DE102011075912A1 - Method for providing three dimensional image data set of element e.g. screw implanted into biological body of patient, involves changing gray values of subsequent three-dimensional image data set by registering initial image data sets - Google Patents

Abstract

An initial three-dimensional image data set is provided for description of an element such as a screw. The subsequent three-dimensional image data set is recovered with respect to a biological body (14) by a computer tomograph (18) with an X-ray C-arm (36). The registration of initial image data sets is performed. The gray values of subsequent three-dimensional image data set, are changed as a function of gray values of initial image data set by registration process to generate a modified three-dimensional image data set with suppressed image artifacts. An independent claim is included for computed tomograph.

Description

The invention relates to a method for providing a 3D image data set with suppressed image artifacts to a biological object, which contains an element made of material that absorbs X-ray radiation of a computed tomography more than biological tissue. The invention also relates to a computer tomograph with an image evaluation device, which is designed to carry out such a method.

In pictures, which are won by a computer tomograph, a variety of image artifacts can occur. Such a group of image artifacts form so-called metal artefacts derived from metallic objects. These artefacts are caused by the fact that a metal implant either almost completely absorbs or scatters the commonly used X-radiation. The metal part present in the object to be examined is thus almost completely opaque or opaque to the X-ray radiation. There is a shadow of the metallic object on the detector, so that at these detector sites, which are shielded from the metal, detected signals originate only from Ausleserauschen or scattered photons. The resulting lack of image information leads to the metal artifacts in the resulting computed tomography image.

Usually, in the context of computed tomography, projection x-ray images of the object are taken from different angles and a 3D image data record is reconstructed from the resultant image data set via backprojection. The shadows in the projection images caused by the metal then lead to erroneous data in the 3D image data set. If a projection image (for example, a non-real measured angular range) is reconstructed from the 3D image data record by means of so-called forward projection, then the error-prone data in this projection image lead to the metal artifacts. The metal artifacts affect the image quality of the resulting computed tomography image and complicate the image interpretation and thus the medical diagnosis. Detection and characterization of metal implants are more difficult, even if no automated procedure is used, but the image interpretation is carried out in the context of human judgment.

The problem of metal artefacts is particularly severe when X-ray C-arms are used whose X-ray radiation is of only low intensity. This is the case in particular with mobile X-ray C-arm devices. In particular, hip implants or implants, which are composed of several sub-elements, can then be difficult to detect.

Methods are known for reducing metal artifacts in computed tomography images. These methods usually start after a 2D image data set has been obtained via the forward projection. The metal implant is located in the 2D projection images, whereupon the projection values of the data associated with the image areas are improved via an interpolation process (eg linear interpolation). For this, however, it is necessary for the 3D image data set generated by backprojection to have as little error as possible and sufficiently good segmentation to be carried out on it to identify three-dimensional image regions (voxels) that can be assigned to the metal implant. Such methods are known, for example, from the following publications:
(1) Calender WA, Lever R, Ebersberger J. Reduction of CT artifacts caused by metallic implants. Radiology 1987; 164: 576-577 ; (2) Klotz E, Calendar WA Sokiranski R and Felsenberg D, Algorithms for reduction of CT artifacts caused by metallic implants Proc. SPIE 1990; 1234: 642-50 ; (3) Wang G, Frei T and Vannier MW, A Fast Iterative Algorithm for Metal Artifact Reduction in X-ray CT Acad. Radiol. 2000; 7 607-14 ; (4) Mahnken AH, Raupach R, Wildberger JE, et al. A new algorithm for metal artifact reduction in computed tomography: in virtue and in vivo evaluation after total hip replacement. Invest Radiol 2003; 38: 769-75 ; (5) Watzke O and Kalender WA 2004, A pragmatic approach to metal artifacts reduction in CT: merging of metal artefact reduced images Eur. Radiol. 2005; 14: 849-56 ; (6) Bal M, Spies L. Metal artifact reduction in CT using tissue-class modeling and adaptive prefiltering. Med Phys 2005; 33: 2852-59 ; (7) Oehler M, Buzug TM, Statistical image reconstruction for inconsistent CT projection data. Methods Inf Med 2005; 46: 261-269 ; (8th) Muller J, Buzug TM, Spurious structures created by interpolation-based CT metal artefact reduction. Med Imaging 2009; Physics of Medical Imaging, Proc. SPIE, vol. 7258, 13; March 2009; Lake Buena Vista, Florida ; (9) Prell D, Kyriakou Y, Beister M, WA Calendar, A novel forward projection-based metal artefact reduction method for flat-detector computed tomography, Phys. Med Biol. 2009; 54: 6575-6591 ; (10) Prell D, Kyriakou Y, Struffert T, Doerfler A, WA Calendar, Metal Artifact Reduction for Clipping and Coiling in Interventional C-arm CT, AJNR Am J Neuroradiology 2010; 31: 634 ,

Another problem is that the metal implant may not be fully captured during acquisition of computed tomography images. The result is truncation artifacts. This can lead to image artifacts, which occur primarily in the area in which the metal implant is figuratively cut off. However, it is conditional on this also image artifacts in other areas of a forward projection image. Cut-off artifacts should therefore be avoided.

It is an object of the invention to even better suppress image artifacts in a computed tomography image due to an implant in a biological object.

This object is achieved by a method having the features of claim 1, and a computed tomography with the features of claim 10.

• a) Bereitstellen zumindest eines ersten 3D-Bilddatensatzes zur Beschreibung des Elements;
• b) Gewinnen eines zweiten 3D-Bilddatensatzes bzgl. des biologischen Objekts mittels des Computertomographen, wobei der zweite 3D-Bilddatensatz Daten betreffend das Element umfasst;
• c) Registrieren des ersten 3D-Bilddatensatzes mit dem zweiten 3D-Bilddatensatz;
• d) Anhand der Bildregistrierung Ändern von Grauwerten des zweiten 3D-Bilddatensatzes in Abhängigkeit von Grauwerten des ersten 3D-Bilddatensatzes und so Erzeugen eines modifizierten zweiten 3D-Bilddatensatzes mit unterdrückten Bildartefakten.

The inventive method is used to provide a 3D image data set with suppressed image artifacts to a biological object containing an element of material that absorbs X-radiation of a computed tomography more than biological tissue. The method according to the invention comprises the following steps:

• a) providing at least a first 3D image data set for describing the element;
• b) obtaining a second 3D image data set with respect to the biological object by means of the computer tomograph, wherein the second 3D image data set comprises data relating to the element;
• c) registering the first 3D image data set with the second 3D image data set;
• d) On the basis of image registration changing gray values of the second 3D image data set as a function of gray values of the first 3D image data set and thus generating a modified second 3D image data set with suppressed image artifacts.

By means of the method according to the invention, errors in data of the 3D image data record obtained by the CT scanner can be avoided so that it is already ensured, before a possible forward projection is carried out, that artifacts attributable to the element are suppressed in the resulting computer tomography image. While according to the state of the art, image manipulation for the suppression of artifacts only takes place after the forward projection has been carried out, the method according to the invention starts at an earlier image processing stage in which the underlying 3D image data record is already being manipulated or improved. Not only are the 3D image data sets obtained from the computer tomograph available as a data base for this manipulation, but in particular a comparative 3D image data record is provided with which faulty data can be supplemented or replaced and thus improved. In particular, by comparing an image having the artifacts with an artifact-free comparison image, it becomes possible to suppress or eliminate the originally existing image defects.

The element may in particular be a metal implant in the biological object, which may in particular be a body part of a living being. The element may in particular be opaque to X-radiation of a specific wavelength range. In particular, the first 3D image data set describing the element may be arranged to allow an artifact-free pictorial representation of the element. The second 3D image data set can in particular be obtained by projection from projection images, which are recorded by the computer tomograph in different angular position to the biological object on the same. The registering or image registration in step c) is to be understood as meaning, in particular, a positional and dimensionally correct assignment of the first 3D image data record to the second 3D image data record. It can be given an imaging rule, which allows a vote of the first 3D image data set associated coordinate system to the second 3D image data set associated coordinate system. In step c), it may be provided, in particular, to replace data of the second 3D image data record, which are assigned to an artifact-related image area, by corresponding data of the first 3D image data record.

Preferably, with respect to the second 3D image data set, a segmentation process is performed so that image characteristics attributable to the element are emphasized. In the context of the segmentation method, in particular voxels (three-dimensional pixels) resulting from the second 3D image data set are assigned to regions of the biological object which are occupied by the element. In particular, intensity threshold values for gray values are defined in the context of the segmentation method, with the voxel being assigned to the element when the threshold value is exceeded or fallen short of. In this way a clear identification of the element in the biological object is possible. The matching between the first and the second 3D image data set to be carried out as part of the image registration is very simple.

Preferably, a 2D image data set is obtained from the modified second 3D image data record and a computer tomography image is generated therefrom. The computer tomography image is particularly preferably a forward projection image and / or an X-ray sectional image. Preferably, an interpolation method is then applied to the computed tomography image to achieve a reduction in artifacts in the computed tomography image. Particularly preferred this is a linear interpolation. Then the artifacts are not only suppressed by manipulation of the 3D image data set, but there is a further improvement of the resulting image by a final smoothing. In particular, metal implants can thus be identified particularly well in the biological object in the resulting computed tomography image. Overall, the two-step nature of the method improves the resulting image quality.

Preferably, the second 3D image data set comprises data which can be assigned to volume elements of the biological object. Preferably, in step d) of the method, at least gray values are then changed in the second 3D image data set to those volume elements which, due to the image registration, can be assigned to spatial positions of the element in the biological object. In this case, in particular, replacement or exchange of volume elements (voxels) in the second 3D image data record can be effected by corresponding volume elements of the 3D image data set. The modified second 3D image data record then results in particular by an additive combination of data of the first 3D image data set with data of the second 3D image data set. Erroneous data of the second 3D image data set can be added particularly effectively in this way. Even single errored voxels, which lead to image artifacts, can be avoided.

Preferably, in step a) the at least one 3D image data record is provided in a database, wherein the database comprises at least two different 3D image data records which describe different elements. In particular, it can be provided that each first 3D image data record in the database is assigned to a specific type of implant. In the context of image registration, it can then be provided, in particular, that the first 3D image data record is used for the modification of the second 3D image data set, which has the greatest pictorial similarity to a specific image area in the first 3D image data set. For this purpose, an image registration between the second 3D image data set and all first 3D image data sets in the database can take place, in which case exactly the first 3D image data set having the greatest similarity values is used.

It can preferably be provided that the first 3D image data set provided in step A is obtained in a preceding step via an image capture of a real element and / or is obtained by means of a model of the constructive solid state geometry.

The first 3D image data record can thus be provided in particular by a photographic or tomographic acquisition of the real element. Models of standard implants (screws, hips, rods, etc) can be provided using constructive solid geometry (CSG) methods. In this way, the first 3D image data set can be designed in a particularly realistic way, thereby contributing to the particularly effective compensation of image artifacts. The use of a database is expedient since usually only a manageable number of defined implants is used.

• – Prüfen ob der in Schritt b) gewonnene zweite 3D-Bilddatensatz ein Messfeldüberschreitungsartefakt umfasst, welches von einer nicht vollständigen geometrischen Erfassung des biologischen Objekt im Schritt des Gewinnens des zweiten 3D-Bilddatensatzes verursacht ist, und falls dies der Fall ist:
• – Unterdrücken des Messfeldüberschreitungsartefakts mittels eines Extrapolationsverfahrens, welches an dem zweiten 3D-Bilddatensatz durchgeführt wird. Auf diese Art lassen sich auch solche Artefakte unterdrücken, die nicht nur auf das Material des Elements sondern auch auf seine nicht vollständige Erfassung im Rahmen der Computertomographiebildgewinnung zurückzuführen sind.

Preferably, the method comprises the following additional steps:

• Check whether the second 3D image data record obtained in step b) comprises a field-exceeding artifact, which is caused by an incomplete geometric detection of the biological object in the step of obtaining the second 3D image data set, and if this is the case:
• Suppressing the overfield artifact by means of an extrapolation method performed on the second 3-D image data set. In this way, even those artefacts can be suppressed, which are due not only to the material of the element but also its incomplete detection in the context of computed tomography image acquisition.

In the context of the extrapolation method, in particular data of the second 3D image data set can be changed and / or supplemented and / or replaced depending on data of the first 3D image data set. In this case, extra few assumptions are required to supplement truncated image areas by extrapolation. The first 3D image dataset provides a comprehensive database for a particularly realistic extrapolation. The resulting computed tomography images are then particularly meaningful and make it easier for the attending physician to identify an implant in the biological object.

A computer tomograph according to the invention comprises an X-ray source, a detector and an image evaluation device, which is designed to carry out the method according to the invention. The computer tomograph may in particular be a moveable X-ray C-arm CT scanner, which works only with the aid of soft X-radiation (ie X-ray radiation of low intensity). In this type of computed tomography, metal artifacts are particularly evident as implants almost completely shield the soft X-ray radiation from the detector.

The preferred embodiments illustrated with reference to the process according to the invention Embodiments and their advantages apply correspondingly to the computer tomographs according to the invention.

Reference to exemplary embodiments, the invention is explained in more detail below. Show it:

1 a schematic view of an X-ray C-arm computer tomograph; and

2 a schematic illustration of an embodiment of the method according to the invention.

In the figures, identical or functionally identical elements are provided with the same reference numerals.

1 shows a computer tomograph 18 with an X-ray C-arm 36 , at one end of which is an X-ray source 28 is fixed and X-radiation S in the direction of an X-ray detector 30 sending out. Between the X-ray source 28 and the X-ray detector 30 is a patient 34 arranged on a table, with a body part 14 of the patient 34 is irradiated by the X-ray radiation S.

The X-ray C-arm 36 is rotatably formed and can in this way the body part 14 from different perspectives or at different angles. In this way, you can use the X-ray detector 30 different X-ray projection images are captured, which the computer 32 be transmitted. In the calculator 32 can use a method for rear projection from the projection images, a 3D image data set 22 be reconstructed.

The 3D image data set 22 of the body part 14 is schematic in 2 illustrated. In the embodiment, the body part contains 14 a metal screw 16 , which is an implant in the patient's body 34 is. The screw 16 is intransparent for X-ray S This causes image artifacts 12 in the 3D image data set 22 conditionally. Therefore, a method is proposed in which predefined three-dimensional models of implants are used to provide improved segmentation on the 3D image data set 22 to enable. This type of segmentation then allows for improved identification of the screw 16 in three-dimensional space. One finding is to intervene in the segmentation step so as to avoid image artifacts caused by metal implants. Insufficient segmentation of the screw 16 Namely, in three-dimensional space, interpolation methods known from the prior art would inevitably fail to improve the image quality or would only provide unsatisfactory results. For an effective interpolation, it is necessary to already know the correct position of the screw 16 in the body part 14 to have.

The procedure is now carried out as follows:
In the calculator 32 becomes a database 26 in which 3D models of typical medical implants are stored. With these models, data regarding the correct shape and dimension of the implant are stored. Typical implants here are screws, plates or prostheses. In the exemplary embodiment, the 3D models of the implants are provided via CSG (constructive solid geometry) object modeling. Since the spatial resolution of typical computer tomography systems is not particularly high, even comparatively low spatial resolutions of these 3D models are sufficient.

Already in the 3D image data set 22 allows an image processing program in the computer 32 the rough identification of the screw position 24 , By adjusting the screw position 24 with the data in the database 26 can the calculator 32 the 3D image template 20 the 3D image data set 22 assign. The 3D image data set 22 was generated from the truncated computed tomography data obtained using low dose X-ray. The 3D reconstruction then takes place in the manner known from the prior art, wherein a three-dimensional reconstructed volume region which contains the metal, the 3D image data set 22 underlying. On the 3D image data set 22 then conventional extrapolation methods can be used to compensate for possible clipping artifacts.

Because of the screw 16 however, is the 3D image data set 22 erroneous, so that the three-dimensional voxels only insufficiently reflect the real situation. The 3D image data set 22 is therefore unsuitable for correct segmentation.

In a step R, therefore, an image registration of the 3D image template takes place 20 with the 3D image data set 22 or the voxels, which are assigned to the screw position. It can also be provided that the 3D image template 20 at the patient 34 actually implanted screw 16 was won.

• – Es wird eine einfache intensitätsschwellwertbasierte Segmentierung am 3D-Bilddatensatz 22 durchgeführt, um Voxel zu entfernen, die sich Luft und Wasser zuordnen lassen. Hierbei wird der Schwellwert für Wasser so gewählt, dass Knochen oder Metallsegmente im 3D-Bilddatensatz 22 bestehen bleiben. Durch diesen Schritt ist sichergestellt, dass Rechenzeit und Rechenkosten gering gehalten werden und dennoch ein sehr guter Abgleich mit der 3D-Bildvorlage 20 gewährleistet ist.
• – Nun wird ein Algorithmus ausgeführt, mit dem die 3D-Bildvorlage 20 mit dem 3D-Bilddatensatz 22 abgeglichen wird. Dieser Algorithmus kann auf einem Kreuzkorrelationsverfahren beruhen, um die wahrscheinlichste Lage der implantierten Schraube 16 (Schraubenposition 24) im 3D-Bilddatensatz 22 zu identifizieren.
• – Die 3D-Bildvorlage 20 wird dem 3D-Bilddatensatz 22 überlagert, wobei ein rigides oder nicht nicht-rigides Verfahren zur Bildregistrierung Anwendung finden kann. Nicht rigide Bildregistrierungsverfahren eignen sich insbesondere für elastische Implantate.

The image registration in step R takes place in three stages:

• It becomes a simple intensity-threshold-based segmentation on the 3D image data set 22 performed to remove voxels that can be assigned to air and water. Here, the threshold for water is chosen so that bones or metal segments in the 3D image data set 22 remain. This step ensures that computing time and computational costs are kept low and still a very good comparison with the 3D image template 20 is guaranteed.
• - Now an algorithm is executed, with which the 3D-Bildvorlage 20 with the 3D image data set 22 is adjusted. This algorithm may be based on a cross-correlation method to determine the most probable position of the implanted screw 16 (Screw position 24 ) in the 3D image data set 22 to identify.
• - The 3D image template 20 becomes the 3D image data set 22 superimposed using a rigid or non-rigid image registration process. Non-rigid image registration methods are particularly suitable for elastic implants.

In this way, a modified 3D image data set is created, which is the 3D image 10 underlying. The 3D image 10 can now be projected forward again to generate a 2D image data set. Finally, image interpolation can be performed on the 2D image data set to further improve image quality.

In the embodiment, the screw position can be 24 in 3D image data set 22 only guess. Edges and extension of the screw 16 are difficult to identify and the shape of the screw appears washed out. In this case, reconstruction methods known from the prior art would fail, since the amount of data carrying errors is particularly large. This applies in particular to conventional threshold-based segmentation methods. The present method overcomes this disadvantage by removing the fuzzy image of the screw 16 in the 3D image data set 22 through the 3D image template 20 is replaced. To automate this replacement, image registration is performed in step R.

To determine if the implementation of the procedure is necessary, it may initially be based on the 3D image data set 22 a quality factor is determined. Alternatively, the quality factor can already be determined from the original projection data (ie before the backprojection). In this case, a minimum gray value G0 is set, which for the respective X-ray detector 30 is characteristic. Then, the number of pixels whose gray value is smaller than G0 is divided by the total number of all pixels. This provides a measure of the proportion of erroneous data. If this proportion exceeds a definable threshold, then a high probability of the presence of a metal implant can be assumed and the image modification process can be carried out.

In the embodiment, the computed tomography is 18 movable trained. Movable X-ray C-arm tomographs have a comparatively low X-ray power so that metal artifacts frequently accumulate on them in the resulting computed tomography images. The proposed method therefore proves particularly useful for this type of computed tomography. Alternatively, however, the method can also be used in all other clinical computed tomography devices.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited non-patent literature

• Calender WA, Lever R, Ebersberger J. Reduction of CT artifacts caused by metallic implants. Radiology 1987; 164: 576-577 [0005]
• Klotz E, Calendar WA Sokiranski R and Felsenberg D, Algorithms for reduction of CT artifacts caused by metallic implants Proc. SPIE 1990; 1234: 642-50 [0005]
• Wang G, Frei T and Vannier MW, A Fast Iterative Algorithm for Metal Artifact Reduction in X-ray CT Acad. Radiol. 2000; 7 607-14 [0005]
• Mahnken AH, Raupach R, Wildberger JE, et al. A new algorithm for metal artifact reduction in computed tomography: in virtue and in vivo evaluation after total hip replacement. Invest Radiol 2003; 38: 769-75 [0005]
• Watzke O and Kalender WA 2004, A pragmatic approach to metal artifacts reduction in CT: merging of metal artefact reduced images Eur. Radiol. 2005; 14: 849-56 [0005]
• Bal M, Spies L. Metal artifact reduction in CT using tissue-class modeling and adaptive prefiltering. Med Phys 2005; 33: 2852-59 [0005]
• Oehler M, Buzug TM, Statistical image reconstruction for inconsistent CT projection data. Methods Inf Med 2005; 46: 261-269 [0005]
• Muller J, Buzug TM, Spurious structures created by interpolation-based CT metal artefact reduction. Med Imaging 2009; Physics of Medical Imaging, Proc. SPIE, vol. 7258, 13; March 2009; Lake Buena Vista, Florida [0005]
• Prell D, Kyriakou Y, Beister M, WA Calendar, A novel forward projection-based metal artefact reduction method for flat-detector computed tomography, Phys. Med Biol. 2009; 54: 6575-6591 [0005]
• Prell D, Kyriakou Y, Struffert T, Doerfler A, WA Calendar, Metal Artifact Reduction for Clipping and Coiling in Interventional C-arm CT, AJNR Am J Neuroradiology 2010; 31: 634 [0005]

Claims (10)

Method for providing a 3D image data record ( 10 ) with suppressed image artifacts ( 12 ) to a biological object ( 14 ), which is an element ( 16 ) of material containing X-ray radiation from a computer tomograph ( 18 ) is absorbed more strongly than biological tissue, with the steps: a) providing at least one first 3D image data set ( 20 ) for the description of the element ( 16 ); b) obtaining a second 3D image data set ( 22 ) with respect to the biological object ( 14 ) by means of the computer tomograph ( 18 ), wherein the second 3D image data set ( 22 ) Dates ( 24 ) concerning the element ( 16 ); c) Registering the first 3D image data set ( 20 ) with the second 3D image data set ( 22 ); d) On the basis of image registration changing gray values of the second 3D image data set ( 22 ) as a function of gray values of the first 3D image data set ( 20 ) and thus generating a modified second 3D image data set ( 10 ) with suppressed image artifacts ( 12 ). Method according to Claim 1, characterized by the step: c1) carrying out a segmentation method with respect to the second 3D image data set ( 22 ), so that image characteristics ( 24 ), which the element ( 16 ) are to be highlighted. Method according to claim 1 or 2, characterized by the further step that from the modified second 3D image data set ( 10 ) a 2D image data set is obtained and from this a computed tomography image, in particular a forward projection image and / or an X-ray sectional image, is generated. A method according to claim 3, characterized by the further step of applying an interpolation method, in particular a linear interpolation, to the computed tomography image for reducing artifacts in the computed tomography image. Method according to one of the preceding claims, characterized in that the second 3D image data set ( 22 ) Dates ( 24 ), which volume elements of the biological object ( 14 ) and in step d) in the second 3D image data set ( 22 ) at least grayscale values are changed to such volume elements, which due to the image registration spatial positions of the element ( 16 ) in the biological object ( 14 ) are assignable. Method according to one of the preceding claims, characterized in that in step a) the at least one first 3D image data set ( 20 ) in a database ( 26 ), the database ( 26 ) at least two different first 3D image data sets ( 20 ), which different elements ( 16 ). Method according to one of the preceding claims, characterized in that the first 3D image dataset provided in step a) ( 20 ) in a previous step via an image capture of a real element ( 16 ) and / or is obtained by means of a model of the constructive solid state geometry. Method according to one of the preceding claims, characterized by the additional steps: - checking whether the second 3D image data record obtained in step b) ( 22 ) comprises a field of view artifact which is due to an incomplete geometric detection of the biological object ( 14 ) in the step of obtaining the second 3D image data set ( 22 ), and if so: suppressing the overfield artifact by means of an extrapolation method applied to the second 3D image data set ( 22 ) is carried out. Method according to Claim 8, characterized in that, in the context of the extrapolation method, data of the second 3D image data set ( 22 ) depending on data of the first 3D image data set ( 16 ) and / or supplemented and / or replaced. Computer tomograph ( 18 ) with an X-ray source ( 28 ), a detector ( 30 ) and an image evaluation device ( 32 ), which is designed to carry out a method according to one of the preceding claims.

Images