medical diagnosis based on the human body three-dimensional athletic posture of video and have great using value.Then be key in application how according to its 3 d pose of human synovial two-dimensional coordinate reconstruct in the known frame of video.Under the perspective projection model, if the scale factor of known joint correspondence, so just can calculate the three-dimensional coordinate of this joint under world coordinate system, and then obtain the Eulerian angle that this joint rotates, promptly obtain the three-dimensional motion attitude of human body according to inverse kinematics and skeleton model.

At present, scale factor evaluation method commonly used is that the perspective projection model approximation with reality is a ratio rectangular projection model, under this projection model, estimate a best proportion factor according to certain constraint condition, thereby go out the 3 d pose of human body according to ratio rectangular projection Model Calculation.But there is following shortcoming in this method: 1) the corresponding same scale factor of all human synovial, but in fact be not on the same imaging surface owing to each joint, thereby the scale factor of each joint correspondence is different, so the scale factor and the fict scale factor that are estimated by this method.2) the perspective projection model approximation with reality is a ratio rectangular projection model, can make that the human synovial three-dimensional coordinate and the true coordinate value deviation of coming out according to this Model Calculation are bigger.

[summary of the invention]

Given this, the object of the present invention is to provide a kind of simple accurate scale factor calculation method.The constraint that its bone length equated when this method utilized constraint of bone length unchangeability and symmetrical bone to rotate comes the scale factor of root joint correspondence in the accurate Calculation skeleton model.Behind the scale factor that calculates root joint correspondence, just can go out the three-dimensional motion attitude of human body in the present frame according to inverse kinematics and skeleton Model Calculation.

For achieving the above object, the present invention by the following technical solutions:

1, from the skeleton model, chooses the bone section of two symmetries, such as left hipbone bone section and right hipbone bone section.

2, in frame of video, mark three articulation points that these two bone sections comprise, obtain the two dimensional image coordinate of these three articulation points.

Three joint two dimensional image coordinates that 3, will obtain import in the Nonlinear System of Equations of setting up according to constraint condition, utilize quasi-Newton method to separate the scale factor that this system of equations obtains root joint correspondence.This step obtains below also can adopting step by step.

Give one greater than zero scale factor 3.1 appoint, the constraint condition that equates according to two symmetrical bone length calculates the variable quantity dz of bone section two joints on the Z axle that causes when bone rotates under this scale factor.

3.2 the variable quantity dz with previous step calculates obtains under the situation of this scale factor and variable quantity dz corresponding bone length according to distance calculation formula any in the three dimensions at 2.

3.3 the bone length that previous step is calculated obtains the variable quantity dz of bone section two joints on the Z axle according to the proportionate relationship of this bone length in itself and the skeleton model ₁

3.4 the variable quantity dz that previous step is calculated ₁Constraint calculates the scale factor s of root joint correspondence according to the bone length unchangeability.

Compared with prior art, the present invention has following significant advantage:

1, computing method are simple, only need separate several equations or separate the scale factor that a Nonlinear System of Equations just can obtain root joint correspondence.

2, the scale factor precision height that calculates.Because the imaging model that adopts in computation process is real imaging model (perspective imaging model), thereby the scale factor precision height that calculates.Theoretically, if the resolution height of video, articulation point mark accurately, imaging process is undistorted, the scale factor that then calculates is exactly an actual value.

3, the human body three-dimensional attitude that can be applied to monocular video is extracted.The scale factor in the root joint of being calculated by the present invention can obtain the three-dimensional motion attitude of human body according to inverse kinematics and skeleton constraint, can be widely used in fields such as man-machine interaction, interaction entertainment, virtual reality.

[description of drawings]

Fig. 1 is the skeleton illustraton of model that the present invention adopts;

Fig. 2 is bone two candidate's bone synoptic diagram under the same z coordinate in three dimensions on the image;

Fig. 3 is the synoptic diagram of two candidate's bones in three dimensions that satisfies bone equated constraint condition;

Fig. 4 is bone postrotational synoptic diagram in three dimensions;

Fig. 5 is the two parallel candidate's bone synoptic diagram that satisfy bone equated constraint condition;

Fig. 6 is that the present invention is applied to 3 D human body attitude extraction example figure;

[embodiment]

Below in conjunction with the drawings and the specific embodiments the present invention is described in further detail.

We regard human body as a kind of tree type rod shape model, and this skeleton model is made up of 16 articulation points and 15 body segment as shown in Figure 1, wherein J ₁Be the root node of tree, the basin osteoarthrosis of corresponding human body, L ₉, L ₁₂Be respectively left and right sides hipbone bone.Line segment in the model (skeleton section) length obtains according to anthropometry, is a relative scale length, should be according to actual measured value setting, wherein L in application ₉Length equal L ₁₂Length.

The perspective projection imaging model that we adopt is as follows:

$\left(\begin{array}{c}u\\ v\end{array}\right)=\frac{1}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">s</figure-callout>}}\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\end{array}\right)\left(\begin{array}{c}x\\ y\\ z\end{array}\right)---\left(1\right)$

Wherein (x, y z) are the coordinate figure of certain point in three dimensions, and (u v) is this coordinate figure on the two-dimensional imaging face.Parameter s is a scale factor, is tried to achieve by s=z/f, and wherein z is this z coordinate figure in three dimensions, and f is a focal length of camera.From equation (1) as can be known, when z changed, the s value changed linearity, and the variable quantity ds of s is expressed as with respect to the variable quantity dz of z value: T (dz)=ds.

Prove that at first two theorems are as follows:

Theorem 1: the bone L on the image ₉And L ₁₂It under a certain z coordinate in corresponding all candidate's bone sections, exists two candidate's bone sections to satisfy bone L at most on three dimensions ₉And L ₁₂The constraint of equal in length.

Proof: because bone L ₉And L ₁₂Rotation on the z axle has two kinds of directions, is illustrated in figure 2 as one of them direction, known bone L ₉And L ₁₂Its imaging on two dimensional image is respectively line segment J _{1 '}J _{10 '}And J _{1 '}J _{13 '}, the bone L that it is corresponding ₉And L ₁₃Any two candidate line sections in the locus are J ₁₃J ₁J ₁₀And J _{13 "}J ₁J _{10 "}Cross some J _{10 "}Work is parallel to the ray intersection section J of z axle ₁J ₁₀In a J _{M '}, cross some J _{10 "}Work is parallel to the ray intersection section J of y axle ₁J ₁₀In a J _{N '}Cross some J _{13 "}Work is parallel to the ray intersection section J of z axle ₁J ₁₃Ray in a J _m, cross some J _{13 "}Work is parallel to the ray intersection section J of y axle ₁J ₁₃In a J _n

As shown in Figure 2, line segment J _{13 "}J _nLength be L _x, line segment J _nJ _mLength be L _y, line segment J ₁J _nLength be L _z, line segment J ₁J ₁₃Length be

Line segment J ₁J _{13 "}Length be

Line segment J _{10 "}J _{N '}Length be L _{X '}, line segment J _{N '}J _{M '}Length be L _{Y '}, line segment J ₁J _{N '}Length be L _{Z '}, line segment J ₁J ₁₀Length be

Line segment J ₁J _{10 "}Length be

Prove with reduction to absurdity, suppose two candidate line sections J ₁₃J ₁J ₁₀And J _{13 "}J ₁J _{10 "}All satisfy bone L ₉And L ₁₂The constraint of equal in length, promptly

Angle between these two candidate line sections is Δ θ.Triangle as seen from the figure

Similar in appearance to triangle

, the character similar by triangle can get:

$\frac{L_{x^{\&prime;}}}{L_x}=\frac{L_9^1}{L_{12}^1}\&DoubleRightArrow;L_x=L_{x^{\&prime;}}$

In like manner can get: L _z=L _{Z '}(2)

Because angle α equals angle α ', so triangle

Similar in appearance to triangle

, thereby following formula is arranged:

$\frac{L_x}{L_{x^{\&prime;}}}=\frac{L_y}{L_{y^{\&prime;}}}\&DoubleRightArrow;L_y=L_{y^{\&prime;}}---\left(3\right)$

Composite type (2) and formula (3) be as can be known: L _y+ L _z=L _{Y '}+ L _{Z '}

So have as shown in Figure 2:

$\left\{\begin{array}{c}{L}_y+L_z>L_{12}^2\\ L_{y^{\&prime;}}+L_{z^{\&prime;}}<L_9^2\end{array}\right.\&DoubleRightArrow;L_{12}^2\&NotEqual;L_9^2$

This conclusion and null hypothesis are run counter to, thereby inevitable Δ θ=0, so as can be known under any s value of root joint correspondence, bone L ₉And L ₁₂The anglec of rotation θ in root joint is only value when rotating according to a kind of direction.In like manner as can be known as bone L ₉And L ₁₂The anglec of rotation θ in root joint also is only value when rotating according to another kind of direction.To sum up can in three dimensions, exist two candidate's bone sections to satisfy bone L at most ₉And L ₁₂The constraint of equal in length.

Theorem 2: under a certain sense of rotation, the candidate segment that satisfies the bone equated constraint is spatially inevitable parallel

Proof: as shown in Figure 3, establish bone L ₉And L ₁₃Imaging on the projecting plane is respectively line segment J _{1 '}J _{10 '}And J _{1 '}J _{13 '}, the bone L that it is corresponding ₉And L ₁₃Any two candidate line sections in three dimensions are J ₁₃J ₁J ₁₀And J _{13 "}J _{1 "}J _{10 "}, i.e. line segment J ₁J ₁₀Length equal line segment J ₁J ₁₃Length, line segment J _{1 "}J _{10 "}Length equal line segment J _{1 "}J _{13 "}Length.

Prove with reduction to absurdity, suppose line segment J ₁₃J ₁J ₁₀Be not parallel to line segment J _{13 "}J _{1 "}J _{10 "}Cross some J _{10 "}Work is parallel to line segment J ₁₃J ₁J ₁₀Straight line hand over ray of in a J _{1 " '}, hand over ray op in a J _{13 " '}, cross some J _{13 " '}Work is parallel to the straight line intersection section J of ray of _{13 "}J _{1 "}In a m.Because line segment J ₁J ₁₀Be parallel to J _{1 " '}J _{10 "}, thereby triangle Similar in appearance to triangle

, therefore following equation is arranged:

$\frac{L_{J_1{J}_{10}}}{L_{J_{1^{\&prime;\&prime;\&prime;}}{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;\&prime;}}}}=\frac{L_{o{J}_1}}{L_{o{J}_{1^{\&prime;\&prime;\&prime;}}}}---\left(4\right)$

Wherein

Be line segment J ₁J ₁₀Length, other is similar.

In like manner can get equation:

$\frac{L_{J_1{J}_{13}}}{L_{J_{1^{\&prime;\&prime;\&prime;}}{\mathrm{<figure-callout\; id="13"\; label="j"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">j</figure-callout>}}_{{13}^{\&prime;\&prime;\&prime;}}}}=\frac{L_{o{J}_1}}{L_{o{J}_{1^{\&prime;\&prime;\&prime;}}}}---\left(5\right)$

Wherein

Be line segment J ₁J ₁₃Length, other is similar.

Composite type (4) and formula (5) can get:

$\frac{L_{J_1{J}_{10}}}{L_{J_{1^{\&prime;\&prime;\&prime;}}{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;\&prime;}}}}=\frac{L_{J_1{J}_{13}}}{L_{J_{1^{\&prime;\&prime;\&prime;}}{J}_{{13}^{\&prime;\&prime;\&prime;}}}}---\left(6\right)$

Because

, therefore can get:

(7)

In addition: because line segment J _{13 " '}M is parallel to line segment J _{1 " '}J _{1 "}, so triangle

Similar in appearance to triangle

, so following equation is arranged:

$\frac{L_{J_{1^{\&prime;\&prime;\&prime;}}{J}_{{13}^{\&prime;\&prime;\&prime;}}}}{L_{J_{{10}^{\&prime;\&prime;}}{J}_{1^{\&prime;\&prime;\&prime;}}}}=\frac{L_{J_{1^{\&prime;\&prime;}}m}}{L_{J_{{10}^{\&prime;\&prime;}}{J}_{1^{\&prime;\&prime;}}}}$

Because $L_{J_{1^{\&prime;\&prime;\&prime;}}{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;\&prime;}}}=L_{J_{1^{\&prime;\&prime;\&prime;}}{J}_{13^{\&prime;\&prime;\&prime;}}},$

Therefore ${\mathrm{<figure-callout\; id="1"\; label="L\; J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}={\mathrm{<figure-callout\; id="10"\; label="L\; J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}---\left(8\right)$

Be positioned at line segment J owing to put m _{13 "}J _{1 "},

Thereby ${\mathrm{<figure-callout\; id="1"\; label="L\; J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}<{\mathrm{<figure-callout\; id="1"\; label="L\; J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">L</figure-callout>}}_{J_{}}---\left(9\right)$

Composite type (8) and formula (9) be as can be known:

, i.e. line segment J _{1 "}J _{10 "}Be uneven in length in line segment J _{1 "}J _{13 "}Length, this conclusion and null hypothesis are runed counter to.So can get: under a certain sense of rotation, satisfy two bone length equated constraints candidate segment its spatially must be parallel.

The method of scale factor in the perspective projection imaging model is calculated in the bone constraint that utilizes that the present invention proposes, and may further comprise the steps:

1,, from the two-dimensional video image frame, marks out joint J according to Fig. 1 ₁, J ₁₀, J ₁₃Coordinate be respectively $({\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x,{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y),({\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^x,{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^y),({\mathrm{<figure-callout\; id="13"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{13}^{\&prime;}}^x,{\mathrm{<figure-callout\; id="13"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{13}^{\&prime;}}^y).$

2, according to the bone constraint, following as shown in Figure 4 system of equations is set up.

$\left\{\begin{array}{c}{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2={\left({\mathrm{Len}}_9\right)}^2\\ {[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x-(s-\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="13"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{13}^{\&prime;}}^x]}^2+{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y-(s-\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="13"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{13}^{\&prime;}}^y]}^2+{\left(\frac{-\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2={\left({\mathrm{Len}}_{12}\right)}^2\end{array}\right.---\left(10\right)$

Here

Ds is known as between s and the z coefficient between the linear changing relation, specifically ask the method for ds can be, Chen Shu, Peng Xiaoning etc. referring to Zou Beiji. the unmarked 3 d human motion that is applicable to monocular video is followed the tracks of. computer-aided design (CAD) and graphics journal, 2008,20 (8): 1047-1055; Δ s, Δ z are corresponding bone L ₉Variable quantity during rotation, wherein Len ₉Be bone L ₉Relative length in skeleton model shown in Figure 1, Len ₁₂Be bone L ₁₂Relative length in skeleton model shown in Figure 1.

System of equations (10) is a Nonlinear System of Equations, adopts quasi-Newton method to calculate root joint J ₁Bone L in corresponding scale factor s and the present frame ₉Perhaps L ₁₂Rotation and cause variation delta s on the z coordinate direction.By two theorems of front as can be known, this Nonlinear System of Equations has two to separate, according to bone L ₉Perhaps L ₁₂Sense of rotation from these two are separated, select one and correctly separate.

By the analysis of front as can be known, we also can resolve into following steps with group (10) process of solving an equation:

Give one greater than zero s value 2.1 appoint, formula is tried to achieve a Δ s below utilizing.

${[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2=$

${[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x-(s-\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="13"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{13}^{\&prime;}}^x]}^2+{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y-(s-\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="13"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{13}^{\&prime;}}^y]}^2+{\left(\frac{-\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2---\left(11\right)$

Wherein Δ s is bone L ₉The displacement that on the z coordinate, produces during rotation.

Because formula (11) is a quadratic equation with one unknown, has two to separate, according to bone L ₉Sense of rotation therefrom select one correctly to separate.

2.2 equation below the Δ s substitution that previous step is tried to achieve obtains satisfying bone L ₉And L ₁₂L under the equal in length constraint condition ₉Bone length Len _Sel

${\mathrm{Len}}_{\mathrm{sel}}=\sqrt{{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;s})\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2}$

Wherein s is a given s value in 2.1 steps.

2.3 among Fig. 5, bone section J _{10 '}J _{1 '}J _{13 '}Actual position in three dimensions is line segment J _{10 "}J _{1 "}J _{13 "}, line segment J ₁₀J ₁J ₁₃Be corresponding position in 2.1 steps, by theorem 2 line segment J as can be known _{10 "}J _{1 "}J _{13 "}Be parallel to line segment J ₁₀J ₁J ₁₃So, bone section J _{10 '}J _{1 '}J _{13 '}The s variation delta s of actual position in three dimensions on the z coordinate ₁Must satisfy following equation:

$\frac{{\mathrm{Len}}_{\mathrm{sel}}}{{\mathrm{Len}}_9}=\frac{\mathrm{\&Delta;s}}{\mathrm{\&Delta;}{s}_1}---\left(12\right)$

Wherein, Len ₉Be bone L ₉Length in the skeleton model, Δ s is 2.1 step middle conductor J ₁₀J ₁The s variable quantity of the correspondence of trying to achieve during rotation.

Separate formula (12) and try to achieve Δ s ₁

2.4 the Δ s that formula (12) is tried to achieve ₁Value substitution following formula

${[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;}{s}_1)\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HSA00000140212600021.png,HSA00000140212600022.png"\; state="\{\{state\}\}">J</figure-callout>}}_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;}{s}_1)\&CenterDot;{\mathrm{<figure-callout\; id="10"\; label="J"\; filenames="HSA00000140212600012.png,HSA00000140212600021.png"\; state="\{\{state\}\}">J</figure-callout>}}_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;}{s}_1}{\mathrm{ds}}\right)}^2={{\mathrm{Len}}_9}^2---\left(13\right)$

Separate formula (13) and then tried to achieve root joint J ₁Corresponding scale factor s.

This method is applied to the results are shown in Figure 6 based on the human body three-dimensional athletic posture extraction of monocular video, wherein Fig. 6 (a) is an original video frame, 6 (b) are for having marked the frame of video of articulation point, 6 (c) try to achieve the 3 d pose that extracts behind the scale factor of root joint correspondence for adopting this method, the result that 6 (d) observe from different viewpoints for the human body three-dimensional attitude of extracting.

Claims (2)

1. one kind is utilized bone to retrain the method for calculating scale factor in the perspective projection imaging model.It is characterized in that may further comprise the steps:

A) proved theorem 1: the bone L on the image ₉And L ₁₂It under a certain z coordinate in corresponding all candidate's bone sections, exists two candidate's bone sections to satisfy bone L at most on three dimensions ₉And L ₁₂The constraint of equal in length.

B) proved theorem 2: satisfy between the candidate segment of bone equated constraint condition inevitable parallel.

C) exist two candidate segment to satisfy L ₉And L ₁₂Bone length equated constraint and the constraint of bone length unchangeability, promptly following Nonlinear System of Equations has two groups to separate.

$\left\{\begin{array}{c}{[s\&CenterDot;J_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;s})\&CenterDot;J_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;J_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;s})\&CenterDot;J_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2={\left({\mathrm{Len}}_9\right)}^2\\ {[s\&CenterDot;J_{1^{\&prime;}}^x-(s-\mathrm{\&Delta;s})\&CenterDot;J_{{13}^{\&prime;}}^x]}^2+{[s\&CenterDot;J_{1^{\&prime;}}^y-(s-\mathrm{\&Delta;s})\&CenterDot;J_{{13}^{\&prime;}}^y]}^2+{\left(\frac{-\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2={\left({\mathrm{Len}}_{12}\right)}^2\end{array}\right.$

Adopt quasi-Newton method to separate top Nonlinear System of Equations.From two groups are separated, select one and satisfy the variable factor that separating of root joint sense of rotation then tried to achieve root joint correspondence.

2. a kind of method of utilizing the bone constraint to calculate scale factor in the perspective projection imaging model according to claim 1 is characterized in that, separates non-linear side's system of equations and resolves into following steps:

1) appoints and give one, utilize following formula to try to achieve a Δ s greater than zero s value.

${[s\&CenterDot;J_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;}s)\&CenterDot;J_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;J_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;}s)\&CenterDot;J_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;}s}{\mathrm{ds}}\right)}^2=$

${[s\&CenterDot;J_{1^{\&prime;}}^x-(s-\mathrm{\&Delta;s})\&CenterDot;J_{{13}^{\&prime;}}^x]}^2+{[s\&CenterDot;J_{1^{\&prime;}}^y-(s-\mathrm{\&Delta;s})\&CenterDot;J_{{13}^{\&prime;}}^y]}^2+{\left(\frac{-\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2$

Equation below the Δ s substitution of 2) previous step being tried to achieve obtains satisfying bone L ₉And L ₁₂L under the equal in length constraint condition ₉Bone length Len _Sel

${\mathrm{Len}}_{\mathrm{sel}}=\sqrt{{[s\&CenterDot;J_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;s})\&CenterDot;J_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;J_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;s})\&CenterDot;J_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;s}}{\mathrm{ds}}\right)}^2}$

3) calculate following formula and try to achieve bone L ₉Owing to be rotated in the variation delta s on the z coordinate ₁

$\frac{{\mathrm{Len}}_{\mathrm{sel}}}{{\mathrm{Len}}_9}=\frac{\mathrm{\&Delta;s}}{\mathrm{\&Delta;}{s}_1}$

4) the Δ s that previous step is tried to achieve ₁Value substitution following formula is tried to achieve root joint J ₁Corresponding scale factor s

${[s\&CenterDot;J_{1^{\&prime;}}^x-(s+\mathrm{\&Delta;}{s}_1)\&CenterDot;J_{{10}^{\&prime;}}^x]}^2+{[s\&CenterDot;J_{1^{\&prime;}}^y-(s+\mathrm{\&Delta;}{s}_1)\&CenterDot;J_{{10}^{\&prime;}}^y]}^2+{\left(\frac{\mathrm{\&Delta;}{s}_1}{\mathrm{ds}}\right)}^2={{\mathrm{Len}}_9}^2$

Images