JP2008261662A - Three-dimensional shape restoration device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To execute factorization even if low-reliability data exist in an observation matrix (a feature-point position series), as to a three-dimensional shape restoration device. <P>SOLUTION: In factorizing the observation matrix W, a reliability matrix Q is used which expresses the reliability (variance of probability distribution (normal distribution) expressing the position of a feature point) of respective observation values x<SB>t</SB>constituting the observation matrix W. By causing the variance Σ<SB>s</SB>of test distribution q(S) of a shape matrix to reflect the reliability matrix Q, factorization is performed in which the higher the reliability of feature points is, the more they are emphasized. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a three-dimensional shape restoration apparatus that restores a three-dimensional shape of a target object from an image (two-dimensional shape) obtained by photographing the target object.

  Conventionally, an image sequence obtained by capturing a target object is input, the positions of the feature points of a plurality of feature points set in advance for the target object are tracked on the image plane, and the feature point position sequence obtained by the tracking is used. A factorization method is known as one of methods for restoring the three-dimensional shape of a target object.

  This factorization method generates an observation matrix from a feature point position sequence, and converts the observation matrix into a shape matrix that represents the shape of the target object (three-dimensional position of the feature point) and a motion matrix that represents the motion of the target object. It is factorized.

  However, since the factorization method cannot obtain effective results unless all the data that make up the observation matrix is available, the feature point position series (and thus the observation matrix) may be affected by feature point hiding, mistracking, frame out, etc. There is a problem that it is very difficult to apply to actual problems in which loss of data) is frequently generated.

On the other hand, remove the missing data from the observation matrix and perform factorization calculation, or generate a partial observation matrix by removing the missing data from the observation matrix, and factorize the partial observation matrix A method has been proposed in which missing data is estimated from a shape matrix and a motion matrix obtained by performing the above, and factorization is performed using an observation matrix in which the missing data is replaced by the estimated value (see, for example, Patent Document 1). .
Japanese Patent No. 3711203

  However, in the conventional method, when generating an observation matrix, it is necessary to distinguish between normal data and abnormal data. However, since the identification is difficult, automatic processing is difficult and sufficient accuracy is obtained. There is a problem that there is no problem, a procedure for removing identified abnormal data, a procedure for repeatedly estimating missing data, and the like, resulting in an increase in the amount of necessary computation.

  In addition, in the conventional factorization method, in order to improve the estimation accuracy of the three-dimensional shape, it is necessary to increase the number of image sequences used for the calculation (that is, to increase the dimension of the observation matrix). The quantity (calculation time) increases exponentially.

  And when the amount of calculation increases, there is a problem that it becomes difficult to apply when there is a limit to the calculation capability of an arithmetic unit that can be used, such as when a three-dimensional shape restoration device is mounted on a vehicle. It was.

  In order to solve the above problems, the present invention makes it possible to perform factorization in a three-dimensional shape restoration apparatus even if data with low reliability exists in an observation matrix (feature point position series). Furthermore, it aims at reducing calculation time.

  In the three-dimensional shape restoration apparatus of the present invention made to achieve the above object, the observation matrix generation means inputs an image sequence obtained by photographing the target object, and sets the positions of a plurality of feature points preset for the target object. A position reliability evaluation value indicating the reliability of the position of the feature point for each feature point by generating an observation matrix that is tracked on the image plane and generating a time series of the positions of the feature points. Is generated.

  Then, the decomposition means factorizes the observation matrix generated by the observation matrix generation means to generate a shape matrix representing the three-dimensional shape of the target object and a motion matrix representing the motion of the target object. At this time, the decomposition means performs factorization that places importance on feature points having high position reliability evaluation values.

  That is, in the three-dimensional shape restoration apparatus of the present invention, it is possible to apply a feature point with high reliability (position reliability evaluation value) without removing feature points with low reliability due to noise superimposition or the like. Factorization is performed to improve.

  Therefore, according to the three-dimensional shape restoration apparatus of the present invention, even if it exists in unreliable data or observation matrix based on hiding, mistracking, frame-out, etc. of feature points, it is unnecessary to remove this. Therefore, factorization can be reliably executed without requiring a simple procedure, and more reliable data is emphasized. Therefore, the accuracy of the generated shape matrix and motion matrix can be improved.

  In the present invention, as described in claim 2, the decomposition means has a distribution in which the observation matrix is W, the motion matrix is M, the shape matrix is S, and the values of the elements of the matrix X are stochastically indicated. As represented by q (X), the likelihood P (W |) is based on a Bayesian estimation formula that defines the relationship between the posterior probability P (M, S | W) and the likelihood P (W | M, S). The test distribution q (M) of the motion matrix M that maximizes M, S) and the test distribution q (S) of the shape matrix S are reflected in the variance of the test distribution q (S) of the shape matrix. Further, the factorization calculation may be executed probabilistically by obtaining the above.

  According to the three-dimensional shape restoration apparatus of the present invention configured as described above, since the motion matrix M and the shape matrix S are obtained probabilistically by Bayesian estimation, the position of the feature point tracked on the image plane is determined. The influence of superimposed noise can be greatly reduced, and the reliability evaluation value is reflected in the variance of the test distribution q (S) of the shape matrix. Therefore, emphasis is placed on feature points with high reliability evaluation values. Factorization can be realized.

  Then, when factorization using Bayesian estimation is performed in this way, the decomposition means, as described in claim 3, the estimation means fixes the motion matrix test distribution q (M) and tests the shape matrix. The first step of estimating the distribution q (S) and the second step of estimating the test distribution q (M) of the motion matrix by fixing the test distribution q (S) of the shape matrix are mutually estimated results. Are repeatedly executed alternately, and the end means terminates the estimation means when the preset end condition is satisfied, and the finally obtained shape matrix test distribution q (S) is the shape As a matrix distribution, the shape matrix may be obtained from the shape matrix distribution.

In this case, the decomposition means implements a variational Bayesian estimation method, and the first step corresponds to the E step and the second step corresponds to the M step.
However, even if the variational Bayesian estimation method is used, it should be avoided that the calculation amount (calculation time) increases exponentially in accordance with the increase of the image sequence used for the calculation (that is, the increase of the dimension of the observation matrix). I can't.

  Therefore, as described in claim 4, the decomposition means fixes the motion matrix test distribution q (M) each time the estimation means generates the observation matrix and the shape matrix. A first step of estimating the test distribution q (S) of the movement matrix, and a second step of estimating the test distribution q (M) of the motion matrix by fixing the test distribution q (S) of the shape matrix. The update unit updates the shape matrix distribution to be output based on the shape matrix test distribution q (S) estimated by the estimation unit, and the end unit is preset. When the termination condition is satisfied, it is desirable that the estimating unit and the updating unit are terminated, and the shape matrix is obtained from the distribution of the shape matrix finally obtained by the updating unit.

  In other words, the estimation means limits the image series used for the calculation, executes the first step (E step) and the second step (M step) once, repeatedly executes this, and from the estimation means Each time a calculation result is obtained, the distribution of the shape matrix is updated based on the calculation result. This realizes the variational Bayesian estimation method by sequential calculation (so-called online).

  Thus, according to the three-dimensional shape restoration apparatus of the present invention, the image sequence to be used is divided into a plurality of parts, and factorization is performed for each of the divided image sequences. Since it only increases incrementally in units of one process in the estimation means and does not increase exponentially, the processing load required for factorization (and thus the time required for processing) can be greatly reduced. it can.

  In addition, as described above, when the decomposition unit is configured to perform factorization by the variational Bayes estimation method, as described in claim 5, the energy calculation unit performs the test distribution q by the estimation unit. Each time the estimation results of (S) and q (M) are obtained, the free energy related to the test posterior distribution q (S, M) = q (S) q (M) is calculated, and the ending means is energy calculating means. The calculation result may be set to be larger than a preset energy threshold as an end condition.

  Originally, the variational Bayesian estimation method estimates the motion matrix and the shape matrix so that the free energy is maximized. Therefore, using this free energy as the termination condition ensures the shape matrix with the desired accuracy. Can be obtained.

  Further, as described in claim 6, the ending means sets the ending condition that the number of times the estimation means calculates the test distribution q (S) of the shape matrix is larger than a preset number threshold. It may be configured.

In this case, since it is not necessary to calculate free energy, the processing load on the apparatus can be further reduced, and the processing can always be terminated within a certain time.
By the way, as described in claim 7, the reliability evaluation unit may be configured to use a variance value of the distribution of the observation matrix as the position reliability evaluation value. In particular, when feature points are tracked using Bayesian estimation, the distribution value of the distribution of feature point positions (each element of the observation matrix) is always calculated. Can be reduced.

And the said three-dimensional shape decompression | restoration apparatus may be comprised so that it may mount and use for a motor vehicle, as described in Claim 8.
An arithmetic unit mounted on an automobile generally has a low calculation capability, but can be applied even in such a case.

Embodiments of the present invention will be described below with reference to the drawings.
[First Embodiment]
FIG. 1 is a block diagram showing an overall configuration of an image processing apparatus 1 as a three-dimensional shape restoration apparatus to which the present invention is applied. The image processing apparatus 1 is mounted on a vehicle and executes processing for obtaining a head posture in time series, which is information for detecting a driver's sidewalk, doze, or the like from an image obtained by photographing the driver's head. Device.

<Overall configuration>
The image processing apparatus 1 is installed on the front upper portion or lower portion (for example, in a meter) of the driver seat, and acquires a camera 2 that acquires an image including the driver's head as shown in FIG. When an image capture device 3 to be captured and an initialization command are input, a plurality ((t represents time)) of the facial features of the driver are represented from the input image z _t captured via the image capture device 3 (t represents time). N _f feature point positions (two-dimensional coordinates on the image plane: hereinafter referred to as feature point positions) p ⁽ⁿ⁾ (n = 1, 2,... N _f ) are extracted. When, for each of the feature points initial feature point extracting unit 4 is extracted position p ^(n), cutting out an image of predetermined size centered at characteristic points position p ⁽ⁿ⁾ as a template tp ⁽ⁿ⁾ Template generation / storage unit 5 to be stored and the three-dimensional position of feature points ( Based on the input model z _t , template tp ⁽ⁿ⁾ , and face model C _a , the time model supply unit 6 that supplies _a face model (shape matrix) C _a that defines the three-dimensional shape of the head) by performing the series Bayesian estimation, the estimated affine parameters a _t representing the head posture, feature points estimated distribution parameters for defining the distribution of positions of the feature points calculated in the course of the estimated (mean x _t, the variance V _t), the estimation unit 8 supplies the face model supply unit 6, according to the affine parameters a _t the estimation unit 8 estimates, head posture [theta] x, [theta] y, the head orientation calculation unit that calculates the θz It is composed of nine.

Among these, the initial feature point extraction unit 4 extracts the corners of the eyes, the eyes, the mouth, the nose (the nostrils, the center of the nose, the right and left ends of the nose) and the like as the feature points, as shown in FIG. However, in this embodiment, it is assumed that 7 (= N _f ) points are extracted from the left and right eye corners, left and right eye heads, left and right mouths, and the center of the nose. The initialization command is input by an operation of the driver when the camera 2 captures an image in which all the feature points are reflected (no feature points are hidden).

Specifically, the template tp ⁽ⁿ⁾ generated by the template generation / storage unit 5 is as shown by a dotted white frame in FIG. However, in the figure, only the left mouth, the center of the nose, and the left eye corner are shown.

The face model C _a supplied from the face model supply unit 6, the feature point is intended to define the position of the three-dimensionally in (each vertex of the diagram shown in FIG. 2 (b)), shown in FIG. 3 As described above, the horizontal coordinate axis on the image plane is the u axis, the vertical coordinate axis is the v axis, the horizontal coordinate axis in the three-dimensional space is the X axis, the vertical coordinate axis is the Y axis, and the optical axis direction (depth direction). The coordinate axis is represented by the equations (1) and (2) with the Z axis. However, s ⁽ⁿ⁾ is within the three-dimensional space of the ^nth feature point (feature point position p ⁽ⁿ⁾ = (u ⁽ⁿ⁾ , v ⁽ⁿ⁾ )) extracted by the initial feature point extraction unit 4. Coordinates.

Then, affine parameters A _t estimated by the estimating unit 8, a coordinate transformation in the real world (three-dimensional XYZ space), expressed as a coordinate transformation on the image plane is a projection plane (two-dimensional uv plane) This is a conversion matrix used at the time, and has the relationship shown in equations (3) and (4).

However, the three-dimensional coordinates of a certain feature point are (X, Y, Z) ^T , the three-dimensional coordinates after coordinate transformation are (X ′, Y ′, Z ′) ^T , and these three-dimensional coordinates are projected onto the image plane. Two-dimensional coordinates, that is, the coordinates of feature points on the image plane are (u, v) ^T and (u ′, v ′) ^T , and X = u, Y = v (that is, X ′ = u ′, Y ′ = v ′).

Then, the head posture calculation unit 9 calculates the three-axis angles θx, θy, and θz of the head using equations (5) to (7) as head posture information.

That is, Rx is a transformation matrix that rotates three-dimensional coordinates about the X axis by the angle θx, Ry is a transformation matrix that rotates the Y axis about the angle θy, and Rz is a transformation matrix that rotates the Z axis about the angle θz. If the three-dimensional coordinates are moved from (X, Y, Z) ^T to (X ′, Y ′, Z ′) ^T by applying these transformation matrices Rt (= RxRyRz), these relationships are , (8) and (9).

Further, in addition to the above rotation, when taking into account the transformation that translates the three-dimensional coordinates by t _{1 on} the X-axis, t _{2 on} the Y-axis, and t _{3 on} the Z-axis, the conversion formula is expressed by equation (10). The

Then, by comparing the equations (3) and (10), the correspondence between the affine parameters a _{1 to} a ₈ and the elements r _{1 to} r ₆ , t ₁ , t ₂ of the transformation matrix shown in the equation (10). Relations are obtained, and the relational expressions shown in (11) to (18) are obtained by rearranging the formula (9).

That is, the equations (5) to (7) are derived from these equations (11) to (18).

Then, as long obtained affine parameters A _t representing the head posture at the time t, the affine parameters A _t the be to act on the face model C _a, the position of the hidden feature points not appearing in the image at time t In addition, the positions of all feature points at time t can be predicted.

Further, such a affine parameter A _t, camera parameters (the focal length of the camera, location, orientation, etc.) can be reflected all the changes in the head pose of and driver.
<Configuration of estimation unit>
Here, FIG. 4 is a graph showing a state space model handled by the estimation unit 8.

As shown in FIG. 4, the estimation unit 8, and the upper layer obtained as hidden state affine parameter a _t representing the orientation of the face model at time t, the feature points at time t the position x _t = ^(x _t ^{(1 )} , X _t ⁽²⁾ ,..., X _t ^(Nf) ) N _f lower layers (only one is shown in the figure) provided for each feature point for which ^T is determined as a hidden state These hidden states A _t and x _t are estimated by time series Bayesian estimation from the input image sequence z _{1: t} input from 1 to t.

  As shown in FIG. 5, time-series Bayesian estimation treats all state variables as random variables, obtains a predicted distribution at time t from an estimation result (estimated distribution) at time t-1 regarding the hidden state, and By repeating the procedure of obtaining the likelihood (likelihood) that is the hidden state to be detected from the observation data and obtaining the estimation result (estimation distribution) at time t in consideration of these prediction distribution and likelihood, The hidden state is estimated.

That is, in the estimation unit 8, the input image sequence (the observed data) z _1: based on _t, affine parameters a posteriori probability distribution estimated the A _t (hidden state of the head pose) (estimated distribution) p (A _t | z _{1: t} ), which is expressed by equations (19) and (20).

_{Here, p (A t | z 1} : t-1) is the prior probability distribution (predictive distribution) of affine parameters _{A t, p (x t |} A t, z 1: t-1) is the position of the feature point group prior probability distribution of x _t (prediction _{distribution), p (x t | a} t, z 1: t-1), p (z t | x t) represents the likelihood.

Then, the lower layer estimates the part of equation (20) using a particle filter, and the upper layer estimates the part of equation (19) using a Kalman filter.
When the probability distribution of a certain parameter f follows a Gaussian distribution (normal distribution), the probability distribution can be expressed by equation (21), where the average is μ and the variance is Σ. In other words, in this case, the calculation of the probability distribution of parameters is actually sufficient if the average μ and variance Σ are obtained.

Next, FIG. 6 is a block diagram showing a specific configuration of the estimation unit 8.

As shown in FIG. 6, the estimation unit 8 includes N _f trackers BK ⁽ⁿ⁾ provided for each ^(Nf) feature point, and each tracks the position x ⁽ⁿ⁾ of one feature point. A feature point tracking unit 10 that generates a feature point estimation distribution parameter (mean, standard deviation) that defines a probability distribution obtained by Gaussian approximation of the probability distribution obtained by estimating the position x _t ⁽ⁿ⁾ of the feature point at time t; based on the calculated feature points estimated distribution parameters at each tracker BK ^(n), the predicted value a _{t + 1} of the affine parameter a _t and the affine parameter by using a Kalman filter, the variance V _{t + 1} (hereinafter, the predicted value The affine parameter calculation unit 30 for calculating the affine parameter calculation unit 30, the predicted value holding unit 40 for storing the predicted value of the affine parameter calculated by the affine parameter calculation unit 30, and the time stored in the prediction value holding unit 40 calculated at t-1 The position x _t (= (x _t ⁽¹⁾ , x _t ⁽²⁾ ,..., X _t ^(Nf) ) ^T ) of the feature point group at time t is predicted based on the predicted value of the affine parameter. A prediction distribution parameter calculation unit 41 that calculates upper prediction distribution parameters (average value, variance) that define the probability distribution p (x _t | A _t ) and supplies them to each of the trackers BK ⁽ⁿ⁾ . .

In other words, the affine parameter calculation unit 30 corresponds to the above-described upper layer, and each tracker BK ⁽ⁿ⁾ constituting the feature point tracking unit 10 corresponds to the above-described lower layer.
In addition, since the specific structure which implement | achieves such an estimation part 8 is explained in full detail, for example in Japanese Patent Application No. 2005-368124 etc., the description about the detail is abbreviate | omitted here, and is a feature point below. Only the outline of the tracker BK ⁽ⁿ⁾ related to the generation of the estimated distribution parameter will be described.

<Outline of tracker>
First, the tracker BK ⁽ⁿ⁾ constituting the feature point tracking unit 10 tracks one feature point using a particle filter. Here, an outline of the operation of the particle filter will be described with reference to an explanatory diagram shown in FIG.

  As shown in FIG. 7, in the particle filter, the actual value (coordinates on the image plane) of the target state (feature point position) to be estimated is represented by particles, and the three processes of prediction, observation, and resampling are executed repeatedly. By doing so, the particle distribution is obtained in time series. Note that, unlike the Kalman filter, the particle filter is not limited to the Gaussian distribution but can be an arbitrary probability distribution.

  First, in the prediction process, taking into account the motion of the target to be estimated, the state of each particle (here the position on the image plane) in the state space (here on the image plane) is transitioned, and the motion of the target to be estimated Particles are placed at positions where the target to be estimated is likely to exist by randomly scattering particles in consideration of the noise added to the. As a result, the probability distribution predicting the state of the target to be estimated is discretely and approximately expressed by the position and number of the particle group.

  Next, in the observation process, the likelihood that the state of each particle is the target state to be estimated (in this case, the normalized correlation value with the template representing the feature point) is calculated, and the weight of the particle is calculated according to the likelihood. To do. Thus, the probability distribution of the target state to be estimated is expressed by the weighted particles.

  Also, in the resampling process, the probability distribution of the target state to be estimated is weighted from the representation by weighted particles by erasing the weighted particles and multiplying the weighted particles to multiple unweighted particles. Probabilistic conversion to representation with non-particles.

  Then, by performing the above prediction process using the resampled particles (generated in the resample process), the probability distribution of the target state to be estimated represented by the particles can be obtained in time series. .

Here, the number of particles is N _p , the coordinates of the particles on the image plane are p _i = (u _i , v _i ), and the weight of the particles calculated according to the likelihood in the observation process is w _i (i = 1, 2,..., N _p ), the probability distribution of the target state to be estimated (that is, the position of the feature point) obtained by observation is the average value shown in the equations (22) and (23), and (24 ) Expressed by the dispersion value shown in the equation (25).

That is, the average value of the probability distribution representing the position of the nth feature point at time t is x _t ⁽ⁿ⁾ = (x ⁽ⁿ⁾ , y ⁽ⁿ⁾ ), and the variance is V _t ⁽ⁿ⁾ = (V _x ^{( n)} , V _y ⁽ⁿ⁾ ), x _t = (x _t ⁽¹⁾ , x _t ⁽²⁾ ,..., x _t ^(Nf) ), V _t = (V _t ⁽¹⁾ , V _t ^{(2 ) _{), ..., V t (Nf}} )) is, as a feature point estimation distribution parameter, to be supplied to the face model supply unit 6 at each time t.

<Face model supply department>
Next, the face model supply unit 6 which is a main part of the present invention will be described in detail.
As shown in FIG. 1, the face model supply unit 6 extracts feature points from the images of a plurality of persons whose heads are photographed, and arranges the average feature points set based on the extracted results. The average face model storage unit 61 that stores the average face model S _A that is activated and activated when an initialization command is input, and is based on the feature point estimation distribution parameters x _t and V _t that are sequentially supplied from the estimation unit 8. the personal face model S _P representing the arrangement of the feature point of the object to the camera 2 (the driver), learning and personal face model learning unit 62 for generating, in accordance with the switching signal from the personal face model learning unit 62, the average face model storage Face model switching which selects either the average face model S _A stored in the unit 61 or the individual face model S _P generated by the individual face model learning unit 62 as the face model C _a and supplies it to the estimation unit 8 Part 63.

<Summary of learning>
The personal face model learning unit 62 performs learning by the following method.
That is, the shape matrix representing the three-dimensional shape to be obtained (that is, the individual face model S _P ) is S, the observation matrix generated based on the sequence of feature point estimation distribution parameters x _t is W, and the motion of the shape matrix S is represented. If the motion matrix is M, these have the relationship W = MS. The likelihood P (W | M, S) is maximized based on a Bayesian estimation formula that defines the relationship between the posterior probability P (M, S | W) and the likelihood P (W | M, S). The motion matrix M and the shape matrix S are estimated by obtaining the motion matrix test distribution q (M) and the shape matrix test distribution q (S).

  This is equivalent to obtaining M and S that maximize the free energy F [q (M, S)] defined in the equation (26). Specifically, the equations (27) and (28) are expressed as follows. It only has to be solved.

However, since this calculation cannot be solved easily, the expression (29) is established (that is, an independent occurrence probability is assumed for the motion matrix M and the shape matrix S), and the model structure (the shape matrix S). ) And the occurrence probability of the motion structure (motion matrix M) are calculated by applying a so-called variational Bayes method, assuming that they follow a normal distribution.

Thereby, since the distribution to be obtained also follows the normal distribution, the problem to be solved can be simplified such as optimization of the feature point estimation distribution parameters x _t and V _t representing the shape of the distribution.

  Then, in the E step of the variational Bayes method, the calculation of maximizing free energy may be performed after fixing the distribution q (M) of the motion matrix. Eventually, the equations (27) and (28) are modified ( (30) What is necessary is just to perform calculation of (32) Formula obtained by solving the equation which consists of (31) Formula using the Lagrange's undetermined multiplier method. However, ^ (hat) given to a symbol in the equation represents an updated value (the same applies hereinafter).

Similarly, in the M step of the variational Bayes method, the calculation of maximizing the free energy may be performed after fixing the distribution q (S) of the shape matrix. Eventually, the equations (27) and (28) were modified. (33) The equation (35) obtained by solving the equation (34) using the Lagrange's undetermined multiplier method may be executed.

<Processing in the personal face model learning unit>
Here, the process executed by the individual face model learning unit 62 will be described with reference to the flowchart shown in FIG. Note that this process is started by inputting an initialization command.

However, the three-dimensional coordinates s ^{(n) of} the ^nth feature point, the shape matrix S representing the three-dimensional shape to be obtained, and the homogeneous shape matrix to S obtained by adding the row vector of all 1 elements to the shape matrix S (36 ) To (38). The average face model S _A and individual facial model S _P is assumed to be expressed in the form of homogeneous shape matrix to S.

Further, the i-th basis vector of motion as m _i, movement matrix M, the following motion matrix ~M, theta, as represented by a row vector theta _d of d-th motion matrix (39) - (42) below To do.

When this process is started, first, in S110, a switching signal is output so as to select the average face model S _A as the face model C _a that the face model switching unit 63 supplies to the estimation unit 8, and the process proceeds to S120.

Thus, the estimation unit 8, for each time t on which an image is inputted, the average face model S affine parameter using _A A _t, and the feature point estimation distribution parameter x _t, the calculation of V _t is performed. Further, the head posture calculating portion 9, on the basis of the affine parameters A _t obtained by estimating portion 8, head posture [theta] x, [theta] y, the calculation of θz performed.

In S120, the motion matrix test distribution q (M) is initialized, and the process proceeds to S130.
The shape matrix test distribution q (S) is defined by the shape matrix S and Σ _S (hereinafter referred to as the shape matrix distribution parameter) representing the variance, and the motion matrix test distribution q (M) is the motion matrix. Θ and VΘ representing the variance (hereinafter referred to as motion matrix distribution parameter). The motion matrix distribution parameters Θ and VΘ are set to the same constant value (for example, 0, 1 or 0.5) by this initialization.

In S130, it is determined whether or not the acquisition of the preset predetermined number T of feature point estimation distribution parameters x _t and V _t is completed. If not completed, the process waits until completion.
When the acquisition of the predetermined number T of feature point estimation distribution parameters x _t and V _t is completed, the process proceeds to S140, and the observation matrix W and the reliability matrix are based on the acquired feature point estimation distribution parameters x _t and V _t. Q is generated and the process proceeds to S150.

Note that the position (two-dimensional coordinates on the image plane) of the nth (n = 1, 2,..., N _f ) th feature point is created based on the acquired feature point estimation distribution parameter x _t in time series ( Assuming that the feature point vectors x _{1: T} ⁽ⁿ⁾ arranged in t = _{1 to T} ⁾ are expressed by the equation (43), the observation matrix W is expressed by the equation (44). That is, the observation matrix W is configured by arranging feature point vectors x _{1: T} ⁽ⁿ⁾ as column vectors and arranging them for all feature points.

The reliability matrix Q is created based on the feature point estimation distribution parameter V _t , where d = 2t−1 represents the x component at time t, d = 2t represents the y component at time t, and the nth feature point Assuming that the d-th (d = 1, 2,..., 2T) observation reliability is represented by σ _{x, d} ⁽ⁿ⁾ , it is expressed by the equation (45). That is, the reliability matrix Q has the same order as the observation matrix W.

In S150, the variation matrix Bayes E step for calculating the shape matrix test distribution q (S) is executed, and the process proceeds to S160.

More specifically, in S150, the feature points are based on W and Q obtained in S140 and the latest motion matrix distribution parameters Θ and VΘ initially set in S120 or updated in S160 described later. (n = 1 to n _f) for each, using the following (46) (47) where, s ^(n), by determining the sigma _s ^(n), the distribution parameter S shape matrix, update the sigma _s To do. Note that I _k is a k-th order unit matrix.

However, the equations (46) and (47) are obtained by solving (48), which is the rewrite of the equation (32) using the three-dimensional coordinates s ⁽ⁿ⁾ and the variance Σ _s ⁽ⁿ⁾ of the feature points. Specifically, the calculation is executed using the equations (49) to (56).

In S160, the process as the variational Bayes M step for calculating the motion matrix test distribution q (M) is executed, and the process proceeds to S170.

In this S160, specifically, W obtained in S140, Q, and distribution parameters S of the latest shape matrix set by S150, sigma based on the _S, each row vector theta _d motion matrix Then, using the following equations (57) and (58), θ _d and V _d are obtained to update the motion matrix distribution parameters Θ and VΘ. However, when describing the expected value calculation, the description rule shown in the equation (59) is used.

However, the equations (57) and (58) are obtained by solving (60), which is a rewrite of the equation (35) using the three-dimensional coordinates s ⁽ⁿ⁾ and the variance Σ _s ⁽ⁿ⁾ of the feature points. Specifically, the calculation is executed using the equations (61) and (62).

In S170, based on the distribution parameters S, Σ _s (ie, test distribution q (S)) of the shape matrix and the distribution parameters Θ, VΘ (ie, test distribution q (M)) of the motion matrix calculated in S150 and S160. The free energy F [q (M, S)] is calculated using the above equation (26), and the process proceeds to S180.

  However, the free energy becomes larger as the position estimated based on the motion matrix M and the shape matrix S obtained by the above-described processing and the position obtained by observation (observation matrix W) are closer.

  In S180, it is determined whether or not the free energy calculated in S170 is larger than a preset energy threshold, and whether or not the termination condition is satisfied. If not, the process returns to S150. Then, the processes of S150 to S170 are repeated, and if the end condition is satisfied, the process proceeds to S190.

Here, as the energy threshold, for example, free energy calculated using a shape matrix representing the average face model S _A and the motion matrix M obtained by the above-described processing is used. However, the energy threshold is not limited to this, and may be any fixed value.

In S190, and outputs a finally obtained shape matrix S by the above-described process as an individual face model S _P, as face model C _a supply face model switching unit 63 is in the estimation unit 8, the personal face model S _P The switching signal is output so as to select and the present process is terminated.

Thus, hereafter, the estimation unit 8, for each time t on which an image is inputted, the calculation of the affine parameters A _t with individual facial model S _P is performed, further, on the basis of the affine parameter A _t, head The head posture calculation unit 9 calculates head postures θx, θy, and θz.

<Effect>
As described above, in the image processing apparatus 1, head posture [theta] x, [theta] y, immediately after starting the process of estimating the [theta] z, calculation of the affine parameters A _t using the average face model S _A (the face orientation estimation) In parallel with this, learning of the individual face model S _P is executed, and when the accuracy of the individual face model S _P is sufficiently improved, switching from the average face model S _A to the individual face model S _P is performed. Have been to do.

Therefore, according to the image processing apparatus 1, the estimation of the head postures θx, θy, and θz can be obtained from the initial stage of processing, regardless of who the driver is, and the estimation result with stable accuracy can be obtained. after switching from the average face model S _a to individual facial model S _P can be obtained estimation result of the high accuracy.

That is, when the individual face model S _P is used, the estimation accuracy is more likely to be improved than when the average face model S _A is used, but learning takes time, and if the calculation fails, the average face model S _A Although the error may be increased as described above, the image processing apparatus 1 can solve all of these problems.

In the image processing apparatus 1, since the switching from the average face model S _A to individual facial model S _P, it is determined using the free energy, after switching model is possible to reliably improve the estimation accuracy it can.

That is, individual face model S _P, since there is nothing that correct data, it is difficult to evaluate its accuracy quantitatively. However, when the observation matrix W is factorized into the motion matrix M and the shape matrix S, the factorization is performed so that the free energy is maximized. In other words, this means that the free energy quantitatively represents the degree to which the predicted values calculated from the motion matrix M and the shape matrix S are applied to the observed values (observed matrix W). Can do. Therefore, this free energy can be used as a reference for evaluating the accuracy of the face model.

In the image processing apparatus 1, when the observation matrix W is factorized, the reliability of each observation value x _t constituting the observation matrix W (the distribution of the probability distribution (normal distribution) representing the position of the feature point) is expressed. By using the reliability matrix Q and reflecting this in the variance Σ _s of the test distribution q (S) of the shape matrix (see formulas (43) to (53)), factorization that emphasizes higher reliability feature points Have been to do.

Therefore, according to the image processing apparatus 1, even if the observation value _xt having low reliability based on the hiding, mistracking, frame-out, etc. of the feature point exists in the observation matrix W, it is unnecessary to remove it. Therefore, factorization can be reliably executed without requiring a simple procedure, and more reliable data is emphasized. Therefore, the accuracy of the generated shape matrix and motion matrix can be improved.

Also, according to the image processing apparatus 1, when factorizing the observation matrix W, the variational Bayes method is applied to test distribution q (M) of the motion matrix M and test distribution q (S) of the shape matrix S. Since the factorization calculation is executed probabilistically, the influence of noise superimposed on the observation value x _t can be greatly reduced.

[Second Embodiment]
Next, a second embodiment will be described.
In the present embodiment, only a part of the processing contents in the personal face model learning unit 62 is different from that in the first embodiment, and thus this difference will be mainly described.

<Processing in the personal face model learning unit>
FIG. 8 is a flowchart showing the contents of processing executed by the individual face model learning unit 62.
As in the case of the first embodiment, this process is activated by the input of an initialization command, and S210 to S250 are the same as S110 to S150 of the first embodiment, and thus description thereof is omitted.

However, the specified number used in S230 may be a smaller number (for example, about a fraction to a fraction of a tenth) than in the first embodiment.
In S260, the process as a variational Bayes M step for calculating the test distribution q (M) of the motion matrix is executed, and the process proceeds to S270.

In S260, specifically, W, Q obtained in S240, distribution parameters S, Σ _S of the latest shape matrix set in S250, statistics calculated in the previous cycle (described later (66 ) (See equation (67)), for each row vector θ _d of the motion matrix, θ _d and V _d are obtained using the following equations (63) to (67), whereby the motion matrix distribution parameter is obtained. Θ and VΘ are updated.

In S270, the shape matrix S is updated using the equations (68) to (70) based on the statistics calculated in the previous cycle (see the equation (70) described later).

Hereinafter, S280 to S300 are the same as S170 to S190 of the first embodiment, and thus description thereof is omitted. However, in S290, if the end condition is not satisfied, the process returns to S230.

<Effect>
As described above, in the present embodiment, the order (that is, the specified number T) of the observation matrix W is limited to a small number, the E step and the M step are executed once, and the motion matrix test distribution p ( M) and the process of obtaining the shape matrix test distribution p (S) are repeated, and the so-called online variational Bayesian estimation method in which the results are multiplied by a coefficient that decreases the ratio as the past data is added. Used to perform factorization.

  Therefore, according to the present embodiment, even if the number of image sequences to be used is increased, the amount of processing increased by that is incremental with the processing amount when executing the E step and the M step once as a unit. Therefore, the processing load required for factorization (and thus the time required for processing) can be greatly reduced.

As a result, an arithmetic unit mounted on an automobile generally has a low calculation capability, but even in such a case, it can be applied without any problem.
[Other Embodiments]
Although the embodiment of the present invention has been described above, the present invention is not limited to the above-described embodiment, and can be implemented in various modes without departing from the gist of the present invention.

  For example, in the above embodiment, an affine parameter is used to estimate the head posture. If the head posture can be estimated, for example, an extended Kalman filter is used without using the affine parameter. For example, a method of directly performing head estimation may be employed.

Further, used as the end condition for terminating the factorization, the energy threshold of the free energy obtained from the average face model S _A, that free energy obtained from individuals face model S _P output in the training is larger than its energy threshold However, the energy threshold value may be a preset fixed value.

  Furthermore, instead of using free energy, the end condition may be that the number of repetitions of processing is greater than a preset number of times threshold. In this case, since it is not necessary to calculate free energy to determine whether or not to end the processing, the processing load on the device can be further reduced, and the processing is always performed within a certain time. Can be terminated.

  In the above embodiment, the factorization is performed by the Bayesian estimation method and the variational Bayesian estimation method. However, any method can be used as long as the reliability can be reflected in each element of the observation matrix W during the factorization. For example, factorization may be performed by singular value decomposition.

1 is a block diagram showing the overall configuration of an image processing apparatus to which the invention is applied. Explanatory drawing about a feature point and a template. Explanatory drawing which shows the coordinate system which an image processing apparatus uses. The graph showing the state space model which an estimation part handles. Explanatory drawing which shows the operation | movement outline | summary of time series Bayes estimation. The block diagram which shows the structure of an estimation part. Explanatory drawing which shows the operation | movement outline | summary of a particle filter. The flowchart which shows the processing content of the personal face model learning part in 1st Embodiment. The flowchart which shows the processing content of the personal face model learning part in 2nd Embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Image processing apparatus 2 ... Camera 3 ... Image capture apparatus 4 ... Initial feature point extraction part 5 ... Template production | generation / storage part 6 ... Face model supply part 8 ... Estimation part 9 ... Head posture calculation part 10 ... Feature point tracking Unit 30 ... Affine parameter calculation unit 40 ... Predicted value holding unit 41 ... Prediction distribution parameter calculation unit 61 ... Average face model storage unit 62 ... Individual face model learning unit 63 ... Face model switching unit BK ⁽ⁿ⁾ ... Tracker

Claims (8)

An image series obtained by photographing the target object is input, the positions of a plurality of feature points set in advance for the target object are tracked on the image plane, and an observation matrix is generated by arranging the positions of the feature points in time series. An observation matrix generating means;
Factorizing the observation matrix generated by the observation matrix generating means to generate a shape matrix representing the three-dimensional shape of the target object and a motion matrix representing the motion of the target object;
In a three-dimensional shape restoration apparatus equipped with
For each feature point, comprising a reliability evaluation means for generating a position reliability evaluation value representing the reliability of the position of the feature point,
The three-dimensional shape restoration apparatus, wherein the decomposition means performs factorization focusing on a feature point having a high position reliability evaluation value. The observation matrix is W, the motion matrix is M, the shape matrix is S, and the distribution of each element of the matrix X stochastically expressed as q (X),
The decomposition means is based on a Bayesian estimation formula that defines the relationship between the posterior probability P (M, S | W) and the likelihood P (W | M, S). The reliability distribution of the test distribution q (S) of the shape matrix and the test distribution q (S) of the shape matrix are reflected on the variance of the test distribution q (S) of the shape matrix. The three-dimensional shape restoration apparatus according to claim 1, wherein the factorization calculation is executed probabilistically by obtaining the above. The disassembling means includes
A first step of estimating the test distribution q (S) of the shape matrix by fixing the test distribution q (M) of the motion matrix, and fixing the test distribution q (S) of the shape matrix to the motion Estimating means for alternately and repeatedly executing the second step of estimating the test distribution q (M) of the matrix using each other's estimation results;
Ending means for ending the estimating means when a preset ending condition is satisfied;
The shape matrix S is obtained from the distribution of the shape matrix, assuming that the finally obtained test distribution q (S) of the shape matrix is the distribution of the shape matrix. The three-dimensional shape restoration apparatus described. The disassembling means includes
A first step of fixing the test distribution q (M) of the motion matrix and estimating the test distribution q (S) of the shape matrix each time an observation matrix is generated by the observation matrix generation means; Estimating means for executing the second step of estimating the test distribution q (M) of the motion matrix by fixing the test distribution q (S) of the shape matrix using each estimation result;
Updating means for updating the distribution of the shape matrix to be output based on the series of the test distribution q (S) of the shape matrix estimated by the estimating means;
Ending means for ending the estimating means and the updating means when a preset ending condition is satisfied;
3. The three-dimensional shape restoration apparatus according to claim 2, wherein the shape matrix S is obtained from the distribution of the shape matrix finally obtained by the updating means. Energy for calculating the free energy for the test posterior distribution q (S, M) = q (S) q (M) every time the estimation means obtains the estimation results of the test distributions q (S) and q (M). A calculation means,
5. The three-dimensional shape restoration apparatus according to claim 3, wherein the termination unit sets the termination condition that a calculation result of the energy calculation unit is larger than a preset energy threshold value. .   5. The tertiary according to claim 3, wherein the termination unit uses the termination condition that the number of times the shape matrix is calculated by the estimation unit is larger than a preset number of times threshold. Original shape restoration device.   The three-dimensional according to any one of claims 2 to 7, wherein the reliability evaluation means uses a distribution value of a distribution that stochastically represents the position of the feature point as the position reliability evaluation value. Shape restoration device.   The three-dimensional shape restoration apparatus according to any one of claims 1 to 7, wherein the three-dimensional shape restoration apparatus is used by being mounted on an automobile.