CN1804904A - Method for directly performing three-dimensional model transformation with three-dimensional bench marks - Google Patents

Abstract

The invention relates to a method for using three-dimensional mark point directly to do three-dimensional model deformation in the field of image processing technology. It comprises the following steps: 1)normalizing the top point data at the range of [-1, 1], using a cube with the edge length 2 to limit it; 2) transferring the screen obtained points into boundary beacon, complementary operating the screen obtained Y coordinate, reading the current frame buffer in the internal memory, at last computing the three-dimensional coordinate point; 3) preserving the three-dimensional mark points, obtaining another model corresponding position mark point; 4) using thin plate stripe bracketing method to do elastic deformation, using the three-dimensional points to displace the two-dimensional points to directly obtain the new coordinate.

Description

Method with directly performing three-dimensional model transformation with three-dimensional bench marks

Technical field

The present invention relates to a kind of method of technical field of image processing, specifically is a kind of method with directly performing three-dimensional model transformation with three-dimensional bench marks.

Background technology

Image more and more is subject to people's attention as a kind of crucial medium and means, and image has become the object of learning and studying between each subject of field such as engineering science, computer science, information science, statistics, physics, chemistry, biology, medical science even social science.Distortion is a method more common in the computer graphics, is mainly used in the purposes such as registration of image or figure.Elastic deformation to two dimensional image has obtained very fast development at present, comprises multiple algorithms such as light stream, resampling, thin plate spline, B batten, on the overall situation and local deformation a lot of classification has been arranged also, makes present deformation ratio more careful, true.But for the distortion of three-dimensional model, great majority are based on the cylinder unwrapping of model, obtain two dimensional image, utilize existing algorithm then, realize distortion on two dimensional image, the three-dimensional model after reduction obtains being out of shape at last.

Find through literature search prior art, people such as Volker Blanz are at " IEEE transaction onPattern Recognition and Machine Intelligence " Vol.25, No.9, September2003,1063-1074 (IEEE pattern-recognition and machine intelligence, the 25th volume, the 9th phase, in September, 2003 version, the 1063-1074 page or leaf) on, adopt the method for light stream that the three-dimensional face coordinate that launches is carried out elastic registrating.By the calculating of high dimension vector, obtain the Strength Changes between the different models.The model that such method is bigger to spatial variations, the smoothness assumption of optical flow algorithm can not be satisfied, and the result of calculation correspondence is undesirable.Also find in the retrieval, Hu Yongli etc. were " Chinese journal of computers " 2005, the 10th phase, in " based on the three-dimensional facial reconstruction method and the improvement thereof of deformation model " literary composition of delivering on the 91-99 page or leaf, be that three-dimensional model is launched equally, obtain the distortion of correspondence markings point with the method that resamples, thereby realize the registration of three-dimensional face model.

Such expansion is more suitable for desirable cylinder model, but also occurs distortion inevitably.If not desirable cylinder, the two dimensional image that then obtains has overlapping, and when reducing once more, a part of information of model must be lost, and effect is undesirable.Simultaneously, need a large amount of computing times owing to launch and reduce, make counting yield also wordy, on-line performance reduces greatly.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of method with directly performing three-dimensional model transformation with three-dimensional bench marks is proposed, make it not need three-dimensional model is launched into two dimensional image, be reduced to these redundant steps of cylinder three-dimensional model after utilizing the two-dimensional marker point deformation again, but can be on model the three-dimensional feature point that needs of mark, directly carry out model deformation.Experiment showed, that the present invention has saving operation time, improve operational precision, reduce because many-sided advantages such as aliasing error that two-dimensional development brings.

The present invention is achieved by the following technical solutions: adopt based on improved thin plate spline (Thin-plateSpline) elasticity interpolation algorithm, three-dimensional gauge point with same feature and number calculates each coordinate of model, obtains the corresponding three-dimensional coordinate points of new model; Texture or RGB information remain unchanged simultaneously, have guaranteed the out of Memory of original model like this, are unlikely to distortion.

The present invention specifically may further comprise the steps:

(1) normalization vertex data.Here relate to projection matrix, model matrix, viewing matrix etc.In order to keep the accuracy and the consistance of the three-dimensional gauge point in back, must be to [1,1] scope with the original vertices data normalization.Here can be that 2 cube retrains with a length of side;

(2) point of obtaining on the screen is converted into world coordinates.According to the ask for something that transforms, preserve viewing matrix, model matrix and the projection matrix (matrix size is 4 * 4) of model this moment.In order to realize the corresponding relation of coordinate in screen coordinate and the frame buffer, with the screen Y coordinate " supplement " (promptly according to viewing matrix, trying to achieve according to the lower left corner is the three-dimensional Y coordinate of initial position) that obtains this moment.Again current frame buffer is read in internal memory (reading in pixel format is depth component).The last mapping according to three matrixes that obtain before this obtains three-dimensional coordinate point;

(3) get a little, preserve three-dimensional gauge point.Similarly, can obtain gauge point on the another one model correspondence position.The feature of gauge point and number must be consistent with the gauge point of model that will be to be out of shape;

(4) carry out elastic deformation with the thin-plate spline interpolation algorithm.All two-dimensional points all replace with three-dimensional point, and corresponding distance function, biharmonic function, the equal correct of function of asking for new coordinate points become the variable of three-dimensional coordinate, directly ask for new coordinate, and at this moment, distortion is finished.What adopt here is through the thin plate spline algorithm after improving, and is used for directly carrying out 3 D deformation.

The present invention's directly performing three-dimensional model transformation with three-dimensional bench marks, the method with respect to cylinder unwrapping becomes two dimensional image to be out of shape has following advantage: save operation time; Improve operational precision; Reduce because the aliasing error that two-dimensional development brings.

Description of drawings

Fig. 1 is the inventive method block diagram

Embodiment

As shown in Figure 1, realize method, need four steps with directly performing three-dimensional model transformation with three-dimensional bench marks:

1. normalization vertex data

This step is to get for next step screen a little to be converted into three-dimensional coordinate and to prepare.To the x of three-dimensional system of coordinate, y, the z component is sought the maximal value of absolute value respectively, formula below utilizing:

$X_{\mathrm{new}}=\frac{X_{\mathrm{ori}}}{{\left|X\right|}_{\max }},Y_{\mathrm{new}}=\frac{Y_{\mathrm{ori}}}{{\left|Y\right|}_{\max }},Z_{\mathrm{new}}=\frac{Z_{\mathrm{ori}}}{{\left|Z\right|}_{\max }}$

Vertex data all is limited between [1,1].Like this, each all normalization of group coordinate with the depth coordinate that obtains later (system exports between [1,1]) correspondence, can directly be used as world coordinates after the inverse transformation.

2. the point of obtaining on the screen is converted into world coordinates

This step can be utilized the inversion among the OpenGL to bring and obtain world coordinates (three-dimensional coordinate).For this reason, obtain viewing matrix, model matrix and the projection matrix (matrix size is 4*4) of current model in advance.Because screen coordinate is to be initial point with the upper left corner, and the coordinate in the frame buffer is to begin with the lower left corner, in order to realize the corresponding relation of coordinate in screen coordinate and the frame buffer, the screen Y coordinate " supplement " that must be obtained this moment (, utilizing " viewport coordinate-current screen coordinate Y component-1 " to try to achieve the needed Y coordinate of inverse transformation) promptly according to the screen viewport.Again current frame buffer is read in internal memory (reading in pixel format is depth component), can obtain the depth value of correspondence position.

This depth value is in [1,1] scope.Last obtain three-dimensional coordinate point with the inverse transformation mapping according to the data in three matrixes that obtain before this and the present frame buffer memory.

3. get a little, preserve three-dimensional gauge point

As Fig. 1 right side, can obtain the gauge point on the object module character pair similarly.The feature of gauge point and number must be consistent with the gauge point of model to be out of shape;

4. carry out elastic deformation with the thin-plate spline interpolation algorithm

General elastic deformation algorithm relates to following three aspects:

1) in reference picture and image subject to registration, selects reference mark and determine their corresponding relation;

2) type and the parameter by known coordinate and reference mark decision mapping function;

3) treat registering images with mapping function and carry out geometric transformation.

Here, the present invention selects existing overall situation distortion, and the thin-plate spline interpolation algorithm of local deformation is also arranged.This arthmetic statement is as follows:

Thin plate spline is the instrument that is used for spaced point data set interpolation is obtained curved surface, is the elasticity interpolation, and it is modeled as the flexural deformation of metal sheet under a constraint with interpolation problem, represents the energy that is out of shape with terse algebraic expression.Thin plate spline obtains like this.

The basis function of thin plate spline is U (r)=r ²Logr ²

Wherein, $r=\sqrt{x^2+y^2}$

Can be regarded as the one dimension cubic spline function | the x3| natural expansion is to the result of two dimension.

Suppose to have a two-dimentional point set, (x ₁, y ₁), (x ₂, y ₂) ..., (x _n, y _n), be referred to as monumented point, make P _i=(x _i, y _i), i=1,2 ..., n defines r simultaneously _{I, j}=| P _i-P _j|, be a P _iWith a P _jEuclidean distance.

Definition n * n matrix

And n * 3 matrixes $P=\left|\begin{array}{ccc}1& x_1& y_1\\ 1& x_2& y_2\\ .& .& .\\ .& .& .\\ .& .& .\\ 1& x_n& y_n\end{array}\right|$

$L=\left|\begin{array}{cc}K& P\\ P^T& 0\end{array}\right|$

0 represent 3 * 30 matrix, P at this ^TIt is the transposition of P.Want to make sheet metal at point (x _i, y _i) locate highly to be z _i, thereby make up row vector V=(z ₁, z ₂..., z _i) and column vector Y=(V000) ^T, dimension is (n+3) * 1.

By following formula definition column vector W=(w ₁, w ₂... w _n) and coefficient a ₁, a _x, a _y:

L ^-1Y＝(W|a ₁?a _x?a _y) ^T

The function that obtains requiring according to above definition:

$f(x,y)=a_1+a_{x}x+a_{y}y+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_{i}U(P_i-(x,y))$

For this reason, thin plate spline function is done following improvement: all two-dimensional points all replace with three-dimensional point, corresponding basis function, make up matrix, variable that the equal correct of function of asking for new coordinate points becomes three-dimensional coordinate.Like this, the gauge point of getting by three-dimensional just now, directly new coordinate is asked in substitution.At this moment, distortion is finished.

This method is equally applicable to the radial basis function of other type, as linear interpolation, Gauss interpolation, many surface interpolations etc.Utilizing direct three-dimensional point to carry out interpolation, eliminated because the data distortion that the two-dimensional coordinate expansion causes has also been saved operation time greatly, is more satisfactory deformation method.

Use the present invention can realize data processing such as the registration of three-dimensional model or surface transformation.With the registration is example, if 100 three-dimensional face models are arranged, needs realization point-to-point to deserved registration, then can realize with the method in our bright.At first these 100 models are averaged, obtain average face model.At 60 three-dimensional gauge points of this averaging model subscript (as eyes, eyebrow, lip etc.), as the target label point of all model deformations.Each faceform is got equally 60 corresponding gauge points, this 2 group echo point is as the P, the V vector data that improve the back thin plate spline again.Try to achieve the faceform's who needs registration new three-dimensional coordinate at last with the thin plate spline algorithm.So 100 models are all done this type of distortion, can obtain with the gauge point is corresponding registration model.Can find, the three-dimensional registration model of Huo Deing like this, basic configuration does not change, and only model press the direction variation of gauge point, and what obtain is the model of the more satisfactory point-to-point correspondence of effect.

Claims (4)

1, a kind of method with directly performing three-dimensional model transformation with three-dimensional bench marks is characterized in that, may further comprise the steps:

(1) normalization vertex data relates to projection matrix, model matrix, viewing matrix, in order to keep the accuracy and the consistance of the three-dimensional gauge point in back, to [1,1] scope, is that 2 cube retrain with a length of side with the original vertices data normalization;

(2) point of obtaining on the screen is converted into world coordinates, preserve viewing matrix, model matrix and the projection matrix of model this moment, matrix size is 4 * 4, in order to realize the corresponding relation of coordinate in screen coordinate and the frame buffer, with the screen Y coordinate " supplement " that obtains this moment, again internal memory is read in current frame buffer, the last mapping according to three matrixes that obtain before this obtains three-dimensional coordinate point;

(3) get a little, preserve three-dimensional gauge point, in like manner, obtain the gauge point on the another one model correspondence position;

(4) carry out elastic deformation with the thin-plate spline interpolation algorithm, all two-dimensional points all replace with three-dimensional point, and corresponding distance function, biharmonic function, the function of asking for new coordinate points all are modified as the variable of three-dimensional coordinate, directly obtain new coordinate, at this moment, distortion is finished.

2, the method with directly performing three-dimensional model transformation with three-dimensional bench marks according to claim 1, it is characterized in that described screen Y coordinate " supplement " is meant: according to viewing matrix, trying to achieve according to the lower left corner is the three-dimensional Y coordinate of initial position.

3, the method with directly performing three-dimensional model transformation with three-dimensional bench marks according to claim 1 is characterized in that, described internal memory is read in frame buffer, and reading in pixel format is depth component.

4, the method with directly performing three-dimensional model transformation with three-dimensional bench marks according to claim 1 is characterized in that, described gauge point, and its feature and number must be consistent with the gauge point of model to be out of shape.

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