WO2012150150A1

WO2012150150A1 - Method for estimating the position of an object in a computer-assisted manner

Info

Publication number: WO2012150150A1
Application number: PCT/EP2012/057458
Authority: WO
Inventors: Wendelin Feiten; Thilo Grundmann
Original assignee: Siemens Aktiengesellschaft
Priority date: 2011-05-05
Filing date: 2012-04-24
Publication date: 2012-11-08
Also published as: DE102011075335A1

Abstract

The method for estimating the position of an object in a computer-assisted manner uses a model database with features (m) of the object (0), each feature (m) being assigned to a local position (x) on the object. A hypothesis for an object pose is ascertained on the basis of camera images (B) of the object (0). An improved estimation of the object position is obtained by minimizing an error function (f_err) using a sensor model of the camera system and the hypothesis for the object pose. Finally, a probability distribution (p) of the estimated object pose is ascertained using a function (f) that is implicitly defined by the minimization of the error function (f_err). A precise estimation of an object pose is obtained together with a measurement of the uncertainty of said estimation in the form of a probability distribution. The latter can be used in order to reject estimated object positions if the spread of the probability distribution is too large.

Description

description

Method for the computer-aided estimation of an object The invention relates to a method for computer-assisted

Estimation of an object and a corresponding Vorrich ^¬ tion and a computer program product.

In a variety of applications, a machine-accurate location of an object is required. For example, in robotic applications, it must be ensured that a corresponding robot accurately manipulates its environment, e.g. to edit or move certain objects.

From the prior art a variety of methods is known by which the position or pose of an object is estimated based rechnerge ^¬. Pose is the combination of position and orientation of the object to understand. As part of a three-dimensional localization, a pose includes a 3D position and 3D orientation and thus a total of 6 dimensions. Known methods for estimating the position evaluate images taken with a corresponding camera system, in order thereby to identify the objects contained therein and to determine their position. While such procedures provide accurate results, however, is not set by the method by which the uncertainty determined according ^¬ object pose is associated. However, this information may be helpful in certain applications. For example, at too high uncertainty of the estimate, the estimated pose can ver ^¬ worfen are or are acquired more data to accurately position estimate.

The object of the invention is therefore to provide a method for computer-assisted estimation of an object which, in addition to an exact object pose, also specifies a measure for the uncertainty of the estimated object pose. This object is achieved by the independent claims ge ^¬ triggers. Further developments of the invention are defined in the dependent claims. The inventive method for computer-aided location estimate of an object using a model database, wel ^¬ surface includes a plurality of features of the object, wherein each feature is assigned to a local position on the object and a first covariance matrix for the local position. The model database is considered as given and their generation is not part of the method according to the invention. It is known from the prior art to generate ent ^¬ speaking model databases for estimating the position of an object.

In the context of the inventive method, in a step a) features of the object, which are extracted from one or several ^¬ reindeer, recorded with a camera system camera images of the object, as compared with characteristics of the object from the model database, whereby a hypothesis for a object pose is obtained in a reference coordinate system. Corresponding methods for carrying out step a) are described in the prior art. In particular, such a method can be found in reference [1]. The entire disclosure content of this document is incorporated by reference into the content of the present application.

In a step b) of the process according to the invention will ba ^¬ sierend on a sensor model of the camera system and the hybrid pothese for the object pose an error function depending on the object pose minimized as a variable, whereby an estimated object pose is obtained. The sensor model ^¬ be overwriting the association between a local position on the object (ie, a position in a fixed communication system of the object) and an image position in the corresponding camera image, depending on the object pose. Furthermore, the sensor model defines a second covariance matrix for each image position in the respective camera image. The Error function describes an error measure between about the sensor model determined image positions contained in the respective camera image features of the object and on the Kame ^¬ rasystem measured image positions of the features of the object. With the aid of step b) improving the location estimation of the object is achieved by inclusion of the model of the camera sensor ^¬ system and associated uncertainties. The corresponding second covariance matrix is predetermined and can be determined empirically for the corresponding camera system, for example.

To now a measure of the uncertainty of the ge ^¬ estimated in step b) to determine position, determining a probability distribution of the object pose estimated in step c). This is done by means of a functi ^¬ on which implies on the minimization of the error function is defined and describes the dependence of the estimated object pose from the measured image positions of the features of the object, determining a Jacobian matrix for the implicit function using implicit differentiation and from this, using the first and second covariance matrices, the probability distribution of the estimated object pose is determined. According to the invention, use is made of the fact that a probability distribution for the estimated pose can be derived from the minimization of the error function using the known method of implicit differentiation. The inventive method thus provides not only a highly accurate estimate of the object pose as another Informa ^¬ tion a measure of the uncertainty of the estimated object pose in the form of a probability distribution.

In a particularly preferred embodiment of the inventive method, the to be minimized Fehlerfunkti ^¬ on is a sum of distance measures, wherein a respective distance ^¬ measure the difference between an over the sensor model he ^¬ mediated image position of a respective, in the corresponding describes the feature of the object contained in the camera image and the image position of the feature measured via the camera system. In a further embodiment of the invention, a third covariance matrix from the first and second covariance matrix is determined for each measured image position of a feature contained in the corresponding camera image. In a particularly preferred variant, just be ^¬ signed third covariance matrix is included in the error function. Here, the error function is a weighted sum of the distance measures, wherein a distance measure in such a way by the third covariance matrix of the gehöri- the respective distance measure gene measured image position dependent in that the distance measure is weighted less so, the larger the scattering described by the third Ko ^¬ variance matrix is ,

In a particularly preferred embodiment of the method according to the invention, a covariance matrix for the probability distribution of the estimated object pose is determined from the third covariance matrices and the Jacobi matrix by means of matrix multiplication. In particular, a block diagonal matrix is formed from all third covariance matrices and this matrix is multiplied by the Jacobian matrix and the transposed Jacobian matrix.

In a further embodiment of the invention, the probability distribution of the estimated object pose is described by a Gaussian distribution with the estimated object pose as mean value. In particular, the matrix described above is used as the covariance matrix ^¬, which was determined from the third and covariance matrices of the Jacobian matrix by matrix multiplication.

To describe the camera system, in a particularly preferred embodiment, a sensor model is used, which is based on a hole camera model. The Lochkameramodell to describe optical images is well known in the prior art and will be described again in the detailed description. This model is non-linear. In a preferred embodiment, therefore, a linearization of the hole camera model is used to determine the third covariance matrix. The detailed description explains how such a linearization can be performed to determine the third covariance matrix.

The features of the object which are considered within the scope of the estimation of the position are, in a particularly preferred ^embodiment, the SIFT features sufficiently well known from the prior art (SIFT = scale-invariant feature transform).

In a further preferred embodiment of the method according to the invention are prepared from the determined in step c) the probability distribution of the estimated object pose with- means of sampling object poses removed and determines a His ^¬ diffractogram of extracted object poses, which satisfy a predetermined threshold criterion, whereby a new probability distribution is obtained. In this way, an even more accurate estimation of the uncertainty for the object pose can be determined. In a preferred variant, the threshold criterion is dependent on the value of the error function for the removed object pose. In particular, the threshold criterion is defined such that the extracted object pose satisfies the threshold criterion when the exponential function multiplies by -1

Value of the error function for the extracted object pose as Ex ^¬ components is greater than a predetermined threshold. The appropriate choice of the predetermined threshold lies within the scope of expert action.

In a further preferred embodiment of the method according to the invention, an estimated object pose is rejected if the probability distribution determined in step c) is rejected. ment and / or the sampled new probability distribution have a dispersion which is greater than a predetermined threshold. The appropriate choice of the predetermined threshold is within the scope of expert action.

In addition to the method described above, the invention further relates to a device for computer-aided position estimation of an object, wherein in the device a model database is stored, which contains a plurality of features of Ob ^¬ jects, each feature a local position on the object and a associated first covariance matrix for the local Po ^¬ sition, the apparatus comprising a camera system for recording images from the camera of the object as well as a computing unit, said computing unit is such out ^¬ staltet that the erfindungsge ^¬ Permitted method with this computer unit or a or several variants of the method according to the invention are feasible.

The invention further relates to a robot comprising the device according to the invention, wherein the robot, in operation, performs its movements using the object poses estimated by the device.

The invention further relates to a computer program product with a program code stored on a machine-readable carrier for carrying out the method according to the invention or one or more variants of the method according to the invention, when the program runs on a computer.

Embodiments of the invention are described below in detail with reference to the accompanying drawings.

Show it: 1 shows an exemplary representation of an object, on the basis of which the determination of SIFT features is clarified;

FIG. 2 is a flow chart depicting determination of an object position hypothesis based on an embodiment of the invention; FIG.

FIG. 3 shows a schematic illustration which illustrates the estimation of an object position based on the minimization of an error function on the basis of an embodiment of the method according to the invention; FIG. and

Fig. 4 is a schematic representation which with a

Embodiment of the invention reproduced probability distribution and another probability distribution, which is determined by sampling from the original probability distribution.

An embodiment of the method according to the invention based on the position estimation of an object with the aid of a 3D camera system will be described below. The object estimation can be used, in particular, in a corresponding arithmetic unit of a robot, in order to specify a pose that is as exact as possible for the objects, which are then to be processed or adopted by the robot as part of the execution of a task. In the embodiment described here, in addition to the estimated object pose, a probability distribution is also determined which takes into account the uncertainty of the estimation of the object pose. In the imple ^¬ out the method in a robot can then be dispensed with using the object pose as part of the process performed by the robot action for example at a large scattering of the Wahrscheinlichkeitsvertei ^¬ lung or the inclusion of additional 3D camera images to determine a more accurate Estimate the object pose to be initiated. The method according to the invention is based on a so-called. ^¬ model-based object recognition method, of one or more objects to be recognized is included in the corresponding in a database models, the object pose, that is their position and orientation in space, can be estimated. The model of an object is described by a large number of so-called SIFT features on the surface of the object (SIFT = Scale-Invariant Feature Transform). SIFT features are out ^¬ long known from the prior art and are not explained in detail. These characteristics were determined for informative ^¬ strong local positions on the object and are stored in the database. Methods for determining SIFT features of objects are known and not the subject of the invention. Rather, the invention assumes that there is already a corresponding model database which contains a large number of features of at least one object whose position is to be estimated.

One way to determine SIFT features of an object is to place the object on a rotating

Disc is placed and recorded via a stereo camera system from a variety of different angles. Known software can then be used to determine corresponding SIFT features in combination with associated local locations on the object (i.e., positions defined in a local coordinate system of the object).

FIG. 1 again illustrates the determination of the SIFT features on the basis of an object in the form of a juice bag. The object 0 is in the left part of Fig. 1 as a point cloud again gege ^¬ ben. From this object x SIFT features of the object are determined for a plurality of local positions, which is indicated by the arrow P. The object reproduced in the right-hand part of FIG. 1 indicates the positions at which SIFT features are determined on the object surface. It can be seen that there are more SIFT features in certain areas than in others. In Fig. 1, an SIFT feature m is given by way of example, where ^¬ in the following, the SIFT features with the index k with

e ^ 0, ÄT], where K denotes the total number of local positions for which SIFT features were determined. The local position x = jx,>, z] of a SIFT feature m _k = | χ, Σ _χ , χ ^ν , 5, ύ? | is a three-dimensional position in space, for which a (first) covariance matrix Σ _χ exists. Furthermore, the SIFT feature contains a list of v

Line of sight x ^v , a per se known scale s and the classical, also known SIFT descriptor d.

In the embodiment described here, the SD position x is determined by the Bundler software known per se (see document [2]), and the corresponding covariance matrix is calculated using the covariance matrix of the minimum distance between the calculated 3D position of the Determined by the SIFT feature and the corresponding lines of sight. The descriptor d is the average of all v descriptors that contribute to the corresponding 3D point of the feature. The list of line-of-sight x ^v consists of normalized vectors from the 3-D positions of the corresponding features to the v camera poses taken into account in the determination of each feature and, together with the averaged scale, represents the range of visuals. directions from which a corresponding SIFT feature can be detected. The model uses only SD positions with v> 5 lines of sight.

Based on the stored in a database SIFT features of the object to be located then an estimate of the pose of the object is made via a pair of shots of a 3D stereo camera system, wherein the Ka ^¬ merasystem detects the corresponding object. The images of the two cameras j ^ [L, R] of the stereo camera system are analyzed (L = left, R = right). The object localization takes place in several steps, which are illustrated in FIG. In a first step Sl ^¬ the first, the SIFT features and their image positions calculated z .. in the images of the two cameras j ^ [L, R] or ext rahiert, wherein the image positions of 2D locations in the form of pixel positions in the respective camera images are. In a step S2, the corresponding local positions x _; , on the object over

Triangulation determined and stored together with the corresponding positions z .. from the two images. Then, in step S3, it is determined which local descriptors d of the extracted features match well with descriptors from the database. The resulting SIFT features _k from the database are then clustered to form sentences that are spatially and in terms of ent ^¬ speaking object types concentrated. The clustering takes place in step S4. From this, finally, in step S5, a hypothesis is determined for the object pose of the object recorded by the camera system. The method for object localization just described is known per se from the prior art and is described in detail in the document [1].

In order to obtain, according to the invention, an hypothesis of the object pose which is improved compared to the hypothesis and, at the same time, a corresponding probability distribution for this estimated object pose, the probabilistic sensor model explained below is used. For an arbitrary hypothesis of an object pose ω in the 6D-

Camera coordinates C. can be the projected image coordinates z _; .. be determined in the corresponding camera image j <[L, R] with a known standard hole camera model h _j (^, Χ,) as follows / 0 0 0

0/0 0 (1)

0 0 1 0

1

Here, f denotes the BE for the corresponding camera system ^¬ known focal length of the camera, and T _r is the per se known homogeneous transformation from the local 3-dimensional position on the object in the left and right images of the 3D camera system camera coordinates. This homogeneous transformation depends DA ω when the object pose in a stationary Weltkoordina ^¬ tensystem from. In the following, the sentence z = (ζ.,., Ζ ^) denotes the

Image positions (i.e., pixel positions) of N SIFT features of an object for which correspondence of the respective

Characteristics was found with characteristics from the database. Each entry z _n = z _{ij of} this sentence indicates an image position in the left and right image of the camera system. As mentioned above, the SIFT features contain m. from the ^{database ¬} a covariance matrix Σ _ι . Similarly, for the sensor model suitably a covariance matrix Σ. which was determined empirically. The determination of such a covariance matrix is within the scope of expert action.

In the embodiment of the method according to the invention described here, the two covariance matrices Σ. and Σ. about the linearization of the above

Lochkameramodells a new (third) covariance matrix be ^¬ true. For linearization, the Gaussian model _error modeled via the covariance matrix Σ 1 is determined at the corresponding local position x _; , projected into the image planes of the two cameras of the camera system. Under these assumptions is normally distributed _ζ κ near ^¬ approximately as follows:

J _hj = ie _J ((o, x _i ) ldx _J (3) (4)

Where J _h denotes the Jacobi matrix (also called function matrix or derivative matrix) of the perspective projection according to equation (2) with respect to the local 3D positions ^x ; ·

Using the settings via the linearization of the sensor model he ^¬ mediated covariance matrix Σ is then improved ..

Estimation of the object pose ω determined. For this purpose, the vector of the image positions of corresponding features actually determined in the image (ie measured) is used, which is as follows: z = {z, ζ ^,}. Using the distribution of the errors in the image according to equation (5) and the designations z _i . (ω) =: z _n (iy) and Σ _υ =: Σ _{η the} following quantities are calculated:

In this case, d _K (z _K , iy) denotes the distance between an image position determined via the hole camera model according to equation (2) and the corresponding image position measured with the camera system. Based on this difference, the above error function f _{err is} defined, which is a sum of the squares of the distances including the values of the (third) covariance matrix. In this way it is achieved that the greater the uncertainty in the measurement, that is the greater the corresponding weighting, the less weighted the corresponding distance

Scatter according to the third covariance matrix. Finally, an improved estimated object position based on the minimization of the above error function f _err under variation of the original hypothesis of the object pose. This minimization can be described by the following equation: g (z, a>) ^{■ d} ferr (ζ, ω) = 0 (8)

δω

The minimization is done numerically by methods known per se, e.g. the gradient descent method, solved. The minimization according to equation (8) implicitly defines a function / (ζ) = ώ which represents the optimal (estimated) object pose ώ for a given measurement z.

FIG. 3 illustrates again in schematic representation the just described estimation of an object pose ώ. There is shown schematically at ^¬ an object 0, which has an object pose ω, which is specified with respect to a stationary world coordinate system, which is designated in Fig. 3 with WK. Furthermore, FIG. 3 is indicated schematically the Kamerasys ^¬ tem C, are recorded with the images of the object 0 in order to estimate its pose. For a corresponding SIFT feature m at a local position of the object x on a corresponding measured 2D position z is obtained in the camera image B which is only partially again gege ^¬ ben. Furthermore, with the sensor model described above, based on a pinhole camera, a 2D image position can be calculated via the local position x. This calculated position is designated z in FIG. According to the invention, the ^distances d between these positions are now calculated for all SIFT features of the object in image B (see equation (6)) and from this by means of the above-defined error function from equation (7) the minimization problem indicated in FIG solved. As already mentioned above, is defined by the minimization problem ^¬ the implicit function / (z).

Based on this implicit function, the derivation of this implicit function in the form of the Jacobian matrix is now determined in a step essential to the invention, which is as follows: J _f (9)

dz

This Jacobi matrix becomes the above by applying the per se known method of implicit differentiation

Function g determined according to equation (8). In this case, the partial derivatives of a measurement z _n

^• . = £ (*. · «») = F - (* .. ») ⁱ⁾ explicitly from the closed form for h. determined. In the embodiment described here, a computer algebra system is used for this purpose. Finally, we obtain the Jacobian matrices for the entire measurement vector z, which are as follows:

Using these partial derivatives, we then obtain the Jacobi matrix for the implicit function as follows:

Finally, using the 2N x 2N block diagonal covariance matrix of the actual measurement z, which is a composition of all third covariance matrices for the measured pixels in the two images of the camera system, one obtains a Gaussian model for the pose ω, which is described by the following probability distribution:

This probability distribution is an essential to the invention result because hereby how big the spread is for an estimated Whether ^¬ jektposition also stated DIE This object position is. Is the covariance matrix of the above probability distribution, the through

is given, very large, for example, the estimated position ver ^{¬ be} discarded or further recordings are initiated by the camera system, to thereby obtain a better estimate of the object pose.

4 shows, by way of example, a diagram DI which, in the left-hand column C1 for the six coordinates of an object pose, represents the probability distribution p determined in accordance with equation (13) in the context of an embodiment of the invention. In a particularly preferred embodiment of the invention, a sampling is carried out also with this probability distribution p, in which, by Stichprobenentnah- me based on the function p a new improved International ^¬ scheinlichkeitsverteilung for the object pose is determined. In this case, an object pose taken from the sampling is only included in a histogram according to a threshold ^criterion if the value e ^{~ ferr is} greater than a suitably defined threshold value. The, based on this histogram it ^¬ maintained probability distribution represents the new probability distribution. This is shown in Fig. 4 in the column C2 for the individual dimensions of the pose and denoted by p '. In particular, it can be seen from FIG. 4 that the new probability distribution p 'better reflects the actual non-Gaussian uncertainty than the proposed Gaussian probability distribution

P- The above-described embodiments of the method according to the invention have a number of advantages. In particular, a good estimate of an object pose on the Mi ^¬ minimization of an error function is achieved by using a suitable sensor model. Moreover, based on the minimization of the error function using the method of implicit differentiation, it is also possible to determine a probability distribution for the estimated object pose and thus an uncertainty of this object pose. the. If necessary, this probability distribution can be determined more accurately by sampling. The probability distribution of the estimated object pose can then be used, for example, to reject the estimated object pose, if the scatter according to the probability distribution is very large. If the method is employed in the motion of a robot, which processes the object pose definitely be appreciated ^¬ te example, a further accurate Po sitionsschätzung be initiated on other camera images by the robot at a high dispersion of the probability distribution. The robot then performs coupled to the ge ^¬ estimated object pose action, such as the gripping of the object, only then made when the estimation of the object pose has a scattering which is below a predefined threshold NEN.

Bibliography :

T. Grundmann, R. Eidenberger, M. Schneider, M. Fiegert, and G. Wiehert v., "Robust high precision 6d pose determination in complex environments for robotic manipulation," in ICRA 2010 Workshop: Best Practice in 3D Perception and Modeling for Mobile Manipulation, 2010.

[2] N. Snavely, S.M. Seitz and R. Szeliski, "Photo tourism: exploring photo collections in 3d," ACM Trans. Graph., Vol. 25, no.3, pp. 835-846, 2006.

Claims

claims

1. A method for computer-aided estimation of an object (0), wherein a model database is used, which contains a plurality of features (m) of the object (0), where ^¬ in each feature (m) a local position (x) on associated with the object and a first covariance matrix (Σ _χ ) for the local position (x), in which:

a) Characteristics (m) of the object (0), which camera images captured from one or sev- eral, (with a camera system C) (B) of the object (0) are extracted with shopping ^¬ paint (m) of the object (0 ) are compared from the model database, whereby a hypothesis for a Objektpo ^¬ se (ω) is obtained;

b) C) and the hypothesis for the object pose (ω) an error radio ^¬ tion (f _e rr) i is minimized ⁿ depending on the object pose (ω) as variables based (on a sensor model of the camera system, whereby an estimated object ^¬ pose ( Sens), wherein the sensor model describes the Zu-order between a local position (x) on the object (0) and an image position (z) in the respective camera image in dependence on the object pose (ω) and in the sensor model a second covariance matrix ( E _j ) is defined for each image position (z) in the respective camera image (B), the error function (f _er r) defining an error measure between image positions (z) determined by the sensor model and features (m ) of the object (0) and over the camera system (C) ge ^¬ measured image positions (z) of the features (m) of the object (0) describes;

c) by means of a function (f), which is on the minimization of the error function (f _he r) defined implicitly and the dependence of the estimated object pose (ώ) of the ge ^¬ measured image positions (z) of the features (m) of the object (0 ) describes a Jacobi matrix for the implicit

Function (f) is determined by means of implicit differentiation, and from this a probability ratio is calculated using the first and second covariance matrices (Σ _χ , Σ- _j ). division (p) of the estimated object pose (ώ) is determined.

2. The method of claim 1, wherein the error function (f _e rr) a sum of distance measures (d), wherein a jewei ^¬ liges distance measure (d) the difference between a determined via the sensor model image position (z) of each of a, the feature (m) of the object (0) contained in the corresponding camera image (B) and the image position (z) of the feature (m) measured via the camera system (C).

3. The method of claim 1 or 2, wherein for each measured image position (z) of a feature contained in the corresponding camera image (C) feature (m) a third covariance matrix of the first and second covariance matrix (Σ _χ , Σ- _j ) is determined ,

4. Method according to claims 2 and 3, in which the error function (f _e rr) is a weighted sum of the distance measures (d), whereby a distance measure (d) from the third covariance matrix of the measured image position belonging to the respective distance measure d ( z) depends on that the distance measure (d) is less ge ^¬ is weighted the more, the larger the scattering described by the third covariance matrix.

5. Method according to claim 3, wherein a covariance matrix for the probability distribution (p) of the estimated object pose (ώ) is determined from the third covariance matrices and the Jacobi matrix by means of a matrix multiplication.

6. Method according to one of the preceding claims, in which the probability distribution (p) of the estimated object pose (ώ) is described by a Gaussian distribution with the estimated object pose (ώ) as mean value.

7. The method according to any one of the preceding claims, wherein the sensor model is based on a Lochkameramodell.

8. The method of claim 7, when dependent on claim 3, wherein the third covariance matrix is determined via a linearization of the hole camera model

A method according to any one of the preceding claims, wherein the features (m) of the object (0) are SIFT features.

10. The method according to any one of the preceding claims, wherein from the probability distribution (p) of the estimated object pose (ώ) by means of sampling object poses (ω) are removed and a histogram of extracted object poses (ω) is determined, which meet a predetermined threshold ^¬ criterion , whereby a new probability distribution (ρ ') is obtained.

11. The method of claim 10, wherein the predetermined

Threshold value depends on the value of the error function for the extracted object pose (ω) and is defined in particular such that the extracted object pose (ω) satisfies the ^threshold value criterion if the exponential function matches the value of the error function (f _e rr) (for the extracted object pose ω) is an exponent greater than a given threshold value before ^¬.

12. The method according to claim 1, wherein an estimated object pose is rejected if the probability distribution determined in step c) and / or the new probability distribution have a variance greater than a predetermined one

Threshold is.

13. The apparatus for computer-aided location estimate of an object (0), in which device a model database stores Ge, containing a plurality of features (m) of the Ob ^¬ jekts (0), with each feature (m) a local Posi ^¬ tion (x) is assigned to the object and a first covariance matrix (Σ _χ ) for the local position (x), wherein the Vor- direction comprises a camera system (C) for recording camera images (B) of the object (0) and a computer unit, wherein the computer unit is designed such that it carries out a ^method in which:

a) features (m) of the object (0), which are extracted from one or meh ^¬ rere, with the camera system (C) recorded camera images (B) of the object (0), with features (m) of the object (0) the model database, whereby a hypothesis for an object pose (ω) is obtained;

b) C) and the hypothesis for the object pose (ω) an error radio ^¬ tion (f _e rr) i is minimized ⁿ depending on the object pose (ω) as variables based (on a sensor model of the camera system, whereby an estimated object pose ( ώ) is obtained, wherein the sensor model (for ^¬ order between a local position x) 0), and an image position (z) in the corresponding camera image, depending on the object pose (ω) describes and (on the object (a second covariance matrix in the sensor model E _j ) is defined for each image position (z) in the respective camera image (B), the error function (f _er r) determining an error measure between image positions (z) determined by the sensor model and features (m) of the image contained in the respective camera image (B) Object (0) and via the camera system (C) measured image positions (z) of the features (m) of the object

(0) describes;

c) by means of a function (f) which is implicitly defined by the minimization of the error function (f _er r) and the dependence of the estimated object pose (ώ) on the measured image positions (z) of the features (m) of the object

(0), a Jacobi matrix for the implicit function (f) is determined by means of implicit differentiation and from this using the first and second covariance matrices (Σ _χ , Σ- _j ) a probability distribution (p) of the estimated object pose (ώ ) is determined.

14. The apparatus of claim 13, which is configured such that with the device, a method according to any one of claims 2 to 12 is feasible.

A robot comprising an apparatus according to claim 13 or 14, wherein the robot, in use, performs its movements using the object poses (ώ) estimated with the apparatus.

16. Computer program ^product with a program code stored on a machine-readable carrier for carrying out a method according to one of claims 1 to 12, when the program runs on a computer.