Note: Descriptions are shown in the official language in which they were submitted.
CA 02264179 2001-11-02This invention relates to an ultrasound imaging system, athreeâdimensional ultrasonographic-image acquisition device,and a procedure for the acquisition of threeâdimensionalultrasound images.A system for determining the position of a sensor within a givenobject and for the display of previously recorded images of theobject corresponding to the sensor position has been describedearlier by BUCHHOLZ in US patent 5.383.454. With that system itis also possible to guide the tip of a sensor to a particularlocation within an object, while the position of the sensor canbe observed on a monitor screen which also displays a previouslyrecorded image of that particular region within the object. inthat earlier concept, the position of the sensor is determinedusing a commercially available, three-dimensional sounddigitizer.CA 02264179 1999-02-22Another example of an earlier method and appropriate system forthe acquisition of diagnostically useful, threeâdimensionalultrasound image data has been described by POLZ in the Europeanpatent EP 0 736 284 A2. That system incorporates a device bymeans of which it is possible, by freely and manually guidingthe ultrasound scanning head, to assemble from a set ofthree-dimensional data tomographic images of an entirethree-dimensional volume object or space to be examined. Theposition and orientation of the ultrasound scanning head areregistered by an additional, electromagnetic sensor system. Theultrasound scanning head, freely guided by hand by thediagnostician, is preferably provided with a holder which alsoaccommodates the receiver of the said electromagnetic sensorsystem. The sensor system, whose receiver coils pick up magneticfields emitted by a transmitter, produces sensor output data(both positional and rotational data) which precisely define thespatial position and orientation of the ultrasound scanninghead. These are translational X, Y and Z axis data as well asrotational data around these axes.A prerequisite for sufficiently precise positional andorientational determinations using magnetic field measurementsis very detailed information on such extraneous parameters as:â interference fields generated for instance by displaymonitors, computers or electric motors;CA 02264179 1999-02-22- interference patterns produced by highly permeable materialsin the magnetic field, for instance metal objects moving withinthe measuring region; orâ electromagnetic interference fields emanating from the ACpower supply.Quantifying these effects and/or minimizing them by appropriatehardware or procedures, be it shielding or continuouscalibration, is a complex matter. The drawback of the earlierconcept referred to thus lies in the fact that it is difficultto obtain positional and orientational determinations with thenecessary degree of accuracy.Another system for the acquisition of ultrasound images with theaid of a freely movable, manually guided ultrasound scanninghead has been described by NOWACKI in US patent 5.197.476. Thisearlier design is used for locating a target object within thehuman body. The system encompasses a table-mountedthreeâdimensiona1 frame equipped with a number of infraredlight-emitting diodes, a pair of infrared cameras for capturingthe radiation emitted by the infrared LEDs, a computer and anultrasound probe which itself is provided with infrared LEDs.Prior to applying the infrared probe the frame is mounted on thetable and by means of the cameras the position of the infraredLEDs is measured and stored in the computer. The human body isthen positioned within or directly next to the reference volume.CA 02264179 1999-02-22The freely manipulable, manually guided ultrasound probe ismoved within the reference volume defined by thethree-dimensional frame in a manner that the ultrasound proberemains within the measuring range of the cameras. The computercompares the position of the infrared light emitting diodesmounted on the ultrasound probe with the starting positions ofthe infrared LEDs on the three-dimensional frame, which permitsboth the very precise determination of the position of theultrasound probe and the display of the position of the targetobject on a computer monitor screen. The drawback of thisearlier invention lies in the fact that the ultrasound imagescan be acquired only within the reference volume predefined bymeans of the three-dimensional frame.A method for the determination of the position and orientationof a platform in space has been disclosed by DI MATTEO in USpatent 4.396.945. The devices serving to unambiguously identifythe three light sources mounted on the platform include threelight modulators positioned between the light source and thefiber optic links. A code generator supplies each of the threelight modulators with a unique code which produces an on-offmodulation of each individual light source. In a modifiedversion of this earlier method, unambiguous identification ofeach light source is obtained by providing each light sourcewith a color reflector which reflects a specific color thatdiffers from that of the other light sources. The drawback ofthis earlier invention lies in the fact that it is necessary toCA 02264179 1999-02-22equip the three light sources, mounted on the moving object,with on-off modulation or, in the case of reflectors, with colorcoding provisions.It is the objective of this invention to solve the problem. Itspurpose is to provide a means for acquiring three-dimensionalultrasonographic images using a freely movable, manually guidedultrasound scanning head, an ultrasound recording device and apositional-determination i.e. locating device, which locatingdevice permits the determination of the position and orientationof the ultrasound scanning head and thus of the spatial positionand orientation of the tomographic ultrasound images relative toany given base by means of linear measurement.In contrast to NOWACKIâs invention per US 5.197.476 which forthe acquisition of the ultrasound images requires the definitionof a reference volume by means of a three-dimensional frame, theinvention here presented makes it possible for the base thatserves to identify the position of the ultrasound probe to beconstituted of receivers, meaning the very cameras that serve torecord the position of the ultrasound probe.The advantages offered by this invention consist essentially inthe fact that the conceptual design of the device here disclosedsimplifies the manipulation conditions in the following manner:- in terms of precise resolution, the system is not affected byexternal parameters;CA 02264179 2001-11-02ââ''~----- 6â the system is easy to handle; even if the positionaldetermination were to be disrupted for instance by anobject that strayed in between the acquisition deviceand the ultrasound scanning head, measurements cancontinue as soon as a clear view is restored; andâ the tracking accuracy is not negatively affected byextraneous electromagnetic fields produced by displaymonitors and/or electrical equipment.The invention provides an ultrasonographic imaging systemfor the acquisition of ultrasound images by means ofelectronic data processing, whereby A) the position of thetomographic ultrasound images (a) relative to any givenspatial base is unambiguously defined, B) the position andorientation of the tomographic» ultrasound images (a) aredetermined by the position and orientation of theultrasound scanning head (b), and C) a fixed control plane(i) which is freely selectable relative to the ultrasoundscanning head (b), and which is defined by at least threedistinguishable control points (f;g;h) that are selected ina specific relationship to the ultrasound scanning head(b), ensures the determination of the spatial position andorientation of the ultrasound scanning head (b) relative toany given base (j) by appropriate linear measurement.Transmitters (4) are positioned at the said minimum ofthree control points in the control plane (i) and receiversCA 02264179 2001-11-02âââ 6a(6) are positioned in the said minimum of four points ofthe base (j).The invention also provides an ultrasound imaging systemfor creating a threeâdimensional ultrasound image of apatient body, the system comprising an ultrasound scanninghead for acquiring a plurality of ultrasound images, eachof the plurality of ultrasound images having a uniquelydefined position relative to a spatial .base defined byplural base points, a fixed control plane for determiningposition and orientation of the ultrasound scanning headrelative to the spatial base by linear measurement, thefixed control plane vfreely selectable relative to theultrasound scanning head and defined by plural controlpoints, and transmitters for emitting electromagnetic wavesassociated with one of the-plural base points or the pluralcontrol points. The ultrasound imaging system furthercomprises receivers for receiving the electromagnetic waveslocated on the other of the plural base points or theplural control points and an image processor for relatingthe plurality of ultrasound images to one another to createthe threeâdimensional ultrasound image of the body, whereinthe electromagnetic waves are used to determine theposition and orientation of the ultrasound scanning head tothereby position and orient the plurality of ultrasoundimages.CA 02264179 2001-11-026bThe invention also provides an ultrasound imaging systemfor creating a threeâdimensional ultrasound image of apatient body, the system comprising a freely movable,manually guided ultrasound scanning head for acquiring aplurality of ultrasound images, an ultrasound acquisitiondevice for storing and displaying the plurality ofultrasound images, and an image processor for relating theplurality of ultrasound images to one another to create thethreeâdimensional ultrasound image of the body. Theultrasound imaging system further comprising a pmsitionallocating device for determining position and orientation ofthe ultrasound scanning head to thereby position and orientthe plurality of ultrasound images, the locating deviceincluding a plurality of electromagnetic wave emittingdevices located on the ultrasound scanning head, aplurality of electromagnetic wave sensor arrays fordetecting the electromagnetic waves of the emittingdevices, and an evaluation unit for computing the positionand orientation of the ultrasound scanning head relative toa spatial base by linear measurements_ based on theelectromagnetic waves.The invention also provides a system for the acquisition ofthree~dimensional ultrasound images, incorporating a freelymovable, manually guided ultrasound scanning head (2), anultrasound acquisition device (9), an image processing unit(8) as well as a positional locating device (10) whichCA 02264179 2001-11-026cencompasses the ultrasound scanning head (2), an evaluationunit (7) and at least two intraspatially operatingelectromagnetic-waveâdetecting sensor arrays (6),permitting the determination of the position andorientation of the ultrasound scanning head (2) and thus ofthe spatial positional and orientation of the tomographicultrasound images. The ultrasound scanning head (2) isprovided with at least three electromagneticâwave-emittingdevices (4), ensuring the spatial determination of theposition and orientation of the ultrasound scanning head(2) in relation to any given base (j) through linearmeasurements. The tomographically acquired images of athreeâdimensional body (1) can be stored and processed bythe image processing unit (8) of a computer (15) in theform of a threeâdimensional data record.The invention also provides a procedure for the acquisitionof threeâdimensional ultrasound images with a systemincorporating a freely movable, manually guided ultrasoundscanning head (2), an ultrasound acquisition device (9), animage processing unit (8) and a positional locating device(10), whereby the positional locating device (10) permitsthe positional and orientational determination. of theultrasound scanning head (2) and thus of the spatialdetermination of the position and orientation of thetomographic images. In the procedure, the positionallocating device (10) encompasses electromagneticâwaveâCA 02264179 2001-11-026demitting devices (4) mounted on the ultrasound scanninghead (2), an evaluation unit (7) and at least twointraspatially operating sensor arrays (6) detecting thesaid electromagnetic waves, ensuring the determination ofthe position and orientation of the ultrasound scanninghead (2) in relation to any given base (j) through linearmeasurements. The tomographically acquired images of athree-dimensional body (1) can be stored and processed bythe image processing unit (8) of a computer (15) in theform of a three-dimensional data record.In one implementation of the concept of this invention,the means provided on the ultrasound scanning head toemit electromagnetic waves for positional andorientational determinations are in the form of opticallight sources.In another implementation of the concept of thisinvention, the means provided on the ultrasoundscanning head to emit electromagnetic waves forpositional and orientational determinations are in theform of infrared light emitting diodes (IRLEDS).CA 02264179 1999-02-22In a different implementation of the concept of this invention,the means provided on the ultrasound scanning head to emitelectromagnetic waves for positional and orientationaldeterminations are in the form of reflectors orelectrofluorescent reflectors.In another implementation of the concept of this invention, themeans provided on the ultrasound scanning head to emitelectromagnetic waves for positional and orientationaldeterminations are in the form of fiber optics connected to alight source.In yet another implementation of the concept of this invention,the sensor systems serving to detect the electromagnetic waveswithin the measuring region are in the form of spatially fixed,unidimensional (linear-array) cameras, allowing an evaluationunit to determine the position and orientation of the ultrasoundscanning head and thus the spatial position and orientation ofthe tomographic ultrasound images.In another implementation of the concept of this invention, thesensor systems serving to detect the electromagnetic waveswithin the measuring region are cameras which are not spatiallyfixed, the position of the cameras being detectable by theacquisition and evaluation of a spatially fixed controlâpointreference field which in turn allows the evaluation unit todetermine the spatial position and orientation of theCA 02264179 1999-02-22tomographic ultrasound images. The acquisition and evaluation ofthe spatially fixed controlâpoint reference field thus permitsreal-time measurements even under unstable environmentalconditions. Every time the cameras acquire an image, thecontrolâpoint reference field is used to recalculate the currentcamera positions, fully compensating for any positional changesof the cameras.In another implementation of the concept of this invention, thesensor systems serving to detect the electromagnetic waveswithin the measuring region are spatially fixed, permitting thepositional and orientational determination of a spatiallyvariable controlâpoint reference field for instance on apatient.In yet another implementation of the concept of this invention,at least two of the sensors serving to detect theelectromagnetic waves within the measuring region are spatiallyfixed cameras, allowing an evaluation unit tovideogrammetrically determine the position and orientation ofthe ultrasound scanning head and thus the spatial position andorientation of the tomographic ultrasound images.In a different implementation of the concept of this invention,the said minimum of two sensors serving to detect theelectromagnetic waves within the measuring region are cameraswhich are not spatially fixed, the position of the cameras beingdetermined by the acquisition and evaluation of a spatiallyCA 02264179 1999-02-22fixed control-point reference field, allowing the evaluationunit to videogrammetrically determine the position andorientation of the ultrasound scanning head and thus the spatialposition and orientation of the tomographic ultrasound images.The acquisition and evaluation of the spatially fixedcontrol-point reference field thus permits realâtimemeasurements even under unstable environmental conditions. Everytime the cameras acquire an image, the control-point referencefield is used to recalculate the current camera positions, fullycompensating for any positional changes of the cameras.In yet another implementation of the concept of this invention,the freely movable, manually guided ultrasound scanning head,the ultrasound acquisition device, the image processing unit andthe positional locating device are connected to aomputer-assisted surgery system (CAS).One application of the procedure according to this invention isbased on the design implementation in which the means providedon the ultrasound scanning head to emit electromagnetic wavesfor positional and orientational determinations are in the formof optical light sources.Another application of the procedure according to this inventionis based on the design implementation in which the meansprovided on the ultrasound scanning head to emit electromagneticwaves for positional and orientational determinations are in theform of infrared light emitting diodes (IRLEDs).CA 02264179 1999-02-2210Another application of the procedure according to thisinvention is based on the design implementation in which themeans provided on the ultrasound scanning head to emitelectromagnetic waves for positional and orientationaldeterminations are in the form of reflectors orelectrofluorescent reflectors.Another application of the procedure according to this inventionis based on the design implementation in which the devicesprovided on the ultrasound scanning head to emit electromagneticwaves for positional and orientational determinations are in theform of fiber optics connected to a light source.Yet another application of the procedure according to thisinvention is based on the design implementation in which thesensor systems serving to detect the electromagnetic waveswithin the measuring region are in the form of spatially fixed,unidimensional cameras, allowing an evaluation unit to determinethe position and orientation of the ultrasound scanning head andthus the spatial position and orientation of the tomographicultrasound images.Another application of the procedure according to this inventionis based on the design implementation in which the sensorsystems serving to detect the electromagnetic waves within themeasuring region are cameras which are not spatially fixed, theposition of the cameras being detectable by the acquisition andCA 02264179 1999-02-2211evaluation of a spatially fixed controlâpoint reference fieldwhich in turn allows the evaluation unit to determine thespatial position and orientation of the tomographic ultrasoundimages. The acquisition and evaluation of the spatially fixedcontrol-point reference field thus permits real-timemeasurements even under unstable environmental conditions. Everytime the cameras acquire an image, the control-point referencefield is used to recalculate the current camera positions, fullycompensating for any positional changes of the cameras.Another application of the procedure according to thisinvention is based on the design implementation in which thesensor systems serving to detect the electromagnetic waveswithin the measuring region are spatially fixed, permitting thepositional and orientational determination of a spatiallyvariable controlâpoint reference field for instance on apatient.Yet another application of the procedure according to thisinvention is based on the design implementation in which atleast two sensors serving to detect the electromagnetic waveswithin the measuring region are spatially fixed cameras,allowing an evaluation unit to videogrammetrically determine theposition and orientation of the ultrasound scanning head andthus the spatial position and orientation of the tomographicultrasound images.CA 02264179 1999-02-2212Another application of the procedure according to this inventionis based on the design implementation in which the said minimumof two sensors serving to detect the electromagnetic waveswithin the measuring region are cameras which are not spatiallyfixed, the position of the cameras being determined by theacquisition and evaluation of a spatially fixed controlâpointreference field, allowing the evaluation unit tovideogrammetrically determine the position and orientation ofthe ultrasound scanning head and thus the spatial position andorientation of the tomographic ultrasound images. Theacquisition and evaluation of the spatially fixed control-pointreference field thus permits real-time measurements even underunstable environmental conditions. Every time the camerasacquire an image, the control-point reference field is used torecalculate the current camera positions, fully compensating forany positional changes of the cameras.A different application of the procedure according to thisinvention is based on the design implementation in which thefreely movable, manually guided ultrasound scanning head, theultrasound acquisition device, the image processing unit and thepositional locating device are connected to a computer-assistedsurgery system (CAS).The principles of optical and photogrammetric positionaldetermination employed in this invention are described, interalia, in the following textbook:CA 02264179 2001-11-0213Jordan/Eggert/KneisslHandbuch der Vermessungskunde (manual of geodeticsurveying)10th edition, completely revisedVol. IIIa/3Photogrammetry'J.B. Metzlersche Verlagsbuchhandlung, Stuttgart, 1972(see in particular paragraphs 144, 145, 146, 147).As used herein, the terms âinterference measurementsâand âlinear measurementsâ refer not onlyto the kind of interference measurements employed for instancein laser ranging but also, and especially, to the interferenceeffects by virtue of which optical systems can produce images(for instance central perspectives) along an image plane orline.Moreover, the term linear measurements is intended to expresslongitudinal measurements along an image plane (or line) (forinstance on a CCD chip), such as the linear measurement of thedistance zl, 22 in fig. 4 (par. 146.2, fig. 5 in the geodeticsurveying manual), as well as absolute measurements of thelength of the object of interest, as employed for instance inrun-length measuring methodology (for example in a GPS system).CA 02264179 1999-02-2214In lieu of the method shown in fig. 4, employing two projectionplanes, it is also possible to use a measuring method which islikewise based on the array principle but employs at least 3non-colinear, unidimensional CCD chips. One such product iscommercially available, by the name of OptotrakTM.If the cameras in the system according to this invention areequipped with CCD chips, it is possible for four non-coplanarpoints on the CCD chips of the cameras to constitute the minimumreceiver base. In that case, the (linear) measurement can bemade for instance by videogrammetric means or via a beam array,i.e. the images on the CCD chips are planimetrically measured.In this context, given that CCD chips permit relativemeasurements, the base can be selected at will which in turnallows the cameras to be positioned at will. It follows that themutual position of the base points on the CCD chips will have tobe determined which can be accomplished, without any referencevolume, for instance by measuring the distance between thecameras .The following will describe this invention and its conceptualenhancements in more detail, with the aid of partly schematicillustrations of several design examples in which:Fig. 1 is a schematic representation of one design versionof the system according to this invention;CA 02264179 1999-02-2215Fig. 2 is a schematic representation of another designversion of the system according to this invention;Fig. 3 is a schematic representation of yet another designversion of the system according to this invention; andFig. 4 is a schematic illustration serving to explain thephotogrammetric procedure.The design version of the system according to this invention as shown in ï¬g. 1 includes a freelymovable, manually operated ultrasound scanning head 2, an ultrasound recording i.e. acquisitiondevice 9, an image processing unit 8 and a positional locating device 10, serving to acquire three-dimensional ultrasound images of the body 1. The locating device 10 permits positional andorientational determination of the ultrasound scanning head 2 and thus the determination of thespatial position and orientation of the tomographic ultrasound images. Mounted on theultrasound head 2 are transmitters 4 whichemit electromagnetic waves. Spatially ï¬xed cameras 6, for example digital cameras, are providedand serve to capture the said electromagnetic waves emitted by the transmitters 4. Thetransmitters 4 are imaged on the ultrasound scanning head 2. The evaluation unit 7 thencomputes from these images the position and orientation of the ultrasound scanning head 2. Withthe aid of a handle 5, the operator can freely move the ultrasound scanning head 2 and is thusable to assemble a complete three-dimensional tomographic image of the body 1 as derived fromthe three-dimensional data record defined in the image processing unit.CA 02264179 1999-02-22WO 98/08112 PCT/CH97/00311inâ l VFig. 2 shows a design version of the system according to this invention, which includes a freelymovable, manually guided ultrasound scanning head 2, an ultrasound acquisition device 9, animage processing unit 8, a positional locating device 10 and a control-point reference ï¬eld 12consisting of light-emitting diodes (LEDs), serving to acquire three-dimensionalultrasonographic images of the body 1. The locating device 10 permits positional andorientational determination of the ultrasound scarming head 2 and thus the determination of thespatial position and orientation of the tomographic ultrasound images. Attached to the ultrasoundscarming head 2 are transmitters 4 which emit electromagnetic waves. Cameras 6, for exampledigital cameras, serve to capture the said electromagnetic waves emitted by the transmitters 4. Inthis implementation of the invention, the cameras 6 are not spatiallyï¬xed, their position 11 being determined by the acquisition and evaluation of the imagesproduced by a spatially ï¬xed control-point reference ï¬eld 12. As the two cameras 6 capture theelectromagnetic waves emitted by the transmitters 4, these transmitters 4 are imaged onindividual image planes. The evaluation unit 7 then computes from the distorted perspectives ofthe two images the position and orientation of the ultrasound scanning head 2. With the aid of ahandle 5, the operator can freely move the ultrasound scanning head 2 and is thus able toassemble a complete three-dimensional tomographic image of the body 1 as derived from thethree-dimensional data record deï¬ned in the image processing unit.Fig. 3 shows a design version of the system according to this invention, which includes a freelymovable, manually guided ultrasound scarming head b, an ultrasound acquisition device 9, animage processing unit 8 and a positional locating device 10 for the acquisition of ultrasoundimages a. The positional locating device 10 permits positional and orientational determination ofthe ultrasound scanning head b and thus the determination of the spatial position and orientationof the tomographic ultrasound images a. Connected to the ultrasound scarming head b are ï¬xedtransmitters f; g;h which emit electromagnetic waves. Spatially ï¬xed cameras 6, for instancedigital cameras, are provided for recording the electromagnetic waves emitted by the transmittersf;g;h. The cameras 6 capture these electromagnetic waves emitted by the transmitters f;g;h andCA 02264179 1999-02-22W0 98/(')8112 PCT/CH97/00311.11 l 7from the images thus acquired the evaluation unit 7 then calculates the position and orientation ofthe ultrasound scanning head b. With the aid of a handle 5, the operator can freely move theultrasound scanning head b and is thus able to assemble a complete three-dimensionaltomographic image of the body as derived from the three-dimensional data record deï¬ned in theimage processing unit.Fig. 4 is intended to explain the photogrammetric method employed using the speciï¬c exampletitled "reconstruction (of the coordinates) from two perspective views with known positions ofthe image planes relative to each other and with known internal orientation", as perJordan/Eggert/Kneissl, manual of geodetic surveying, 1972, page 2271:146.2 Reconstruction from two perspective views with known positions of the image planesrelative to each other and with known internal orientation:Given the respective internal orientation, one knows the visual rays [0,], [O2] and their positionrelative to the image planes. Knowing the mutual position of the image planes thus meansknowing the mutual position of the visual ray bundles. The known spatial position of H1, H2, 01,02 yields the core axis 0, the straight line s=(H1 Hz), the epipoles K,, K2 and the perspectiveallocation of the epipolar ray bundles relative to s. For any image pair Pâ, P2 tied tocorresponding epipolar rays, this will ensure that the visual rays s,=[O,P'] and s2=[O2P2] willintersect at a spatial point P.One thus knows the position of P in the system of visual ray bundles. To determine the positionof P in a given spatial reference system S one must know the position of 1, 2 within S. If the latteris not readily available, it must be determined per par. 145.3. As an example of an empirical,nonautomatic reconstruction, the following will address the soâcalled plane-tablephoto grammetry.CA 02264179 1999-02-22WO 98/08112 PCT/CH97/003114/2â I <3a) In plane-table photogrammetry (fig. 4) <(a), in its simplest representation, with CCDchips to be assigned to the image planes ,, 2>Iâ is assumed to be a horizontal plane (planimetric plane). The image planes II,, H2 are assumedto be vertical, i.e. the main visual rays [O,, H,], [02, H2] to be horizontal. h,, h2 constitute theimage horizontal in II,, 112. X], z, and x2, z2, respectively, are the image coordinates in , and 2,respectively. The point of origin of each image coordinate system is the main point, the x-axispoints extend in the horizontal direction. ï¬,, F12 are assumed to represent the height of the centralpoints 0,, 02 above Iâ.It is also possible from the coordinates x,, x2 of any given image points Pâ, P2 to enter into theknown planimetric planes 1'I'l, IT2 the planimetric planes P", P2â, identifying the planimetric planePâ of the spatial point P to be reconstructed as a cross section of the planimetric visual-ray planess',=[O',P'[] and sâ,=[O'2P'2] (forward section). While the base line O',O'2 is applied at the mapscale, the image widths and x-coordinates will be multiplied by a suitable factor in a mannerwhich will allow s',, s'2 to be traced with sufï¬cient accuracy.From the similar triangles O2PQ and O2P2Q2 one can derive the height C 2 of P above the plane[O2h2] viaThis yields the height C of P above Iâ by way of C = n2 + C 2. By means of an analogouscalculation of C = fl. â C, one can compensate for any errors.CA 02264179 1999-02-22IWO 98/08112 PCT/CH97/00311,1/r I *ââ~As is shown in ï¬g. 4, the planimetric planes K',, K'2 of the epipoles K,, K2 are determined asintersections i.e. crossover points of the baseline o'=[O',O'2] with H',, II'2, their respective heightabove Iâ, meaning their position in III, 112, is found by inverting the trapezoid O',O'2O2O,,dragging along the vertical carrier line for K, and K2. The epipolar rays are needed foridentifying appropriate epipoles in the images of object characteristics.If the image planes H'*, 112* were to be in some general spatial position, one could easily revertto the case, just discussed, of vertical image planes 11,, H2. One would only have to reproject 1tâ*from O, to II, and 1r2* from O3 to H2. Without such reprojection, the total of the points Pâ per ï¬g.4 would make up the normal plane of the imaged object on a plane perpendicular to IIâ* and H2*and C would be the distance between point P and this plane.
