US20050031180A1 - Method and apparatus for calibration and correction of gray levels in images - Google Patents

Method and apparatus for calibration and correction of gray levels in images Download PDF

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US20050031180A1
US20050031180A1 US10/775,912 US77591204A US2005031180A1 US 20050031180 A1 US20050031180 A1 US 20050031180A1 US 77591204 A US77591204 A US 77591204A US 2005031180 A1 US2005031180 A1 US 2005031180A1
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image
calibration
gray level
sequence
zone
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Fanny Jeunehomme
Serge Muller
Razvan Iordache
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GE Medical Systems Global Technology Co LLC
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Assigned to GE MEDICAL SYSTEMS GLOBAL TECHNOLOGY COMPANY, LLC reassignment GE MEDICAL SYSTEMS GLOBAL TECHNOLOGY COMPANY, LLC ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: MULLER, SERGE, IORDACHE, RAZVAN, JEUNEHOMME, FANNY
Publication of US20050031180A1 publication Critical patent/US20050031180A1/en
Priority to US12/115,596 priority Critical patent/US7548640B2/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/50—Image enhancement or restoration by the use of more than one image, e.g. averaging, subtraction
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
    • A61B6/58—Testing, adjusting or calibrating apparatus or devices for radiation diagnosis
    • A61B6/582—Calibration
    • A61B6/583—Calibration using calibration phantoms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N23/00—Cameras or camera modules comprising electronic image sensors; Control thereof
    • H04N23/30—Cameras or camera modules comprising electronic image sensors; Control thereof for generating image signals from X-rays
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10116—X-ray image
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N5/00—Details of television systems
    • H04N5/30—Transforming light or analogous information into electric information
    • H04N5/32—Transforming X-rays

Definitions

  • the present invention relates to a method apparatus for calibrating and correction of gray levels in images.
  • the present invention is directed to acquiring a sequence of radiographic images and correction images of an object under observation.
  • the present invention relates to a method and apparatus for an acquiring sequence of radiographic images and calibration and correction of images of an object under observation by subtracting from each image of the sequence the spurious variation of a gray level between the images of the same sequence.
  • the present invention can be particularly used in the medical field, such as, for example, in mammography and in the detection of cancerous tumors.
  • a known radiographic apparatus is comprises a console, means for providing a beam of radiation in the direction of means for detection.
  • the means for detecting receives the radiation after passing through an object under observation placed in the observation space arranged in the beam, between on the means for providing the beam of radiation and on the means for detection.
  • the known apparatus also comprises means for processing enabling acquiring and processing a sequence of images of an object sent from the means for detection.
  • the difference in absorption of the radiation by the different parts of the object under observation enables obtaining information on the composition of the object.
  • the image formed on the means for detection comprises different gray levels, from which information can be derived.
  • the object under observation is a human body part, for example, the bones will appear clearly on the image acquired by the means for detection and are distinctly separate from the part formed by the muscles.
  • the means for detection measures an increase in the variation of the gray level. This phenomenon is due to a persistence or remanence of the radiographic information from one image to the other, which causes the gray level to vary between the images.
  • the variation of the gray level in the sequence depends on the thickness and the composition of the object that is being observed. Thus, for an object observed having a first thickness, will have curve of the variation versus time different than a curve for an object having a second thickness different from the first thickness.
  • the variation of the gray level is due principally to the trapping of charges in the photodiodes of the means for detection.
  • the variation can also have a number of causes. It can be a question especially of an increase in temperature of the different elements of the apparatus.
  • the variation of the gray levels from one image to another perturbs the measurements acquired by the apparatus.
  • the quality and the interpretation of the images acquired may deteriorate considerably.
  • the measures made are similarly distorted by the spurious variation of the gray level from one image to the other.
  • the variations can be of the same order of magnitude as the dynamics in gray levels of the signal that one wants to detect.
  • Certain methods enable elimination of this remanence in special applications using special devices.
  • the law of decrease of remanence can be deduced. From the law of decrease of remanence between two acquisitions, the value of the remanence at given second time can be deduced of the following acquired image and thus correct the images acquired in a sequence.
  • An embodiment of the invention provides a method and an apparatus for correction of gray levels in images.
  • An embodiment of the invention is directed to correcting the remanence in a sequence of radiographic images.
  • the method and the apparatus are able to eliminate the utilization of black measurement devices.
  • An embodiment of the invention provides a method and an apparatus for calibration a device capable of acquiring a sequence of radiographic images. Calibration is done so as to be able to correct the effects of the variation of gray level in a sequence of radiographic images of an object under observation.
  • An embodiment of the invention provides a method and an apparatus for calibration and correction of radiographic images applicable to all repeatable variation phenomena; that is, variation phenomena that repeat from one measurement of an acquisition sequence to the next when maintaining identical acquisition phenomena from one measurement of an acquisition sequence to the next.
  • the invention similarly relates to an apparatus capable of acquiring a sequence of radiographic images implementing a method according to an embodiment of the invention.
  • FIG. 1 schematically represents a known apparatus for acquiring a sequence of radiographic images
  • FIG. 2 schematically represents a known development of remanence as a function of time in a sequence of radiographic images
  • FIG. 3 schematically represents a known correction method for remanence according to the state of technology using a black measurement
  • FIG. 4 schematically represents a method of calibration and correction of sequences of image according to an embodiment of the invention, wherein the calibration is done prior to acquisition of the sequence of images of the object under observation;
  • FIG. 5 schematically represents a spatially adaptive embodiment of the method according to FIG. 4 ;
  • FIG. 6 schematically represents a method according to an embodiment of the invention, wherein the calibration is done at the same time that the acquisition of the sequence of images of the object to be observed;
  • FIG. 7 schematically represents a spatially adaptive embodiment of the method according to FIG. 6 ;
  • FIG. 8 schematically represents a longitudinal section of a calibration device used in an embodiment of the invention.
  • FIG. 9 schematically represents the different steps of an embodiment of the invention wherein calibration data of at least two successive sequences are combined.
  • FIG. 10 schematically represents the different steps of an embodiment of the invention wherein calibration data of at least two sequences having different calibration devices are combined.
  • an apparatus 1 comprises a console 5 (having a substantially vertical extension) and means for providing a radiographic beam emitter 4 facing in the direction of a plate 7 comprising means for detection 2 .
  • the means for detection 2 may comprise a photodiode matrix.
  • the means for detection 2 collects the radiation, for example, X-rays, after passing through an object under observation placed in the observation space 6 arranged in the beam 4 , between on the one hand the emitter 3 and on the other hand the detector 2 of the apparatus 1 .
  • the extensions of the emitter 3 and the detector 2 can be, for example, horizontal and perpendicular to the console 5 but any observation direction is possible, especially due to the fact of the possible rotation of the assembly formed by the emitter 3 and the detector 2 about a substantially horizontal axis of extension.
  • the apparatus 1 may also comprise means for processing 8 enabling acquiring and processing a sequence of images of an object sent from the detector 2 .
  • an image formed on the detector 2 comprises different gray levels, from which information can be derived.
  • the object under observation is a human body part, for example, the bones will appear clearly on the image acquired by the detector and are distinctly separate from the part formed by the muscles.
  • FIG. 2 shows that in a succession of images acquired at times t 1 , t 2 , t 3 , for example, the detector measures an increase in the variation L of the gray level. This phenomenon is due to a persistence or remanence of the radiographic information from one image to the other, which causes the gray level to vary between the images.
  • the variation L of the gray level of the image running at time t 1 is represented relative to a first image acquired at time 0 .
  • FIG. 2 similarly shows that the variation L of the gray level in the sequence depends on the thickness and the composition of the object that is being observed.
  • a curve ⁇ 1 for an object observed having a second thickness different from the first thickness
  • a curve ⁇ 2 different from the first.
  • the variation L of the gray level is due principally to the trapping of charges in the photodiodes of the detector.
  • the variation L can also have a number of causes. It can be a question especially of an increase in temperature of the different elements of the device.
  • the variation of the gray levels from one image to another perturbs the measurements acquired by the device.
  • the quality and the interpretation of the images acquired may deteriorate considerably.
  • the measures made are similarly distorted by the spurious variation of the gray level from one image to the other.
  • the variations can be of the same order of magnitude as the dynamics in gray levels of the signal that one wants to detect.
  • FIG. 3 shows that between two acquisitions of images done at times t 1 and t 2 , the remanence diminishes according to an exponential distribution that can be determined. Consequently, at least one black measurement is made between two acquisition instants corresponding to gray levels supplied by the detector in the absence of exposure by x-rays. The black measurement is done at time tm, for example, and enables determining the value of the remanence L m for that instant.
  • the law of decrease of remanence can be deduced. From the law of decrease of remanence between two acquisitions, the value of the remanence at time t 2 can be deduced of the following acquired image and thus correct the images acquired in a sequence.
  • An embodiment of the invention is a calibration method of an apparatus capable of acquiring a sequence of radiographic images and correction of images of an object under observation enabling correcting the unwanted effects of the gray level variations in a sequence of radiographic images.
  • the embodiments of the method can be considered according to two approaches.
  • the calibration step is done prior to acquisition of the sequence of images of the object under observation.
  • the second approach allows performance of the calibration at the same time as acquisition of the images of the object under observation.
  • FIG. 4 An embodiment of a method for implementing the first approach is represented schematically in FIG. 4 .
  • the method represented in FIG. 4 comprises two parts.
  • a first part is the calibration part comprising three steps (a), (b), (c) in FIG. 4 .
  • the second part is the correction of the images of the object under observation.
  • the second part comprises three steps (d), (e) and (f) in FIG. 4 .
  • the calibration part is described as follows. At the time of step (a), using the radiographic apparatus a sequence of images #1, #2, . . . #N are acquired. Acquisition of the sequence is done by observing a calibration device 40 .
  • the calibration device 40 is positioned in the zone of observation over the detector of the apparatus and covers the greater part of the detector surface.
  • This sequence is acquired for a given acquisition frequency.
  • the acquisition frequency can be acquisition of an image every 30 seconds or acquisition of an image every 60 seconds.
  • the images can also be acquired at irregular time intervals.
  • the acquisition frequency of the calibration sequence is preferentially the same as the acquisition frequency that is to be used for acquiring the sequence of images of the object under observation.
  • FIG. 4 ( a ) thus represents schematically a first sequence of images of at least one calibration device 40 having a given thickness.
  • Each calibration device 40 comprises at least one plate, whose thickness is between 1 cm and 8 cm.
  • Each plate has absorption characteristics for the radiation emitted by the device that are substantially equal to the object that is to be subsequently observed.
  • the known type BR 12 plates as used in mammography can be utilized since they have the same attenuation characteristics as glandular tissues like the breast.
  • other materials can be used such as, for example, Lucite or Plexiglas.
  • a mean gray level is determined on a selected homogeneous zone of interest 41 , as shown in FIG. 4 ( a ).
  • the dimensions of the zone of interest 41 are typically 100 pixels ⁇ 100 pixels.
  • acquisition of the images of the calibration device is repeated several times. Thus, typically, each sequence is repeated four to five times. The mean of the results are then determined.
  • a series of acquisition of sequences is then done using calibration devices 40 having different thicknesses.
  • the mean gray levels are obtained regarding the zone of interest 41 different between each sequence of the series.
  • the mean gray level evolves as a function of time; that is, it varies between successive images of the same sequence.
  • the average gray levels in the zone of interest 41 of each image of all the sequences of the series are made.
  • the value of the mean variation of gray level between the current image and the first image is determined.
  • step (b) One then proceeds to the step (b) in FIG. 4 .
  • step (b) for each n th image the relative difference L (n) / ⁇ overscore (C (1) ) ⁇ is determined. Then the graph of L (n) / ⁇ overscore (C (1) ) ⁇ is plotted as a function of ⁇ overscore (C (1) ) ⁇ . Thus, it is confirmed that this function can be approximated by a straight line.
  • L (n) ⁇ overscore (C (1) ) ⁇ [ ⁇ (n) ⁇ overscore (C (1) ) ⁇ + ⁇ (n) ] (2) wherein ⁇ (n) and ⁇ (n) are the coefficients of the linear regression of the curves plotted at the time of step (b) and calculated at the time of a step (c).
  • Step (c) shows that using the means for processing included in the apparatus, the coefficients of regression ⁇ (i) and ⁇ (i) corresponding respectively to the director coefficients and at the ordinate to the origin of each line of image i is determined. These coefficients are stored in the means for providing a memory of the apparatus included in the means for processing 8 or in means arranged outside of the apparatus. The operation of step (c) ends the calibration.
  • Each line depends on the one hand on the priority of the n th image in the sequence as indicated by the superscript (n) and, on the other hand, on the frequency of acquisition of the sequence.
  • the curves of image #2 and image # 3 are different. This also means that for a different acquisition frequency, the curves of images #2 are different.
  • the set of curves are plotted corresponding to all of the images of the calibration sequence.
  • FIG. 4 ( d ) represents schematically that a sequence of images of an object under observation 42 is acquired with the sequence comprising N images. Without correction, an undesirable variation of the gray level is observed between the successive images of the sequence. Therefore, the calibration data is going to be used for correcting these undesirable variations.
  • the mean gray level Y R ⁇ ( i , j ) ( 1 ) _ is measured in a zone of observation R(i,j) centered on the point (i,j) of the first image, for example, zone 43 in FIG. 4 ( d ).
  • Each zone of observation R(i,j) has a typical size of the order of 25 ⁇ 25 pixels. The size of each zone of observation corresponds substantially to the smallest size of the objects that can be observed such as, for example, a tumor in the field of mammography.
  • the method for correction is then applied to the image Y (n) by subtracting from the current image the variation of a gray level relative to the first image of the object.
  • FIG. 4 ( e ) shows that by using the determination of the mean gray level Y R ⁇ ( i , j ) ( 1 ) _ at the time of step (d) and using the calibration data, the value of the variation L (n) can be reached which is a function of Y R ⁇ ( i , j ) ( 1 ) _ . So, it is sufficient to subtract this value from the value of the current gray level.
  • a measurement is thus made of the mean gray level in a plurality of zones of observation, for example, similarly in the zone of observation 44 in FIG. 4 ( d ).
  • the mean gray level of the zone of observation 44 can be different from the mean gray level of the zone 43 .
  • the value of the medial gray level in each zone of observation can also be determined. Thus, the mean gray level is no longer considered.
  • the medial value of a series is the value situated in the middle of the series of values arranged in ascending or descending order.
  • the use of the median avoids the affect of the measured aberrant gray levels on the value of gray levels taken into account in the correction step. In effect, the extreme values of the series have no influence on the calculation of the median value.
  • Such aberrant values can be measured in the zone of the object 42 having a strong thickness gradient and around an abrupt change in thickness of the object under observation.
  • Equation (3) is slightly modified, because the median gray level is being applied instead of the mean gray level.
  • the calculation of the median generally slightly increases the processing time of information done in the processing means of the apparatus.
  • the mean gray level can also be replaced by the value of Y i , j ( 1 ) of gray level of the pixel (i,j).
  • the value of a zone of interest R(i,j) ( 43 and/or 44 , for example) is no longer averaged and the median value is not calculated.
  • the second alternative allows, as did the first alternative, having a good estimation of the variation of gray level in pixels situation near a zone in which the thickness of the object under observation rapidly varies. In contrast to the first alternative, it allows a reduction in the processing time. However, determination of the value of the variation of the gray level is less precise, because there is an enhancement of the quantum noise effect. The effects of quantum noise are significantly reduced by averaging or calculation of the median.
  • the adaptive approach takes into account the inhomogeneity of the variations in gray level over the surface of the detector of the apparatus. It appears that the detectors are not perfect and that there is a disparity of variations of gray level depending on the position on the detector.
  • the steps of an adaptive approach are represented schematically in FIG. 5 .
  • the adaptive approach comprises taking into account the inhomogeneity of the variations by performing a calibration on a plurality of zones of interest 41 .
  • the zones of interest are regularly divided over the surface of the calibration device and cover a maximum of the surface of the detector.
  • step (a) in FIG. 5 an image sequence of a calibration device 40 disposed over the surface of the detector is acquired.
  • acquisition of a series of sequences is done, in order to vary the thickness of the calibration device 40 .
  • step (b) it is not a graph of a set of straight lines corresponding to the different images that is obtained but a set of graphs, each one corresponding to a zone of interest 41 .
  • a set of graphs 411 , 412 , . . . 41 N corresponding to the set of measurements in the N zones of interest 41 .
  • Step (c) approximates the curves obtained by the straight lines that were defined for each graph, the coefficients ⁇ ⁇ ( n ) ⁇ ⁇ and ⁇ ⁇ ⁇ ⁇ ( n ) henceforth dependent on the zone of interest 41 for which they have been calculated.
  • a sequence of images of an object 42 under observation are acquired.
  • the zones of observation 43 and 44 are determined for which one wishes to effect a correction.
  • the position of the zones of observation is marked relative to the different zones of interest 41 .
  • step (e) in order to determine the variation of gray level of each zone of observation, the values of ⁇ ⁇ ( n ) ⁇ ⁇ and ⁇ ⁇ ⁇ ⁇ ( n ) are taken, which have been determined for the corresponding zone of interest 41 . Then the correction is applied using an equation similar to equation (3).
  • a first possible alternative consists of interpolating the ⁇ i , j ( n ) ⁇ ⁇ and ⁇ ⁇ ⁇ i , j ( n ) coefficients of zones of observation arranged outside of the zone of interest.
  • Other alternatives are also possible and utilize the median gray level value or the gray level values on a pixel instead of considering the mean gray level in a zone of observation.
  • an embodiment of the method for the first approach considers a calibration before acquiring the image sequence of the object under observation.
  • An embodiment of the method for a second approach does the calibration at the same time as acquisition of the image sequence of the object.
  • the calibration device 40 is placed in a field of acquisition of the apparatus and this is done during acquisition of the sequence of images of the object 42 under observation. By doing so, the necessity of having to do an acquisition series solely for calibration purposes is avoided. However, it was observed that it was desirable as in the first approach to do a series of acquisitions using different thicknesses of the calibration device 40 . This thickness variation is desirable to the plotting of the curves of step (b).
  • the calibration device 40 comprises at least two zones of interest that have mean gray levels that are different from one zone to the other for each image. This is what has been represented in FIG. 8 .
  • the calibration device 40 comprises a first zone of interest 41 comprising radiation absorption properties different from a second zone 45 .
  • the difference in absorption level can be due to a difference in thickness of the device 40 at the level of the two zones 41 and 45 and/or to a difference in the material of the two zones.
  • the device 40 may comprise more than two zones. The greater the number of zones having different properties, the greater will be the number of significant points that the plotting at step (b) of the calibration curves will have. The more precise the plotting of the curves in (b), the more precise their approximation in (c).
  • step (b) the curves of these relative values are plotted with respect to the mean gray level in the first image as a function of the gray level in the first image.
  • step (c) the different curves of the variations of gray level are approximated as a function of the gray level of the first image by the straight lines and the coefficients of the representative function are calculated.
  • step (e) the calibration of steps (a), (b), (c) are used.
  • the calibration enables calculation of the variation for each image of the object 42 of the sequence.
  • step (f) a corrected series of images is obtained.
  • the following can be recognized. Firstly, the most precise correction of the gray level variations is obtained. The remanence is determined directly using the images of the sequence of the object under observation. It is then reasonably certain that there are no differences in behavior of the apparatus between the calibration sequences and acquisition of the images of the object under observation. Secondly, it is generally not necessary to do an entire series of measurements in order to obtain the calibration curves. The calibration is done directly, at the same time as acquisition of the images of the object under observation. Thus, there is a considerable time savings for the operator of the apparatus.
  • a spatial model is used in order to take into account any disparities of variation of gray level as a function of the position on the detector.
  • the steps of such a variant are represented schematically in FIG. 7 .
  • Steps (a), (b), (c) and (e) remain the same as those of FIG. 6 . However, between step (e) and step (f) a step (e′) is added allowing application of a spatial model of the disparities of the variations.
  • the mean gray level Y R ⁇ ( i , j ) ( 1 ) _ is measured in a zone of observation 44 , for example, centered around the point (i,j).
  • ⁇ i,j gain factor one can, for example, utilize a calibration for a plurality of zones of interest as in the adaptive approach described for the first approach.
  • the different values of ⁇ i,j will be thus entered in the processing means of the apparatus and applied at the time of the correction step.
  • the K ij gain factor of the apparatus compensates the inhomogeneity of illumination of the detector by the emitter and the inhomogeneity of the response of the photodiodes of the detector.
  • K ij (Im+remanence)
  • Im is the image of the object uncorrected in gain and inhomogeneous.
  • the part (K ij Im) is a homogenous image.
  • the inhomogeneous remanence that is observed on the detector is: (K ij remanence).
  • the inhomogeneity of the remanence observed is due to the K ij gain factor.
  • FIG. 9 represents schematically the different steps of this alternative. It can be seen in FIG. 9 that at least two object images 42 ′ and 42 ′′ are acquired at the in these steps (referenced by (a 1 ) and (a 2 )).
  • the two sequences 91 and 92 are both acquired in under the same conditions of acquisition but successively. For example, the sequence 91 is acquired before sequence 92 .
  • the sequence 91 has, in particular, the same acquisition frequency as sequence 92 .
  • step (b) the measurements collected over the calibration device 40 in each of the two sequences 91 and 92 are combined in order to increase the number of points, regarding which the regression coefficients are calculated in step (c).
  • the device 40 comprises three zones of interest 41 , 45 and 46 .
  • FIG. 9 ( b ) represents the different points issuing from each sequence for each image for the zones 41 , 45 and 46 . In this fashion, the number of points is doubled, if the two sequences are combined. The precision of the approximations is thus increased.
  • the two sequences 91 and 92 are then corrected in steps (e 1 ) and (e 2 ), respectively.
  • the correction utilizes the regression coefficients calculated in step (c).
  • (f 1 ) and (f 2 ) corrected images are obtained.
  • the alternative of FIG. 9 can be generalized to as many sequences as may be desired. For each image, there is a cluster of points for each gray level. Furthermore, the alternative of FIG. 9 can be iterative; that is, for each new sequence acquired new regression coefficients can be recalculated.
  • FIG. 10 Another alternative of the second approach compensates for the fact that few functional points are available for the plotting of the calibration curves. Actually, due to the fact of the presence of the object under observation in the acquisition field of the detector, calibration devices of larger dimensions cannot be arranged in the field. Consequently, the devices no not have a large number of different zones of attenuation characteristics.
  • the present variant utilizes different calibration devices from one sequence to another in order to augment the number of functional points.
  • the steps of such an alternative are represented schematically in FIG. 10 .
  • FIG. 10 at least two sequences of images of the object 42 ′ and 42 ′′ are acquired in the steps (a 1 ) and (a 2 ).
  • the two sequences 91 and 92 are both acquired under the same conditions of acquisition, successively.
  • the sequence 91 especially, has the same acquisition frequency as the sequence 92 .
  • the calibration devices 40 ′ and 40 ′′ used in the two sequences are, in contrast, different from one sequence to another.
  • the device 40 ′ has two zones of interest 41 and 45
  • the device 40 ′′ has at least one, preferably two zones of interest 47 and 48 .
  • the zones 47 and 48 have radiation attenuation characteristics different from that of zones 41 and 45 .
  • step (b) the measurements collected using the calibration devices 40 ′ and 40 ′′ in each of the two sequences 91 and 92 are combined in order to increase the number of functional points, using which the regression coefficients of step (c) are calculated.
  • the measurement points of zones 47 and 48 at the time of acquisition of the sequence 92 complements the points of zones 41 and 45 acquired during the acquisition of sequence 91 .
  • the two devices 40 ′ and 40 ′′ are alternatively arranged on the detector at the time of successive acquisitions of two different objects 42 ′ and 42 ′′.
  • the introduction of the gain factor ⁇ i,j during the correction step can be similarly applied to the first approach.
  • the visible graphic representation of FIG. 4 ( b ) for example, by other functions, whose characteristics can be determined or are known.
  • the approximation function chosen depends on the repeatable phenomenon that is observed as well as the precision that one wishes to obtain at the time of calibration.
  • the approximation function can thus, for example, be a polynomial function comprising the powers of ⁇ overscore (C (1) ) ⁇ or an exponential function.
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JP4436695B2 (ja) 2010-03-24
FR2851359B1 (fr) 2005-05-06
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DE102004006853A1 (de) 2004-08-26
FR2851359A1 (fr) 2004-08-20
US7548640B2 (en) 2009-06-16

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