Method, device, and computer program for the virtual fitting of a spectacle frame

Abstract

A method for adjusting spectacles in which a virtual fitting process of a parametric frame model of a spectacle frame on a 3D model of the head of a person, to whom the spectacles are to be fitted, is divided into two fitting procedures. In a first fitting procedure, the parametric frame model is adjusted to the 3D model of the head to meet specific fitting guidelines for the parametric frame model. Fitting guidelines of this nature may be specified by a frame manufacturer to comply with aesthetic criteria in the fitting. Anatomic fitting is then performed in the second fitting procedure.

Claims

1. A computer-implemented method for fitting of a pair of spectacles, the method comprising: virtually fitting a parametric frame model to a 3D model of a head of a person by: performing a first fitting procedure including adapting parameters of the parametric frame model for fitting the parametric frame model to the 3D model of the head to satisfy fitting guidelines that are specific to the parametric frame model; performing a second fitting procedure including adapting the parameters of the parametric frame model for an anatomical fitting of the parametric frame model to the 3D model of the head; determining a first set of parameters in the first fitting procedure; determining a second set of parameters that differs from the first set of parameters in the second fitting procedure, wherein the first set of parameters includes at least one of a scaling of the spectacle frame, an as-worn pantoscopic angle, or a form of a spectacle rim of the spectacle frame, and wherein the second set of parameters includes at least one of a bridge width, an earpiece length, or a nasal wing angle, and wherein adapting the parameters of the parametric frame model changes a geometry of a spectacle frame defined by the parametric frame model; and performing a virtual donning of the parametric frame model having the changed geometry.

2. The method as claimed in claim 1, further comprising: converting at least one of the fitting guidelines or the parametric frame model into a predetermined format.

3. The method as claimed in claim 1, wherein the parametric frame model comprises a multiplicity of parameters.

4. The method as claimed in claim 1, wherein the specific fitting guidelines comprise specifications for features derived from features of the frame, features of the head, or features of the frame and the head.

5. The method as claimed in claim 1, wherein the first fitting procedure employs a syntax tree.

6. The method as claimed in claim 1, wherein the first fitting procedure comprises an optimization process in a target function on a basis of at least one of a deviation of a target value of the specific fitting guidelines or a penalty term when a target range is exceeded.

7. The method as claimed in claim 1, wherein the first fitting procedure comprises a repeated run-through of an optimization loop.

8. The method as claimed in claim 1, wherein the first fitting procedure comprises taking into account a weight of a spectacle lens.

9. The method as claimed in claim 1, wherein at least one of the parametric frame model or the specific fitting guidelines are encrypted.

10. The method as claimed in claim 1, further comprising a calculation of a quality measure for the virtual fitting.

11. The method as claimed in claim 1, further comprising: creating a subset of parameters from the parameters of the parametric frame model; keeping the parameters of the subset at a standard value during the first fitting procedure; and adapting the subset of parameters during the second fitting procedure.

12. A computer comprising: a processor; and a non-transitory storage medium having a program stored thereon and comprising a program code which causes the method as claimed in claim 1 to be carried out when the program code is executed on the processor.

13. An apparatus for virtual fitting of a pair of spectacles, comprising a processor and a memory, in which the computer program as claimed in claim 12 is stored for the purpose of being executed on the processor.

14. A non-transitory computer-readable storage medium comprising instructions that, upon execution by a computer, cause the latter to carry out the method as claimed in claim 1.

15. An apparatus for data processing, comprising a processor configured to carry out the method as claimed in claim 1.

16. A computer-implemented method for fitting of a pair of spectacles, the method comprising: virtually fitting a parametric frame model including a multiplicity of parameters to a 3D model of the head of a person by: performing a first fitting procedure including fitting the parametric frame model to the 3D model of the head to satisfy fitting guidelines that are specific to the parametric frame model and determining a first set of parameters, wherein the first set of parameters includes at least one of a scaling value of the spectacle frame, an as-worn pantoscopic angle, or a form of a spectacle rim of the spectacle frame; performing a second fitting procedure including an anatomical fitting of the parametric frame model to the 3D model of the head and determining a second set of parameters that differs from the first set of parameters, wherein the second set of parameters includes at least one of a bridge width, an earpiece length, or a nasal wing angle, wherein the specific fitting guidelines comprise at least one of a target value or a target range for a distance between a feature of the spectacle frame and a feature of the head of the person, and wherein determining the parameters of the first set of parameters and the second set of parameters changes a geometry of a spectacle frame defined by the parametric frame model; and performing a virtual donning of the parametric frame model having the changed geometry.

17. The method as claimed in claim 16, wherein the at least one of the target value or the target range differs for different spectacle frames.

18. The method as claimed in claim 16, further comprising: creating a subset of parameters from the parameters of the parametric frame model; keeping the parameters of the subset at a standard value during the first fitting procedure; and adapting the subset of parameters during the second fitting procedure.

19. A computer comprising: a processor; and a non-transitory storage medium having a program stored thereon and comprising instructions that, upon execution of the program by a computer, cause the latter to carry out the method as claimed in claim 16.

20. A non-transitory computer-readable data medium, on which the computer program as claimed in claim 19 is stored.

21. An apparatus for data processing, comprising: a processor; and means for carrying out the method as claimed in claim 16.

22. An apparatus for data processing, comprising: means for virtually fitting a parametric frame model to a 3D model of a head of a person, wherein the means for virtual fitting include: means for carrying out a first procedure for fitting the parametric frame model to the 3D model of the head to satisfy fitting guidelines that are specific to the parametric frame model; means for carrying out a second procedure for fitting the parametric frame model to the 3D model of the head for anatomical fitting; means for determining a first set of parameters in the first fitting procedure; means for determining a second set of parameters that differs from the first set of parameters in the second fitting procedure, wherein the first set of parameters includes at least one of a scaling of the spectacle frame, an as-worn pantoscopic angle, or a form of a spectacle rim of the spectacle frame, wherein the second set of parameters includes at least one of a bridge width, an earpiece length, or a nasal wing angle, and wherein the first procedure for fitting the parametric frame model and the second procedure for fitting the parametric frame model change a geometry of a spectacle frame defined by the parametric frame model; and means for performing a virtual donning of the parametric frame model having the changed geometry.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosure will now be described with reference to the drawings wherein:

(2) FIG. 1 shows an apparatus for virtual fitting of a pair of spectacles according to one exemplary embodiment;

(3) FIG. 2 shows an example of an implementation of a camera device of FIG. 1;

(4) FIG. 3 shows a flowchart that provides an overview of a method for fitting a pair of spectacles according to one exemplary embodiment;

(5) FIG. 4 shows a flowchart of a method according to one exemplary embodiment, which is usable in the method of FIG. 3;

(6) FIG. 5 shows a flowchart of a method according to one exemplary embodiment, which is usable within the scope of the method of FIG. 3;

(7) FIG. 6 shows a view for elucidating features of a head that may be referred to in fitting guidelines;

(8) FIG. 7 shows a detailed implementation of method step 40 in FIG. 4 or of step 54 in FIG. 5;

(9) FIG. 8 shows a diagram for explaining auxiliary features;

(10) FIGS. 9A-9F show six schematic views of a head for elucidating a fitting.

(11) FIGS. 10A to 10D show further schematic views of a head for elucidating a fitting on the basis of fitting guidelines;

(12) FIG. 11 shows a flowchart of a method according to one exemplary embodiment, which is usable within the scope of the method of FIG. 3;

(13) FIG. 12 shows a flowchart of a detailed implementation of the method of FIG. 11;

(14) FIGS. 13A to 13D show illustrations for elucidating head models;

(15) FIG. 14 shows another illustrations for elucidating head models

(16) FIG. 15 shows a diagram for elucidating a partial step of fitting a pair of spectacles in the method of FIG. 12; and

(17) FIG. 16 shows a view of a frame model for elucidating a bridge width.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

(18) FIG. 1 shows an exemplary embodiment of an apparatus for virtual fitting of a pair of spectacles according to one exemplary embodiment. The apparatus of FIG. 1 comprises a computing device 11, which comprises a processor 12 and a memory 13. The memory 13 serves to store data and, in the exemplary embodiment of FIG. 1, comprises a random access memory (RAM), a read-only memory (ROM) and one or more mass storage media (hard disk, solid-state disk, optical drive, etc.). A program is stored in the memory 13, the program, when executed on the processor 12, being used to carry out a method for virtual fitting of a pair of spectacles, as already described above or as yet to be explained in more detail below.

(19) The apparatus of FIG. 1 further comprises a display 16 which displays a head of a person together with a spectacle frame when the computer program is executed on the processor 12. User inputs can be implemented by way of one or more input appliances 17, for example keyboard and mouse. Additionally or alternatively, the display 16 can be a touch-sensitive screen (touchscreen) in order to be able to implement inputs.

(20) The apparatus of FIG. 1 furthermore comprises an interface 14 to a network 18, by means of which data can be received. In particular, it is possible to receive here parametric frame models of spectacle frames and associated fitting guidelines from manufacturers of spectacles. In some exemplary embodiments, data are also transmitted to a further computing device via the interface 14 in order there to carry out, e.g., a portion of the calculation required for fitting this pair of spectacles. In order to create a 3D model of a head of a person, to which the pair of spectacles should be fitted, the apparatus of FIG. 1 optionally comprises a camera device 15, by means of which a plurality of images of the person can be recorded from different directions and the 3D model can be determined. Information in respect of such a determination of 3D models on the basis of image recordings is found in, e.g., H. Hirschmüller, “Stereo Processing by Semiglobal Matching and Mutual Information” in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 2, pp. 328-341, February 2008.doi: 10.1109/TPAMI.2007.1166.

(21) FIG. 2 shows an exemplary embodiment for the camera device 15 of FIG. 1. In the exemplary embodiment of FIG. 2, a semicircular arrangement 110 of cameras is fastened to a column 19. A person can then position themselves in such a way that a head 111 of the person, as shown in FIG. 2, is positioned in the semicircular arrangement 110 and can be recorded from different directions. Then, a 3D model of the head 111 can be created therefrom. A texture, i.e., information in respect of colors (as explained above) of the model, also emerges from the image recordings. Moreover, such an apparatus can be used for centration measurements, as described in the European patent application EP 3355100 A1.

(22) FIG. 3 shows a flowchart of an overall method for virtual fitting of a pair of spectacles according to one exemplary embodiment. The present application relates, in particular, to partial steps of this method.

(23) The method begins in step 30. In step 31, a 3D model of the head, including head model metadata, is loaded from a memory. The 3D model can be created with the aid of image recordings, as explained above with reference to FIGS. 1 and 2, or it may be an already available 3D model, for example from earlier fitting of a pair of spectacles to a certain person.

(24) The head model metadata are data that contain information items about the features of the 3D model but not the model itself. In particular, the metadata may supply additional information in respect of the 3D model of the head and/or contain certain points, curves or regions on the 3D model of the head. More details about the use of such metadata is also found in the European patent application EP 3410178 A1.

(25) A basic model of a spectacle frame described by a parametric frame model is selected in step 32. The parametric frame model has free parameters, i.e., parameters to be determined. Examples of such free parameters were already specified further above in the context of the description of the parametric frame model, specifically the bridge width or earpiece length of the spectacle frame, or else a form of a frame rim of the spectacle frame.

(26) In step 312, at least some of the parameters are then calculated on the basis of a fitting guideline associated with the frame model, as described above and explained in more detail below. Other parameters are determined on the basis of anatomical fitting, as likewise already explained.

(27) Then, there is virtual donning of the spectacles with more in-depth anatomical fitting in steps 33 to 310. To this end, in step 33 there is approximate positioning on the basis of a placement point and a nasal bridge resting point, as already described in the European patent application EP 3410178 A1. The spectacle earpieces are bent open to the ears of the head and the earpieces are positioned, wherein there may be a rotation about an x-axis of the pair of spectacles, in steps 34 and 35. Here, the x-axis corresponds to a direction that connects the eyes in the head, the z-direction corresponds substantially to the direction of the earpieces and the y-direction is perpendicular thereto. Contact areas of the pair of spectacles are optimized in step 36 by means of fine positioning in the xy-plane. Moreover, parameters not yet set in step 312 can be adapted further here. Steps 34-36 in this case correspond to the corresponding steps described in the European patent application EP 3410178 A1. Within the scope of this fitting, the parametric spectacle model can be deformed and positioned, in particular, after the parameters were determined in step 312.

(28) The frame and the head are then rendered in step 37, i.e., there is an appropriate representation on the display 16 of FIG. 1. This rendering, too, is already described in the European patent application EP 3410178 A1. Here, rendering, also referred to as image synthesis, is understood to be the creation of an image (e.g., for display on a computer monitor) on the basis of raw data, from the respective models in this case.

(29) Then, there is an interaction of the user with the model in step 38 which, as illustrated in step 39, may have various consequences. Thus, there may simply be navigation, for example in order to observe the head from a different direction. In this case, there is new rendering in step 37.

(30) The interaction in step 39 also allows manual adaptation of the rotation of the frame about the x-axis. In this case, the method returns to step 35, for example to determine the earpieces in accordance with the new position of the frame.

(31) Moreover, the interaction of the user with the model may also adapt the position of the spectacle frame on the nasal bridge of the head model by way of a user of the apparatus. This substantially changes the position of the spectacle frame set in step 33. Therefore, the method returns to step 33 in this case.

(32) The previously described types of interaction, in particular navigation, for example for changing the observation angle, adapting the rotation and adapting the position of the pair of spectacles disposed on the nasal bridge, have likewise already been explained in detail in the European patent application EP 3410178 A1.

(33) Moreover, one of the frame parameters of the parametric frame model can also be set by the user within the scope of the interaction. By way of example, the user can in this case modify the determination of parameters implemented by the automatic calculation in step 312. In this case, this reduces the number of free frame parameters in step 310 and the method is continued in step 36. If the user is finally satisfied with the fit following the interaction, the method is terminated in step 311. In the process, there can still be a final check. The user (e.g., an optician) checks the order data during the final check. In the process, the data of the order and corresponding pictorial representations are presented to the user on an overview monitor. The representations show the parameters of the spectacle frame and/or of the head determined within the scope of the method, such as a bridge width and the nasal wing angle, etc., and also the parameters of the ordered frame, possibly also with notes about deviations from an ideal form which, e.g., are prescribed by the fitting guidelines. The determination of such parameters will still be explained below. Then, the ascertained parameters can be transmitted to an ordering system of the respective manufacturer in order to order a physical spectacle frame with the corresponding parameters.

(34) Individual aspects of the method of FIG. 3 will now be explained in greater detail below with reference to FIGS. 4 to 15.

(35) FIG. 4 shows a flowchart of a method according to one exemplary embodiment. FIG. 4 shows a subdivision of the spectacle fitting into fitting on the basis of fitting guidelines associated with a respective parametric frame model, followed by fitting to an anatomy of the head.

(36) In the method of FIG. 4, the parametric frame model is fitted to a 3D model of the head of the person on the basis of fitting guidelines in step 40, the fitting guidelines being predetermined by the spectacle frame manufacturer of the respective spectacle frame, specifically for the spectacle frame. These fitting guidelines may relate to esthetic prescriptions, as likewise explained in more detail below. Implementation examples for this step will be explained in even greater detail later. By way of example, step 40 can be carried out within the scope of step 312 of FIG. 3.

(37) A first set of parameters of the parametric frame model can be set by the adaptation in step 40.

(38) Then, general fitting to the anatomy of the head of the person is undertaken in step 41, i.e., the fitting in step 41 is implemented independently of the specific fitting guidelines. This fitting can be implemented as described in the prior art cited at the outset, and can likewise be implemented in step 312 or optionally also in the adaptation in steps 34 and 35. Then, the anatomical spectacle fitting can also take place directly on the basis of the metadata of the head model, or else as explained in Johannes Eber, “Anatomische Brillenanpassung”, Verlag Optische Fachveröffentlichung GmbH, 1987, page 23ff.

(39) FIG. 5 shows a detailed flowchart of an implementation of the method of FIG. 4.

(40) Input data for the method are provided in steps 50 to 53 in FIG. 5. In step 51, a frame manufacturer creates a parametric frame model for a spectacle frame. The parametric frame model of step 51 can in this case be transferred into a uniform, standardized format, which is used in the method according to the disclosure if the data are supplied by the spectacle manufacturer in a proprietary CAD (computer aided design) format.

(41) Moreover, there can be a data reduction (e.g., a reduction in the number of triangles or voxels in the 3D model) or a data compression with the aid of conventional compression methods.

(42) In step 50, the frame manufacturer creates specific fitting guidelines for this parametric frame model, which, as explained, can take account of esthetic aspects when fitting the frame.

(43) A 3D model of the head of the person is created and analyzed in steps 52 and 53. Here, the model is initially created in step 52 with a 3D measurement system, in particular with the camera device shown in FIG. 2. Other types of measurement systems, such as 3D head scanners, can also be used. Examples of such head scanners are found at the url cyberware.com/products/scanners/ps.html or www.3d-shape.com/produkte/face_d.php, in each case as of Jun. 8, 2017. In step 53, points or regions are then identified as features on this head model, for example points and features as are also used in the prior art explained at the outset.

(44) Then, the frame is fitted in step 54 in accordance with the specific fitting guidelines, corresponding to step 40 in FIG. 4. Additionally, an intended position and orientation of the spectacle frame can be set as a start value for the adaptation in step 54. A position by means of metadata such as in the European patent application EP 3410178 A1 with predetermined standard parameters for the parametric frame model can serve as intended position and intended orientation, which may serve as a start value for the adaptation. As an alternative thereto, the intended position can be calculated from the specific fitting guidelines in some cases. By way of example, the specific fitting guidelines define the typical position of the frame rim with respect to the pupil centers in the xz-plane, the intended vertex distance (e.g., 12 mm) defines the position in the direction of the y-axis. The as worn pantoscopic angle can also be set as part of the orientation of the frame in space, i.e., the angle about the x-axis, to an intended value of 9 degrees, for example. This may likewise be part of the specific fitting guidelines.

(45) Then, the frame is fitted to anatomical conditions of the head in step 55. Here, parameters that were not yet fitted in step 54, i.e., which are still free parameters, are adapted further.

(46) In step 56 there is virtual donning and rendering, and a manual adaptation in step 57. Here, the virtual donning and manual adapting is implemented as already described with reference to reference signs 33 to 310 in FIG. 3.

(47) In step 58, there is a transfer to an ordering system of the frame manufacturer, corresponding to step 311 in FIG. 3.

(48) The use of frame-specific fitting guidelines and the corresponding adaptation are now explained in more detail with reference to FIGS. 6 to 10.

(49) FIG. 6 shows various features of the face, which are suitable as features and points in the face for such specific fitting guidelines. In other words, a target position or target range of features of the spectacle frame relative to such points of the face is provided in the fitting guidelines in such an exemplary embodiment. Such features of the face are also explained in Johannes Eber, “Anatomische Brillenanpassung”, Verlag Optische Fachveröffentlichung GmbH, 1987, page 17ff.

(50) Examples include: 1. The position of the eyes, in particular the pupil centers (point of intersection of the line L2 with the lines LB in FIG. 6). Line L2 moreover denotes the pupil axis. 2. The box dimensions of the eyes, i.e., the dimensions of a rectangle placed around the eyes—position of each rectangle, width and height of the rectangles. 3. The position of the nose in accordance with lines LA and L3 in FIG. 6. 4. The width of the face and the position of the temples corresponding to the lines LD in FIG. 6. 5. The height of the face between the lines L1 and L5 in FIG. 6, and the line of the chin (line L5) in FIG. 6. 6. The radius of curvature of the chin region, i.e., of the part of the chin touching the line L5. 7. The position of the eyebrows, wherein the line L1 in FIG. 6 represents the central axis of the eyebrows and the lines LC represent a respective outer limit of the eyebrows. 8. The position of the mouth in accordance with line L4 in FIG. 6.

(51) The aforementioned features can be identified by a procedure as described below by means of a parametric head model or else by image analysis methods (image recognition) and/or by machine learning in images recorded by the camera device of FIG. 2, and the position of the features can thus be determined on the 3D model of the head. An option for automatic recognition of such features is also described in V. Kazemi, J. Sullivan, “One millisecond face alignment with an ensemble of regression trees,” Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2014.

(52) In the following description, references such as left eye, right eye, left half of the face or right half of the face should be understood from the view of the person for whom the pair of spectacles is fitted.

(53) FIG. 7 shows a detailed method for fitting the spectacle frame on the basis of the fitting guidelines, i.e., a detailed example for step 40 in FIG. 4 or step 54 in FIG. 5, together with the provision of the data.

(54) Fitting guidelines for a parametric frame model are provided at step 70 in FIG. 7, the fitting guidelines being read into a computing device in step 73 in order to be able to use these in the presented method. Here, the fitting guidelines are stored as a text file, for example, such as an xml file or JSON file.

(55) A parametric frame model is provided in step 71, the fitting guidelines at step 70 being assigned thereto. Metadata that denote certain regions or points of the frame model, for example, may be assigned to the parametric frame model. Such metadata of a frame model are also described in the European patent application EP 3410178 A1. This parametric frame model is read in step 74. In step 77, the parameters of the parametric frame model arising from being read at step 74 and their value ranges are provided for subsequent optimization. Finally, a 3D model of the head of the person, for whom a spectacle frame should be fitted, is provided with the associated metadata at step 72, the model being read in step 75.

(56) The fitting guidelines are parsed in step 76. Parsing is understood to mean a decomposition and conversion of input data into a format more suitable for further processing. A parser is a corresponding device (usually implemented by a computer program), which carries out such parsing. More details in this respect are found in the German Wikipedia article “Parser [Parsing],” as of May 19, 2017.

(57) Here, the fitting guidelines are translated, in particular, into a format that is suitable for the subsequent optimization process. Here, as explained, the fitting guidelines may contain target quantities and/or admissible ranges, in particular for distances between features of the spectacle frame and features on the head, for example a distance between the upper frame rim and the eyebrows, a distance between the upper frame rim of the frame and an upper edge of the eyes, a distance of the lower frame rim to a lower edge of the eyes or a relative position of the pupil with respect to the frame rims. Moreover, it is also possible to use distances to calculated derived features, i.e., points or regions that are derived from a plurality of features of the head and/or of the frame. Such derived features are also referred to as auxiliary features. The use of such derived features allows greater flexibility and/or accuracy of the adaptation.

(58) One example of such an auxiliary feature is illustrated in FIG. 8, which shows a head 80 with a spectacle frame 81. An imaginary circle with a radius of half the width of a face and a center at the lower edge of the nose is denoted by 80. In FIG. 8, yUN denotes the lower edge of the nose, yUK denotes a lower edge of the chin and yUOD denotes a lower edge of the eyes. The width of the face, i.e., the distance between the lines D in FIG. 6, is denoted by yG. An example of a derived auxiliary feature yH which is defined with the aid of a term in the fitting guidelines 70 detected during parsing in step 76 is:
yH=(yUK−(yUN−0.5.Math.xG))/0.5.Math.xG.

(59) This value yH represents a deviation of a calculated chin lower edge of an ideal face from a real chin lower edge as a ratio to half the width of a face and the value is a measure for the vertical length of the face below the nose. Such an auxiliary feature can be used to set the proportions of the lower frame rims of the spectacle frame. As a result of this, it is possible to take account of the fact that the length of the face in the vertical direction may also have an influence on the esthetic impression caused by the spectacle frame and hence that the specific fitting guidelines may predetermine a relationship of the size and/or form of the spectacle frame with respect to the parameter yH.

(60) A further example of a fitting guideline is a position of the pupil within a frame-circumscribing box. This is illustrated in FIG. 10D, which shows the spectacle frame 81 with a frame-circumscribing box 102, for the right eye in this case.

(61) The fitting point height of the pupil (height of the pupil above the lower frame rim) is denoted by y; the horizontal position of the pupil is denoted by x. The width of the box 102 is Δa and the height of the box is Δb. By way of example, the fitting guideline may then provide that, in the horizontal direction, the pupil should be situated between the box center and the nasal golden ratio, i.e., Δa.Math.3.82<x<Δa.Math.0.5. Here, the golden ratio means that the ratio of x to Δa-x equals the ratio of Δa-x to Δa, as is the case for x=Δa.Math.3.82. Eye positions closer to the inner side of the frame rim than this golden ratio are generally found to be less esthetic.

(62) As a similar guideline, the eye position in the vertical direction can be set, specifically in such a manner that the pupil is precisely situated, in the vertical direction, between the box center of the box 102 and the value for the golden ratio above the center, i.e., Δb.Math.0.5<y<Δb.Math.0.618.

(63) The fitting guidelines can also be provided directly as a calculation formula, wherein the variables of the calculation formula then are the above-described features. In other words, the frame parameters in the specific fitting guideline can be specified directly as a term, or they can be determined iteratively by way of an optimization loop. In the latter case, a fitting quality defined with the aid of the terms is optimized; the terms set targets—however, these targets are generally not hit; therefore, e.g., an expression in the form “target quantity=term” would only contribute to the fitting quality within the meaning of an optimization e.g. within the meaning of the method of least squares, but would not directly satisfy this.

(64) Parsing in step 76 is implemented, in particular, for the mentioned auxiliary features, for target quantities and calculation prescriptions to this end and, optionally, for a quality value as a scalar quantity, which is available, for example, in the form of a weighted square sum of the deviation from the target quantities and which may optionally have an additional penalty term, as is already described above.

(65) Then, a list of syntax trees for the terms of step 76 is created in step 79.

(66) Accordingly, the position, orientation and dimension for values such as the position of the pupil center, the position and dimension of the eye (e.g., a rectangle describing the eye), the position, orientation and dimension of the nose, the position, orientation and position of the eyebrows and/or the position of the chin are determined in step 78 for the head model.

(67) The terms of the tree are evaluated for the auxiliary features in step 710, i.e., the auxiliary features present are determined, and values for these auxiliary features, for example for the value yH explained above, are determined in step 711. Then, there is an optimization step in step 712. Here, frame parameters of the parametric frame model are varied and the terms are evaluated until target quantities are reached in step 713. From this, a parameter set for a set of frame parameters that were adapted on the basis of the fitting guidelines emerges at 714. In particular, these are parameters with an esthetic effect, for example scaling of the spectacle frame, as worn pantoscopic angle of the spectacle frame and/or a form of the frame rim in the case of a variable frame rim. Further parameters, such as, e.g., angles of nose pads or a length of spectacle earpieces or a bridge width, are initially kept at standard values that are predetermined by the manufacturer. These are then adapted during the anatomical fitting (e.g., step 41 in FIG. 4).

(68) The optimization loop may also comprise virtual donning, e.g., as described in the European patent application EP 3410178 A1. The preceding steps including the adaptation of the parameters of the parametric frame model ensure a convergence of the optimization to an optimal adaptation for a pair of spectacles.

(69) Emerging as a result during the virtual donning there is, firstly, the parameters of geometric motion (six degrees of freedom, see the German Wikipedia article “Bewegung (Mathematik) [Motion (Geometry)]” as of May 22, 2017), presentable, for example, as a rotation matrix and translation vector, and, secondly, the parameters of the bending of the frame. As a rule, the latter is a single parameter for the angle traversed at the ear resting point during bending. This corresponds to virtual donning, as described in the European patent application EP 3410178 A1. The results of the virtual donning described there are the rotation and translation of the frame and the parameters of the deformation of the earpieces.

(70) After donning, all frame-specific features are available in the coordinate system of the head. To this end, geometric motion is applied to the features. By way of example, the position and orientation of the right and left nose pad of the individualized frame—i.e., of the frame corresponding to the parametric frame model with fitted parameters—is calculated. In the ideal case, this position and orientation should correspond with the previously calculated position in the step of adapting the frame-specific parameters, in which the corresponding feature of the nasal wing was brought into correspondence with the feature on the frame, as will still be explained specifically below. However, on account of restrictions to the individualization in the nose region, it may be the case that the process of virtual donning does not yield the same result as the fitting procedure when determining the position of the frame. By way of example, this may be due to asymmetries of the real nose in conjunction with a symmetric nose rest of the frame. However, as a rule, there should only be very minor differences between the positions. In the case of minor differences (e.g., a distance of the nose pad centers of less than 1 mm), this can be ignored. In the case of relatively large differences, the new position following the virtual donning may trigger a new fitting procedure for the parameters to be determined on the basis of the frame-specific fitting guidelines. Feedback in the form of a notification to the operator in respect of a possible incompatibility of the frame model is also possible.

(71) FIGS. 10A to 10C elucidate this positioning of the eye within the box 102 for different interpupillary distances PD.sub.1 (FIG. 10A), PD.sub.2 (FIG. 10B) and PD.sub.3 (FIG. 10C) in the head 80, wherein PD.sub.1 is a relatively small interpupillary distance, PD.sub.2 is a mid-interpupillary distance and PD.sub.3 is a relatively large interpupillary distance. For esthetic adaptation, an outer rim of the frame form 100 is thickened in the case of FIG. 10A and provided with dominant endpieces, for example in order to maintain the condition of the golden ratio. The endpieces are the outer part of the central part of the spectacle frame; the inner part is referred to as bridge. Thus, the modified parameter in this case is the frame form. In the case of FIG. 10C, a dominant region or dominant bridge is chosen, possibly in conjunction with a greater bridge width, in order to obtain a desired esthetic impression.

(72) FIG. 9 shows examples of adapting the parameters on the basis of fitting guidelines for obtaining the desired esthetic effect. Here, FIGS. 9A to 9C show an effect of a scaling of the spectacle frame 81. In FIG. 9A, a very small frame is virtually placed on the person; it is too small according to esthetic and fashion aspects. The frame is too large in FIG. 9C. In FIG. 9B, the frame has a medium size. In order to ensure an esthetically fitting size for the pair of spectacles, the fitting guidelines may prescribe distances between the frame rim and the edge of the face and/or the eyebrows in this case.

(73) FIGS. 9D to 9F show the influence of the bridge width. In the exemplary embodiment described here, the bridge width is set during anatomical fitting in order to ensure an anatomically correct fit of the spectacle frame on the nose, which will be explained in more detail below. However, it may also alter the esthetic impression, which can be additionally taken into account during the anatomical fitting. A small bridge width b.sub.1 is chosen in FIG. 9D. Here, the frame sits very high due to a collision with the nasal bridge. The bridge width was slightly widened to a bridge width b.sub.2 in FIG. 9E. As a result, the spectacle frame is seated slightly lower and more harmoniously. In the case of FIG. 9F, the bridge width was widened even further to the value b.sub.3. Here, care can be taken within the scope of anatomical fitting that the pupils are situated within a predetermined range relative to the frame rims, for example on the basis of the golden ratio.

(74) Consequently, what can be ensured with the aid of the fitting guidelines and the division into fitting on the basis of fitting guidelines followed by fitting to the anatomy of the head is that prescriptions of a spectacle manufacturer, which are of an esthetic nature in particular, can be satisfied.

(75) In the aforementioned method, and also in other methods for fitting a pair of spectacles, for example in the method described in the European patent application EP 3410178 A1 or in some of the methods explained at the outset as prior art, the position of certain points on the 3D model of the head is required and/or metadata are required, which metadata characterize certain regions for fitting the spectacles, such as a resting point or an ear resting region. One option lies in determining such points or regions manually or by means of the pattern recognition method. A further option will now be described with reference to FIGS. 11 to 15.

(76) FIG. 11 shows a method for setting measurement points onto the 3D model of the head of the person according to one exemplary embodiment. Here, measurement points should be understood to mean points which can be used for the above-described methods, such as, e.g., points which describe facial features such as ears, eyes, eyebrows, and the like.

(77) In step 110, a parametric head model with measurement points is provided. Here, a parametric head model is a parametric model that describes a head. Changing the parameters of the parametric model changes the head form described by the head model. The term parametric head model, as used here, also includes models that only describe part of the head, for example only the parts required for fitting spectacles (in particular, the region of the eyes, nose and ears). An example of a parametric head model is explained below with reference to FIGS. 13A and 13C. Measurement points are set on this parametric head model, for example by manual selection. Examples of such measurement points are likewise explained below with reference to FIGS. 13A and 13C.

(78) Then, in step 111, the parametric head model is fitted to the 3D model of the head of the person. To this end, use can be made of any conventional optimization methods that adapt the parameters of the parametric head model in such a way that there is the smallest possible deviation between the parametric head model and the 3D model of the head of the person (e.g., by means of the least-squares method or the method in the article by J. Booth et al., cited above). Then, in step 112, the measurement points are transferred to the 3D model of the head of the person on the basis of the adaptation. In other words, the position of the measurement points on the fitted parametric head model is used to set corresponding measurement points on the 3D model of the head. This can be implemented by projection from the parametric head model to the 3D model of the head, for example by virtue of a point of intersection of a normal vector, i.e., a vector perpendicular in the case of the measurement point on the parametric head model, with the 3D model of the head being used. In accurate models, it is also possible to use the position of the measurement point on the parametric head model directly as a position on the 3D model of the head.

(79) In this way, it is possible to determine measurement points for substantially any 3D model of any head, with the measurement points only having to be set once on the parametric head model.

(80) FIG. 12 shows a more detailed method, which uses a parametric head model for setting measurement points on a 3D model of the head of a person, embedded in a method for virtual fitting of a pair of spectacles. Instead of the method for virtual fitting of the pair of spectacles in FIG. 12, the methods explained above with reference to FIGS. 1 to 10 may also serve as a possible application for the method of FIG. 11.

(81) In FIG. 12, a parametric frame model with free parameters is provided in step 120. The free parameters in the case of the exemplary embodiment in FIG. 12 serve for anatomical fitting. In other exemplary embodiments, there can be an additional adaptation by means of frame-specific fitting guidelines, as explained above.

(82) In step 121, a parametric head model is provided. The parametric head model can be a face model or head model determined on the basis of principal component analysis (PCA), as described in, e.g., A. Brunton, A. Salazar, T. Bolkart, S. Wuhrer, “Review of Statistical Shape Spaces for 3D Data with Comparative Analysis for Human Faces,” Computer Vision and Image Understanding, 128:1-17, 2014, or else a head model as described in J. Booth, A. Roussos, S. Zafeiriou, A. Ponniah and D. Dunaway “A 3D Morphable Model learnt from 10,000 faces,” 2016 IEEE Conference on Computer Vision and Patent Recognition (CVPR), Las Vegas, Nev. 2016 pages 5543-5552 doi:10.1109/CVPR.2016.598. In step 122, a 3D model of the head of the person is provided, which model may have been created by the camera device of FIG. 2, for example.

(83) In step 123, measurement points are determined on the parametric head model. An example of such a 3D model of at least a part of the face is presented together with coordinate axes in FIG. 14.

(84) In step 123, measurement points are determined on the parametric head model. To this end, a so-called standard head of the parametric head model is provided. A standard head is a head in which the parameters of the parametric head model assume predetermined standard values. In the case of a head model on the basis of principal component analysis, this may be an average head, for example, which corresponds to a first component of the principal component analysis.

(85) In step 123, measurement points are set on the parametric head model. This can take place manually by setting points. An example for such a stipulation is shown in FIG. 13A. Here, a multiplicity of points have been set on a standard head 130 of the parametric head model, for example corner of the mouth, tip of the nose, points along a forehead wrinkle, eye points, nasal bridge and points on the nasal wings. A further example is shown in FIG. 13C. Here, a triangle 132, i.e., three points, is marked on a nasal wing of the head model 130.

(86) In step 124, the parametric head model is fitted to the 3D model of the head of the person using the fitting process. A fitting process is a process in which parameters of the parametric head model are determined in such a way that the parametric head model is fitted as accurately as possible to the 3D model of the head of the person, for example according to the least squares criterion. The steps 123 and 124 can be carried out in any sequence. Step 123 need only be carried out once before the method is carried out, and so the determined measurement points can be used every time the method is carried out for different 3D models of heads of different persons and for different parametric frame models.

(87) Then, in step 125, the measurement points are transferred to the fitted parametric head model. In other words, the position of the measurement points is determined on the fitted head model. To this end, substantially the same transformation, which is used to arrive at the fitted parametric head model from the standard head model, on which the measurement points were determined in step 123, is applied to the measurement points, for example as described in the aforementioned article by J. Booth et al. Optionally, in step 126, the measurement points are transferred to the 3D model of the head. Whether step 126 is used depends on the accuracy of the employed model, i.e., on how accurately the fitted parametric head model corresponds to the 3D model of the head of the person. By way of example, step 126 can be omitted if the mean square deviation lies below a threshold value. The transfer of the measurement points from the fitted parametric head model to the 3D model of the head of the person can be implemented by a projection, in which a normal vector is determined through the respective measurement point on the fitted head model and the point of intersection of this normal vector with the 3D model of the head of the person is then used as a corresponding measurement point on the 3D model of the head of the person. Examples are shown in FIGS. 13B and 13D. In FIG. 13B, the points of FIG. 13A are projected onto a 3D model 131 of the head of the person and, in FIG. 13D, the triangle 132 of FIG. 13C is projected onto the 3D model 131 as a triangle 132′.

(88) This projection operates reliably in the case of many facial models since parametric models often have great smoothness, in particular a greater smoothness than a typical 3D model of the head as illustrated in FIG. 14. Here, the smoothness of surfaces can be defined as a measure of the local deviation of the normal vectors. Alternatively, the local deviation of the point cloud of the 3D model of the head from an approximating polynomial surface may also be defined as a measure, for example in local regions with a diameter of 5 mm in each case. Polynomial surfaces are differentiable infinitely many times and consequently referred to as “smooth” in differential geometry. Local smoothing by means of “moving least squares” (MLS), which may be applied in exemplary embodiments, is described at the url: pointclouds.org/documentation/tutorials/resampling.php, as of Jun. 8, 2017.

(89) Moreover, a manual step can be used (not illustrated in FIG. 12) to mark further measurement points on the 3D model of the head. In particular, these may be points that are not readily detected by the 3D model, for example parts of the person covered by hair. In particular, this may be the case for ears. Therefore, these points are then not accurately identifiable in the 3D model of the head of the person and the points can be added manually. An example of such a measurement point is a resting point of the spectacle earpiece on the base of the ear.

(90) Then, in step 127, features are calculated on the basis of the measurement points (the measurement points at the fitted head model if step 126 is dispensed with or the transferred measurement points when step 126 is carried out). These features, also referred to as measurement features, are based on groups of measurement points and define a region of the head, for example.

(91) The features can be ascertained by means of the direct calculation (e.g., 3 non-collinear points in space uniquely define a plane, the normal vector of which can be calculated by means of the cross product of the normalized difference vectors; 4 non-coplanar points define a sphere, 5 non-coplanar points define a cylinder) or by means of an approximation of a geometric primitive (points, lines or areas) such as a plane or sphere or cylinder to certain measurement points. Then, the feature is determined by the parameters of the adapted geometric primitives, for example by normal vectors and point under consideration of a plane in the case of a plane or by a center and radius of a sphere in the case of a sphere, etc. Examples of such features, which are calculated in step 127, are specified below:

(92) Left or Right Nasal Wing

(93) For the left or right nasal wing of the nose, a plane (e.g., corresponding to the triangle 132′ in FIG. 13D), which is defined by the approximation to a small region of the model in the region of the nose support or the region for the nose pads (e.g., with a diameter of 6 mm), can be used as a feature. The horizontal and vertical nasal wing angle emerge from the position and orientation of the plane. Here, the plane is intersected by the coordinate axes in the center point of the region of the nose support and the arising angle is measured in each case. By way of example, if the three points, corresponding to the triangle 132, are marked on each nasal wing in FIG. 13C, the plane can be calculated from the three points. In the case of more than three points, the plane can be calculated by an adaptation process, for example by way of principal component decomposition on the set of points, or by way of an adaptation with the aid of the least-squares method. As mentioned above, a single plane is representable by a point (x, y and z) in the plane and a normal vector (nx, ny, nz) through this point, with x, y and z being Cartesian coordinates. Therefore, both nosal wings together can be represented as a 12-tuple, i.e., by 12 values (2 points and 2 normal vectors), for example as (x.sub.[N,OD],y.sub.[N,OD],z.sub.[N,OD],nx.sub.[N,OD],ny.sub.[N,OD],nz.sub.[N,OD],x.sub.[N,OS],y.sub.[N,OS],z.sub.[P,OS],nx.sub.[N,OS],ny.sub.[N,OS],nz.sub.[N,OS])

(94) Here, the index N denotes the nose, the index OD denotes the right eye (oculus dexter) and the index OS denotes the left eye (oculus sinister).

(95) Curvature of the Forehead

(96) Here, a section of a circular curve in space can be fitted to measurement points on the forehead, as illustrated in FIGS. 13A and 13C. Parameters of this fit are the center, radius and normal vector of a plane in which the circle lies. This adaptation can be carried out in two steps. Initially, a plane is adapted, as described above for the nasal wings, and then a circle is still adapted in the plane. This adaptation of the circle can take place, for example, by means of a least-squares method or any other conventional fitting method.

(97) Eyebrows and/or Cheekbones

(98) Here, a spline surface S (see the German Wikipedia article “Spline”, as of May 23, 2017) or a bivariate polynomial (see, e.g. the url: en.wikipedia.org/wiki/Polynomial#Definition.fwdarw.“bivariate polynomial”, as of Jun. 8, 2017) is fitted in a region around the eyebrows and/or in a region about the cheekbones to the measurement points in the region of the eyebrows and in the region of the cheekbones. In a spline representation
S.sub.(c1, . . . ,cn):(x,z).fwdarw.y,
coefficients (c1, . . . , cn) of the spline function S are determined in such a way here that for a set of measurement points {(x1,y1,z1), . . . , (xm,ym,zm)} in the corresponding region (eyebrows or cheekbones), a root mean square error F is minimal, i.e., the error F has the following form:
F(c1, . . . ,cn)=Σ.sub.i=1 . . . m(yi−S.sub.(c1, . . . ,cn)(xi,zi)).sup.2.

(99) In this representation, the assumption is made that the process of donning the frame is implemented later by a movement parallel to an xy-plane with, in each case, a fixed y-value in the coordinate system of FIG. 14. If a minimum distance between a back frame rim and the 3D model of the head should be realized by the fitting process, this distance value can be provided in advance as an offset from the spline surface. Then, contact can be detected through correspondence in the y-values (since the y-value is stored in advance as an offset). To this end, each vertex of the back frame rim can then be examined during the later adaptation of the spectacle frame, and a respective vertex, given by the coordinates (x, y, z), is examined in respect of the difference Δy=y−S.sub.(c1, . . . cn): (x, z). Should the vertex be detected to contact or be immersed in the model, then a position of the spectacle frame can be adapted or the frame rim of the spectacle frame can be modified.

(100) Point at the Base of the Ear that serves as a Resting Point for the Spectacle Earpiece

(101) To this end, a single point on the head model can be used; i.e., no measurement points need to be combined in this case. In other exemplary embodiments, an ear resting curve can be determined as described in the European patent application EP 3410178 A1. Should use be made of a model without modeling of the ears (see above), for example a pure facial model, or should the ears have been covered when creating the 3D model of the head of the person, this point at the base of the ear can be generated differently, for example by way of machine learning from images that were used for the creation of the 3D model of the head, wherein a trained feature detector can be used to this end for the purposes of detecting the point at the base of the ear in the images. These points detected in the 2D image are projected onto the 3D model of the head in a further step. Information in respect of such projections is found in background literature in respect of projective geometry and camera calibration, e.g., Hartley and Zisserman, “Multiple View Geometry in Computer Vision,” 2000, from page 7 for the representation of the image pixels as straight lines in space; projection onto a 3D model in space as a calculation of the front-most point of intersection of the triangular mesh with the straight line, also referred to as “ray casting;” see also, e.g., the software library “vtk”, function “vtkModifiedBSPTree:IntersectWithLine”. Alternatively, such a point can also be determined manually, as explained above.

(102) In some exemplary embodiments, certain points such as eye position or pupil position can also be determined by a separate method, for example by means of pupil detection and cornea detection using the images recorded by the camera of FIG. 2. Such determinations are described in the European patent applications EP 3354190 A1 and 17153559.4.

(103) On the basis of the features calculated thus in step 127, frame parameters of the parametric frame model are then calculated in step 128. An example for this calculation is provided below. However, the features can also be used for the frame fitting, described above, on the basis of specific fitting guidelines or for the virtual donning, as described in the European patent application EP 3410178 A1.

(104) In general, for fitting purposes, the features are evaluated in combination in respect of the relative position and orientation and/or of further properties such as angle or curvature. Some examples for the calculation of the frame parameters in step 128 are described below. These may also serve as an example for the anatomical fitting of step 41 in FIG. 4.

(105) Bridge Width

(106) The bridge width is defined in DIN EN ISO 8624:2015-12, appendix A and emerges from the relative position of the nose pads since the nose pads lie further apart from one another in the case of a greater bridge width and the nose pads lie closer together in the case of a narrower bridge width. In the case of a spectacle frame without nose pads, generalized nose pads are defined as specific regions of the nose rest, which are provided as contact regions with the nose. The bridge width arises as the spacing of the center points of these generalized nose pads. Thus, the bridge width can correspond to the spacing of center points of triangles on both nasal wings that correspond to the triangle 132′ in FIG. 13D. Here, the geometric centroid, i.e., the point of intersection of the angle bisectors, can be taken as the center point of the triangle.

(107) For elucidation purposes, FIG. 16 shows a perspective view of a parametric frame model with nose pads 160 (within this sense) and the bridge width 161.

(108) Relative Position and Angle of the Nose Pads

(109) This adaptation is explained in FIG. 15. Here, the nasal wings are presented as a cross section. This is represented by a curve 150 and a nose pad 151 is adapted.

(110) Each of the two nose pads can be adapted by a plane that contacts the respective nose pad (tangential plane). As described for other planes above, this plane of the nose pad can be approximated by a point under consideration (x.sub.P, y.sub.P, z.sub.P) and a normal vector (nx, ny, nz). In particular, the point under consideration can be a center of the nose pad. In the case of the nose pads in the conventional sense, i.e., in the case of metal frames, this center point is defined, e.g., by a projection of the centroid of the nose pad on the outer side, i.e., the contact face of the pad with the nose—wherein the pad center can also be part of the parameterizable frame model as a predefined point—i.e., this point is supplied together with the model. In the case of plastic frames without separate pads, the part of the frame envisaged as a contact area for the nose (160 in FIG. 16) is referred to as nose rest or, in generalized fashion here, as a nose pad. Consequently, the two nose pads can likewise be represented as a 12-tuple, with the representation being implemented in the local coordinate system of the frame in the present exemplary embodiment: (x.sub.[P,OD],y.sub.[P,OD],z.sub.[P,OD],nx.sub.[P,OD], ny.sub.[P,OD], nz.sub.[P,OD], x.sub.[P,OS],y.sub.[P,OS],z.sub.[P,OS], nx.sub.[P,OS], ny.sub.[P,OS], nz.sub.[P,OS]),

(111) where the index P represents the nose pad.

(112) As explained above, the position and orientation of the nose pads then also implies the bridge width.

(113) In this representation of the nose pads, the coordinate origin and the orientation of the coordinate system can be chosen freely because the 12-tuple is transferable into any desired coordinate system by way of a common translation mapping of the points under consideration, or by way of a common rotation mapping of the points under consideration and normal vectors. The precondition is that all parameters of the aforementioned 12-tuple are in fact freely selectable in the parametric frame model. In practice, the parameters are subject to restrictions in a parametric frame model and there are maximum and minimum values for the individual parameters of the parametric frame model (by way of example, a frame cannot have an arbitrarily large size or cannot be manufactured with an arbitrarily large or arbitrarily small bridge width). In any case, both the nose pads and, as mentioned above, the nasal wings can be represented as 12-tuples.

(114) Instead of in Cartesian coordinates as above, the normal vectors can be represented in each case by two angles theta and phi in space (substantially a representation in polar coordinates, wherein 1 is selected as a length (radius) of the normal vector:
(nx,ny,nz)=(sin(phi)*sin(theta),cos(phi)*sin(theta),cos(theta)).

(115) Hence, a total of 10 degrees of freedom then arise for the pads (and hence also for the nose bridge) together; a representation as a 10-tuple is obtained: (x.sub.[P,OD],y.sub.[P,OD],z.sub.[P,OD],theta.sub.OD,phi.sub.OD, x.sub.[P,OS],y.sub.[P,OS],z.sub.[P,OS],theta.sub.OS,phi.sub.OS)=z.sub.[P,OS].

(116) The relationship between nasal bridge width and the position of the nose pads is evident from FIG. 15: If the nasal bridge is broadened, there is an enlargement in the distance between the points under consideration of the planes of the left and right pad accordingly, and vice versa.

(117) A reduction in the number of parameters occurs if the assumption is made that the bridge is symmetrical and the nose pads are symmetrical with respect to one another. With the yz-plane of FIG. 14 as plane of symmetry, the following applies: i. x.sub.[P,OS]=−x.sub.[P,OD] ii. y.sub.[P,OD]=y.sub.[P,OS] and z.sub.[P,OS]=z.sub.[P,OS] iii. theta.sub.[P,OD]=theta.sub.[P,OS] and phi.sub.[P,OD]=−phi.sub.[P,OS].

(118) Then, (w, y.sub.P, z.sub.P, theta, phi) arise as free parameters, with theta=theta.sub.[P,OD]=theta.sub.[P,Os] and phi=phi.sub.[P,OD]=−phi.sub.[P,OS]. Here, w is the bridge width, where x.sub.[P,OD]=w/2 and x.sub.[P,OS]=−w/2 applies. Consequently, five free parameters are present in the symmetric case, which free parameters can be used to adapt the parametric frame model. Depending on the frame, fewer degrees of freedom may be present or the degrees of freedom may be restricted by means of specific fitting guidelines, as explained above.

(119) In order to fit the parametric frame model to the 3D model of the head, the planes of the nose pads may be chosen in such a way that they correspond to the planes of the nasal wings; i.e., in general, the 12-tuples for the nose pads correspond to the 12-tuple for the nasal wings.

(120) By way of example, as a restriction, the position of the bridge or of the nose pads can be fixed in the local coordinate system of the frame (i.e., the values y.sub.P, z.sub.P are fixed), or a fixed and, e.g., linear relationship can be chosen between theta and phi such that theta and phi cannot be chosen independently of one another.

(121) In the case of a reduced set of frame parameters, for example in the aforementioned symmetric case, use can be made of averaging. By way of example, if the corresponding angles theta.sub.[P, OD] and theta.sub.[P, OS] for the nasal wings differ, use can be made of a mean value. Should the difference between the angles be greater than a threshold, a warning to the effect of the symmetric frame form yielding disadvantageous wearing properties in this case can be output. A quality measure that denotes the anatomical fit quality can be used to assess how disadvantageous the wearing properties are. Such a quality measure can be calculated on the basis of the aforementioned distances of the spectacle frame from regions of the head, wherein different distances may be included in the quality measure with different weightings.

(122) Depending on the type of parametric frame, the number of free parameters can be reduced further, for example to two parameters in the region of the nose support, specifically the bridge width and a parameter for the bridge angle. By way of example, the bridge angle is explained in Johannes Eber, “Anatomische Brillenanpassung,” Verlag Optische Fachveröffentlichung GmbH, 1987, page 26, FIG. 24 in respect of the bridge angle.

(123) Pantoscopic Angle of the Frame

(124) Moreover, the pantoscopic angle of the frame (also referred to as as worn pantoscopic angle) can be calculated or adapted by means of the features. In exemplary embodiments in which use is made of frame-specific fitting guidelines as explained above, the pantoscopic angle can already be set during this fitting (step 40 in FIG. 4). The latter can then be adapted further in step 128 of FIG. 12. To this end, a distance is calculated between the frame rim (e.g., the back edge of the lower boundary of the frame rim, left or right bottom corner in a frontal view of the frame) and the aforementioned cheek surfaces, which may be represented by a spline surface. Then, the pantoscopic angle is amended in such a way that a predetermined minimum distance, e.g., 2 mm, is ensured.

(125) Earpiece Length

(126) The earpiece length is calculated in step 128 once the fit of the frame on the nose has been set, for example by way of the aforementioned nose pads. For the purposes of setting the earpiece length of the frame (provided this is a free parameter of the parametric frame model), a front resting point of the earpiece is made congruent with the aforementioned points at the base of the ear.

(127) Then, in step 129, the frame parameters calculated in step 128 are applied to the parametric frame model. In step 1210, there is then virtual donning and rendering, as described with reference to step 56 in FIG. 5. Optionally, a further optimization can take place in step 1211, for example an optimization as described in US 2016/0327811 A1, mentioned at the outset, or a manual adaptation as described in step 57 in FIG. 5. Then, there is a transfer to the ordering system in step 1212. It is also possible to select further frame parameters, for example a color of the central part of the spectacle frame, a color of the spectacle earpieces of the spectacle frame, a material and color of the hinge of the spectacle frame, engravings on the spectacle earpieces of the spectacle frame, design elements, applications to the spectacle earpieces or central part of the spectacle frame. Then, the ordered spectacle frame is manufactured according to the determined parameters, for example using an additive manufacturing method, as explained at the outset.

(128) The foregoing description of the exemplary embodiments of the disclosure illustrates and describes the present invention. Additionally, the disclosure shows and describes only the exemplary embodiments but, as mentioned above, it is to be understood that the disclosure is capable of use in various other combinations, modifications, and environments and is capable of changes or modifications within the scope of the concept as expressed herein, commensurate with the above teachings and/or the skill or knowledge of the relevant art.

(129) The term “comprising” (and its grammatical variations) as used herein is used in the inclusive sense of “having” or “including” and not in the exclusive sense of “consisting only of.” The terms “a” and “the” as used herein are understood to encompass the plural as well as the singular.

(130) All publications, patents and patent applications cited in this specification are herein incorporated by reference, and for any and all purposes, as if each individual publication, patent or patent application were specifically and individually indicated to be incorporated by reference. In the case of inconsistencies, the present disclosure will prevail.