DE10145861B4 - A radiological method for determining the angular relationship between the object and the image receptor in the right-angle technique - Google Patents

Abstract

zu einer interessierenden Rezeptorachse (z) und der Abstand der Kugeln (3) vom Fokus (F) exakt quantitativ berechnet werden, wobei hierfür die exakte quantitative Ermittlung der elliptischen Verzerrung des Röntgenschattens jeder Kugel (3) sowie die Erfassung von deren räumlichen Positionen (M_i') relativ zum Auftreffpunkt (O') des Zentralstrahls auf dem Rezeptor (4) die Grundlage bilden und die tatsächliche Verzerrungslänge

der Röntgenschatten vom Auftreffpunkt (O') des Zentralstrahls auf dem Rezeptor (4) aus betrachtet vermessen wird.Method for the quantitative evaluation of transmission X-ray images, wherein:
Two or three spheres (3) of known dimensions made of X-ray absorbing material attached to the object are brought into a position eccentric to the beam path,
The central ray is oriented strictly perpendicular to the image receptor (4),
- With known distance between focus (F) and receptor (4), the angular relationship (γ) of an object axis of interest

to a receptor axis of interest (z) and the distance of the balls (3) from the focus (F) are calculated exactly quantitatively, for which the exact quantitative determination of the elliptical distortion of the X-ray shadow of each sphere (3) and the detection of their spatial positions (M _i ') relative to the point of incidence (O') of the central ray on the receptor (4) form the basis and the actual distortion length

the X-ray shadow is measured from the point of impact (O ') of the central ray on the receptor (4).

Description

The The invention relates to a method according to the preamble of Claim 1.

The direct quantitative evaluation of (dental) transmission X-ray images is often used (eg in the measurement of bone dimensions). However, due to an unknown, very variable projection geometry and the resulting enlargements / distortions, it is severely flawed, see Hausmann E: Radiographic and Digital Imaging in Periodontal Practice; J Periodontol 2000; 71: 497-503. The actual dimension of an object is therefore only very imprecisely directly measurable. For accurate measurement of linear measurement sections on X-ray images, therefore, the recording must either be strictly standardized, which is often very difficult in clinical practice, or the underlying projection geometry must be known. However, the latter is the case only with very few special X-ray images (eg, lateral cephalograms), but not with normal intra-oral (dental) and many other medical X-ray images. In a commonly used dental X-ray technique, the right angle technique, the central beam is oriented at right angles to the image receptor by means of a film holder, but the position and angle of the object relative to both remains unknown. Different angles of the object relative to the image receptor also have in some cases clinically relevant effects on the imaged length of the structures of interest, see Schulze R, d'Hoedt B: Mathematical analysis of projection errors in "paralleling technique" with respect to implant geometry; Clin Oral Impl Res 2001; 12: 364-371. Regarding the use of reference objects is from the DE 196 19 915 A1 For tomosynthesis recordings, it is known that the imaging location and the distortion of the X-ray shadows of the reference objects can be used for relative position determinations and positional changes between individual recordings.

The Invention is for the so-called right-angle technique has been developed. Object of the invention it is, the projection geometry, under which temporarily with two or three spherical ones reference bodies stocked Object was recorded, based on by the reference balls generated To calculate imaging features a posteriori.

The described tasks are by a method with the features of claim 1. It is made recording both the distance of each individual reference sphere from the x-ray focus calculated, as well as the angular relationship of the spherical system relative to the image receptor. Information is provided by the invention posed with those over yet to be developed algorithms the actual dimensions of the objects, equipped with the reference system are calculated more accurately than with the methods available today can.

advantageous Further developments are subject of the dependent claims 2 to 7.

advantages The invention is the relatively simple applicability and availability. The method is not bound to a fixed projection geometry, It can be carried out with slightly modified right-angle film holders. It is generally on any X-ray recording Applicable, if given the conditions explained below are. After integration of the computational algorithms into a software is the method very quickly applicable. Through quantitative image analysis Be informed about determines the projection geometry underlying the image, provided with no other method known to date can be.

embodiments The invention are illustrated in the drawings and are in Following closer described.

1 Projection geometry in the three-dimensional Cartesian coordinate system as the basis of the mathematical calculation. The individual components are explained in detail in the text.

2 Illustration of the situation (image series no. X / 2A) during the X-ray exposure. The X-ray tube ( 1 ) is by a holding device ( 2 ) at right angles in both room levels to the left side digital image receptor ( 4 ). The two-ball system (ZKS) ( 3 ) is in the object plane. The tilt γ of the ZKS shown here has by definition a negative sign.

3 X-ray of the two balls, as they are using the in 2 illustrated structure was made. The center of the small, circular, bright image marks the point of impingement O '(0, 0, 0) of the central ray, which is the necessary starting point for the further measurement. In addition, the geometric design is drawn on the recording, with the help of which the data for the calculation of the projection geometry are determined.

Theoretical background

• 1. Abstand zwischen Kugel und Fokus
  
• 2. Abstand zwischen Kugel und Bildrezeptor
  
• 3. Abstand zwischen Kugel und Zentralstrahl (d)

The invention is based - on the premise of a rectangular orientation of the central beam to the image receptor - on the quantitative evaluation of the elliptical distortion of spheres, which is induced by an eccentric position in the beam path. Only when the center of the sphere is penetrated by the central ray does the image result in a circular disk, whereas in every other position an elliptical distortion results. Here, the amount of distortion is a function of three parameters:

• 1. Distance between ball and focus
  
• 2. Distance between sphere and image receptor
  
• 3. distance between ball and central jet (d)

The mathematical basis for determining the actual ball position is the in 1 illustrated situation tion in the three-dimensional coordinate system.

• 1. Der Fokus F(X_F, 0, 0) wird durch einen Punkt approximiert und liegt auf der x-Achse des Koordinatensystems (X, Y, Z), wobei der Zentralstrahl mit dieser Achse zusammenfällt und in Punkt O'(0, 0, 0) auf der Bildauffangebene auftrifft.
• 2. Röntgenstrahlen werden als lineare Strahlen beschrieben.
• 3. y- und z-Achse definieren die horizontale bzw. vertikale Achse des Bildrezeptors.
• 4. Der Winkel γ wird zwischen der Achse
  
  die durch die zwei Kugelmittelpunkte (M₁, M₂) festgelegt wird, und einer interessierenden Rezeptorachse (im Beispiel vertikale Achse (z)) berechnet, wobei zwischen
  
  und dieser Achse ein seitlicher Neigungswinkel in einer Parallelebene zur Bildauffangebene (y-z-Ebene) ≤ 45° zu fordern ist.
• 5. Der Fokus-Rezeptor-Abstand FO' ist bekannt.
• 6. Fokus und Mittelpunkte der Referenzkugeln liegen nicht kolinear.

The following assumptions are required for the calculation:

• 1. The focus F (X _F , 0, 0) is approximated by a point and lies on the x-axis of the coordinate system (X, Y, Z), with the central ray coinciding with this axis and at point O '(0, 0, 0) impinges on the image capture plane.
• 2. X-rays are described as linear rays.
• 3. y and z axes define the horizontal and vertical axes of the image receptor.
• 4. The angle γ is between the axis
  
  which is determined by the two sphere centers (M ₁ , M ₂ ) and a receptor axis of interest (in the example vertical axis (z)), where between
  
  and this axis is to require a lateral inclination angle in a parallel plane to the image capture plane (yz plane) ≤ 45 °.
• 5. The Focus Receptor Distance FO ' is known.
• 6. Focus and centers of the reference spheres are not colinear.

All points and routes are in 1 displayed. To simplify the calculation, which is identical for all reference spheres, the ball numbers are replaced by the index "i". In addition, all points in the image capture plane are indicated by a hyphen ('). The sphere center M _i is mapped into _i M '; the intersections of the ellipse edge with O'M ' are labeled R _i '(outside) and S _i ' (inside). The angle α _i defines the outer angle between R _i ', F and S _i '; β _i the inner angle spanned by S _i ', F and O'. Both are calculated:

des Kugelmittelpunktes (M_i) vom Fokus (F) berechnet, indem man eine Hilfsebene aufgespannt durch

und F einführt:

wobei r_i der Radius der Kugel i ist. Da wir den Abstand von M_i relativ zur interessierenden Rezeptorachse z wissen wollen, müssen wir die Projektion

von M_i auf die durch x- und z-Achse definierte Ebene berechnen. Hierzu muß zuerst die Abbildung (V_i') von V_i durch das Ziehen des Lots durch M_i' auf z konstruiert werden. Wir erhalten den Winkel ϵ zwischen dem Strahl durch M_i und

aus:

bestimmt, mit

erhält man durch Berechung aus der umgeformten Gleichung für lineare Funktionen:

Then the distance

of the sphere center (M _i ) of the focus (F) calculated by an auxiliary plane spanned by

and F introduces:

where r _{i is} the radius of the sphere i. Since we want to know the distance of M _i relative to the receptor axis of interest z, we need the projection

from M _i to the plane defined by the x and z axes. To do this, first the map (V _i ') of V _{i must be constructed} by drawing the solder through M _i ' to z. We obtain the angle ε between the ray through M _i and

out:

certainly, with

obtained by calculation from the transformed equation for linear functions:

und

kann nun der vorliegende Winkel zwischen dem Kugelsystem

und z berechnet werden:

γ erhält per definitionem ein positives Vorzeichen, wenn

d. h. das Kugelsystem mit dem oberen Ende in Richtung Fokus geneigt ist. Umgekehrt ist γ negativ, wenn

und damit

mit seinem oberen Anteil (M₁) in Richtung Bildauffangebene gekippt ist. Aus den Berechnungen ergeben sich damit die folgenden Informationen:

• – Abstand der Kugel
  
  zum Fokus
• – Winkel γ zwischen
  
  und der interessierenden Rezeptorachse (hier z).

Here, it should be noted that the vertical location of V _i 'relative to O' is important for the following calculations, which sign is expressed by a positive (V _i '≥ 0) or negative (V _i' <0). From the coordinates

and

Now can the present angle between the ball system

and z are calculated:

By definition, γ is given a positive sign when

ie the ball system is inclined with the upper end in the direction of focus. Conversely, γ is negative if

and thus

is tilted with its upper portion (M ₁ ) in the direction of image capture plane. From the calculations, this yields the following information:

• - distance of the ball
  
  to the focus
• - angle γ between
  
  and the receptor axis of interest (here z).

Experimental evaluation

The procedures were performed using the in 2 Test setup with a commercially available dental X-ray tube (Heliodent MD, Sirona Dental Systems GmbH, Bensheim) evaluated. This prototype used a rectangular, three-sided open wooden box (length: 14 cm, width 12 cm, height = 12 cm) on the front wall of the CCD receptor (Trophy RVG 5, Trophy Radiology SA, Marne la Valle, France) mounted vertically was. For this purpose perpendicular positioning of the central beam was a positioning ring ( 2 ) of a film holder system (RWT, Model anterior, Kentzler-Kaschner Dental GmbH, Germany) at a distance of 45.30 mm from the receptor ( 4 ) so that the ring was parallel to the receptor surface. The X-ray tube ( 1 ) was firmly attached to this ring by means of adhesive tape to allow as little angle error as possible. For marking the impact position O '(0, 0, 0) of the central ray on the image receptor ( 4 ), a circular plastic film (thickness 0.10 mm) corresponding exactly to the ring diameter was glued centered onto the ring side facing the receptor. On the measured film center point, a 0.80 mm large steel ball was glued, the X-ray center of which marks the point O '(0, 0). In each case two reference steel balls (two-ball system: ZKS) of the same diameter (3.15 mm, 5.00 mm) were cast with epoxy resin in a transparent plastic tube (length = 30 mm, ∅ = 9.0 mm) at a distance of about 15 mm and a Tubular side then bevelled. With this bevel, each ZKS was then glued on each screw head of a screw (M8). At a distance of about 20 mm to the image receptor, the corresponding nut was glued to the bottom of the wooden box about 5 mm laterally of the central jet. By screwing in the screws with ZKS, different angular relationships of the ZKS relative to the vertical z-axis of the receptor could thus be set, and at the same time, different angles in the parallel plane to the receptor surface were obtained relative to this axis. The distance focus receptor ( FO ' ) was measured with a caliper gauge to 0.1 mm.

notwendig (3), da diese Strecke die tatsächliche Verzerrungslänge von O' aus betrachtet darstellt. Hierzu sind die folgenden Konstruktionsschritte an jeder Kugelabbildung notwendig:

• 1. Aufsuchen von O'(0, 0, 0).
• 2. Konstruktion der Tangenten von O' an jede Seite der Kugelabbildungen.
• 3. Konstruktion der Winkelhalbierenden zwischen den Tangenten einer Kugel.
• 4. Bestimmung der Punkte R_i' und S_i', die jeweils den äußeren bzw. inneren Schnittpunkt zwischen der Winkelhalbierenden und dem Ellipsenumfang darstellen.
• 5. Vermessung von
  
  und
  
• 6. Halbierung von
  
  dies ergibt den Mittelpunkt M_i' der Abbildungsellipse
• 7. Fällung des Lots von M_i' auf eine Parallele zur interessierenden Rezeptorachse durch O', wobei der Schnittpunkt zwischen Lot und Parallele den Punkt V_i' markiert.
• 8. Vermessung der Strecke
  

With this prototype experimental set-up four angle settings were made with each ZKS and over the in 3 measured illustrated geometric construction. To determine the absolute distortion of each sphere image, the measurement of the distance

necessary (necessary 3 ), since this distance represents the actual distortion length from O '. For this, the following construction steps are necessary on each sphere image:

• 1. Find O '(0, 0, 0).
• 2. Construction of the tangents of O 'on each side of the sphere images.
• 3. Construction of bisectors between the tangents of a sphere.
• 4. Determination of the points R _i 'and S _i ', which respectively represent the outer or inner intersection between the bisector and the ellipse circumference.
• 5. Surveying of
  
  and
  
• 6. Halving of
  
  this gives the center M _i 'of the imaging ellipse
• 7. Precipitation of the lot of M _i 'on a parallel to the receptor axis of interest by O', wherein the Point of intersection between perpendicular and parallel marks the point V _i '.
• 8. Measurement of the route
  

der Referenzkugelmittelpunkte (M_i) zum Fokus (F) errechnet werden müssen, ist bei Anwendung der Methode außer der Winkelbeziehung auch noch der Abstand der Kugel (und damit des Objektes) zu Fokus und Rezeptor ableitbar. Zur Ermittlung der tatsächlich vorliegenden Winkelbeziehung wurde an die Rückwand der Holzbox Millimeterpapier angebracht, so dass die vertikalen Linien parallel zur Rezeptorvorderwand verlaufen. Mit Hilfe einer in einem Abstand von 100 cm zur Box aufgestellten Kamera wurde für jede Winkeleinstellung des ZKS eine digitale Fotoaufnahme vorgenommen, wobei die optische Achse der Kamera durch die Objektebene verlief, lotrecht zur Hinterwand der Box. Durch die Auszählung der vertikalen und horizontalen Millimeter ließ sich über den Tangenssatz der "tatsächliche Winkel γ" (Istwert) errechnen.The steps described under 1. to 8. were measured three times in an image processing software (Adobe Photoshop 5.0, Adobe Software Inc. Mountain View, California, USA) for each X-ray image thus prepared, and γ was determined in each case using the algorithm described above. The mean value of the three measurements is referred to below as the calculated value. Since for the calculation of γ the distances

When the method other than the angular relationship is used, the distance of the sphere (and therefore of the object) to the focus and the receptor can be derived by applying the method to the reference sphere centers (M _i ) to the focus (F). To determine the actual angular relationship, millimeter paper was attached to the back wall of the wooden box so that the vertical lines run parallel to the receptor front wall. Using a camera placed at a distance of 100 cm from the box, a digital photo was taken for each angle setting of the ZKS, with the optical axis of the camera passing through the object plane, perpendicular to the rear wall of the box. By counting the vertical and horizontal millimeters, the tangent set was used to calculate the "actual angle γ" (actual value).

Results

actual values and calculated values are shown in Table 1. On average, the overestimated calculated values the actual value by 0.9 °. The relatively high standard deviation from 3.5 ° between Actual values and calculated values is due to the inaccuracy of the Prototype-like experimental design and the same evaluation method.

Practical use

In the clinical course, the method can be applied by means of a modified film holder, which guarantees a strictly orthogonal orientation of the central ray on the image receptor via a coupling with the X-ray tube. This condition can be achieved by a correspondingly rigid system. In addition, the manufacturer must precisely specify the distance of the focus from the tube leading edge so that the focus-receptor distance ( FO ' ) can be specified exactly. The marking of O 'should take place via a central panel-centered rectangular aperture which is integrated into the film holder and leaves an unexposed edge of approx. ≤ 1 mm on the recordings. The compound of the diagonal of this figure then corresponds to O '. Alternatively, a recess in the image receptor receiving film holder wall would be possible, which guarantees a fixed exact positioning of the receptor to the central beam by this impinges on the center of the receptor. This pixel can be reconstructed on the X-ray image simply by dividing the vertical and horizontal image length.

In The object level can either be a simple ZKS temporarily on the To be examined tooth / implant are adhered in the axial direction, if only distortions with respect to this axis are to be expected. Should Angular divergences between object and sensor in horizontal and vertical level, two ZKS or, more simply, three steel balls (DKS) glued in triangular form in the object plane become. In each case two balls in the parallel plane to reasonably, z-y level be mounted parallel to the respective axis of interest (x, y), to increase the method accuracy. Both ZKS and DKS can be prefabricated, z. B. by pouring into small, transparent Plastic cylinder (ZKS) or plates (DKS). The temporary sticking on the tooth could for exposure with the help of a prosthesis adhesive, with sticky wax or the like, non-toxic material.

The Procedure is not based on the described intra-oral recordings limited, it can in principle for every other transmission x-ray be used. Also here have to the o. g. Requirements met be.

Tabelle 1: Vergleich Istwerte/errechnete Werte für γ für die beschriebene Bildserie von 8 Einzelaufnahmen (IX/2A-X/2D). Zur Verdeutlichung der Richtung der Abweichung ist in Spalte 4 jeweils die Differenz zwischen den absoluten Beträgen beider Werte angeführt. SD = Standard Abweichung.

Table 1: Comparison of actual values / calculated values for γ for the described series of 8 individual images (IX / 2A-X / 2D). To clarify the direction of the deviation, column 4 shows the difference between the absolute values of both values. SD = standard deviation.

Claims (7)

Method for the quantitative evaluation of transmission x-ray images, wherein: - two or three spheres ( 3 ) known dimension of X-ray absorbing material attached to the object are brought into an eccentric position to the beam path, - the central beam strictly perpendicular to the image receptor ( 4 ) - with known distance between focus (F) and receptor ( 4 ) the angular relationship (γ) of an object axis of interest

to a receptor axis of interest (z) and the distance of the spheres ( 3 ) can be calculated exactly quantitatively from the focus (F), for which purpose the exact quantitative determination of the elliptical distortion of the x-ray shadow of each sphere ( 3 ) and the detection of their spatial positions (M _i ') relative to the impact point (O') of the central beam on the receptor ( 4 ) form the basis and the actual distortion length

the X-ray shadow from the point of incidence (O ') of the central ray on the receptor ( 4 ) measured from. Method according to claim 1, characterized in that the balls ( 3 ) along an object axis of interest

be temporarily positioned so that their centers (M ₁ , M ₂ ) are in line with the object axis, which is not colinear with the central ray, and their X-ray shadows on the receptor ( 4 ) are displayed without overlap. A method according to claim 1, characterized in that the required exact positioning of the receptor ( 4 ) to the central beam via a built-in film holder, centered to the central beam rectangular aperture. A method according to claim 1, characterized in that the required exact positioning of the receptor ( 4 ) to the central beam via a recess in the image receptor ( 4 ) receiving film holder wall takes place. Method according to claim 1, characterized in that that the method for the quantitative evaluation of intraoral Serves recordings. Method according to claim 1, characterized in that the balls ( 3 ) are cast in a triangular shape when positioning two balls in a radio-opaque plastic cylinder or when positioning three balls in a plate. Method according to claim 1, characterized in that that the two or three ball system with the help of an adhesive temporary attached to the object.