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Claims  |
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We claim:
1. A device for forming an image, comprising:
a camera system;
a system for acquisition of data of a source image distorted by the camera
system;
a system for digitizing said source image including a first image memory
for storing intensity data of each pixel marked by an address in a
bidimensional matrix; and
a system for processing the digital image for constructing a
distortion-corrected target image corresponding to the source image,
in which the image processing system includes:
a first sub-assembly for predetermining, on the basis of image data of a
distorted TEST source image, an optical center and a polynomial function
for correcting radial distortions around said optical center; and
a second sub-assembly including a memory for storing the optical center and
the polynomial function determined by the first sub-assembly, a computing
block for applying the polynomial function to each pixel address of the
target image, and for supplying an address of a pixel in the distorted
source image in which an intensity data is present which is to be applied
to the initial address in the target image, and a second image memory for
storing data of the target image.
2. A device for forming images as claimed in claim 1, in which:
the first sub-assembly includes blocks for treating the source image TEST,
said source image TEST being formed as a grating, referred to as source
grating, for constructing a target image TEST, referred to as theoretical
grating, said blocks comprising:
a block for extracting reference points at the points of intersection of
the bars of the source grating;
a block for estimating the first approximate theoretical grating, computing
the address of a center and the step size of said first theoretical
grating;
a block for estimating a distortion-corrected theoretical grating,
computing by way of iteration the address of a center and the step size of
said corrected theoretical grating;
a block for computing a correction polynomial of the radial distortions,
providing a transformation rule for passing a point of the corrected
theoretical grating at the iteration n to a reference point of the
distorted source grating, which transformation rule operates at the
iteration n;
a block for computing a patterning error due to the iteration n
transformation rule; and
a block for computing a modified address of the optical center which
minimizes the patterning error.
3. A method of correcting geometrical optical distortions produced in an
image by a camera system, said method comprising the preliminary steps of:
a) acquiring data and digitizing a TEST source image, including storing
intensity data of each pixel marked by an address in a bidimensional
matrix;
b) estimating an optical center located, at best, at the optical distortion
center of the TEST source image and the ratio of said optical center
computed in a digital image to be constructed, referenced TEST target
image representing the corrected TEST source image of the optical
distortions; and
c) estimating a polynomial function for causing the address of a
corresponding point, denoted reference point, in the distorted TEST source
image to correspond to the address of a pixel in the corrected TEST target
image, based on the hypothesis that the geometrical optical distortions in
the TEST source image are radial around the distortion center, so that
said corresponding points are aligned, at best, with the estimated optical
center.
4. A method as claimed in claim 3, comprising, in the preliminary steps,
the iterative steps of:
d) estimating the best polynomial function capable of minimizing, at an
iteration of the order of Nopt, the patterning error realized at the
localization of the pixels of the TEST target image constructed at a
preceding iteration in accordance with the hypothesis of radial
distortions around an optical center estimated at said preceding
iteration; and
e) estimating, at an iteration of the order of Nlast, an optimized modified
optical center and re-estimating under these conditions a new polynomial
function capable of further minimizing the patterning error realized at
the localization of the pixels of the reconstructed target image in
accordance with the hypothesis of radial distortions around said estimated
optimized modified optical center.
5. A method as claimed in claim 4, in which the preliminary steps are
performed once, said method comprising, at the start of the preliminary
steps, the steps of:
a.sub.o) acquiring the data of a source image distorted by the camera
system, digitizing and storing the intensity data of each pixel; and
f') correcting the optical distortions by applying the best estimated
polynomial function to a digital target image to be constructed, so as to
supply, on the basis of each address in said target image, a corresponding
address in the distorted digital source image in which an intensity
function is found which is applied to said address in the target image to
be constructed.
6. A method as claimed in claim 3, in which the preliminary steps are
performed once, said method comprising, at the start of the preliminary
steps, the steps of:
a.sub.0) acquiring the data of a source image distorted by the camera
system, and digitizing and storing intensity data of each pixel; and
f) correcting the optical distortions by applying the estimated polynomial
function to a digital target image to be constructed, so as to supply, on
the basis of each address of this target image, a corresponding address in
the distorted digital source image in which an intensity data is found
which is applied to said address in the target image to be constructed.
7. A method as claimed in claim 3, in which:
in the preliminary step a) of acquiring the data and digitizing, the TEST
source image is the digitized image of a rectangular mesh whose bars are
parallel to the rows and columns of pixels, to the most approximate
optical distortions referred to as source grating;
in the step b), said optical center is estimated in an iterative manner on
the basis of a zero iteration comprising the construction of a first
distortion-corrected TEST target image, referred to as first target
grating, by means of the sub-steps of:
extracting one point per zone of intersection of the bars of the source
grating, these extracted points being denoted as reference points of the
source grating;
estimating a reference point which is nearest to the center of distortions
of the source grating;
transferring this reference point into the first target grating for
constituting a first center of the grating;
estimating a first grating pitch for said target grating; and
estimating a first approximate optical center for said first target grating
coinciding with said transferred reference point and coinciding with the
center of the grating.
8. A method as claimed in claim 7, in which in step d), the iterative
estimation of the best polynomial function comprises the estimation, in a
zero-order iteration, of a first polynomial function comprising the
sub-steps of:
constructing points of the first target grating on the basis of the center
of the grating and the grating step to correspond to the reference points
of intersection of the bars of the source grating;
causing the grating points of the first target grating and the reference
points of the source grating to correspond by localizing the center of the
grating coinciding with the reference point which is nearest to the center
of distortion;
forming the pairs constituted by the grating points and the corresponding
reference points step by step from the center to the edges of the target
grating;
estimating the pairs of radii formed by segments joining the optical center
of the first target grating and each point of the pairs of target grating
points and the reference point; and
computing the first polynomial function as the one which best connects the
pairs of radii in conformity with the hypothesis in accordance with which
the distortions are radial around the optical center.
9. A method as claimed in claim 8, in which in step d), the iterative
estimation of the best polynomial function comprises the estimation, in an
n>0 order iteration, of a polynomial function comprising the sub-steps of:
constructing a target grating at the order of n, having an optical center
and grating points defined by a center of the grating and a grating pitch;
causing the grating points of the target grating to correspond to the
reference points of the source grating by localizing the center of the
target grating by means of its coordinates determined in the preceding
iteration;
forming pairs of grating points and reference points step by step from the
center towards the edges of the target image;
estimating the pairs of radii formed by segments joining the known optical
center and each point of the pairs; and
computing the polynomial function as the one which best connects the pairs
of radii in conformity with the hypothesis in accordance with which the
geometrical distortions are radial around the optical center.
10. A method as claimed in claim 9, in which the construction of a target
grating at the current iteration (n) comprises the sub-steps of:
localizing an optical center which is re-updated;
localizing the grating points and corresponding reference points
constituting pairs formed at the preceding iteration;
estimating the geometrical distances on the abscissa of the grating points
of the radii passing through the re-updated optical center and through the
corresponding reference points of the pairs formed at this preceding
iteration;
estimating a criterion, referred to as radial criterion, which expresses
the radial hypothesis that the best corrected target grating corresponds
to the minimization of the geometrical distances; and
minimizing the radial criterion expressed as a function of the coordinates
of the center and of the components of the grating pitch at the iteration,
supplying the center coordinates and the components of the target grating
pitch at the iteration.
11. A method as claimed in claim 10, in which the step b) of estimating the
optical center is realized in an iteration loop in which, at each current
iteration, the localization of the optical center is modified and then
reintroduced in the construction of the current target grating for
determining a new polynomial function, and estimating the corresponding
patterning error the best localization of the center being that which
results in the smallest patterning error corresponding to the best
polynomial function. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a device for forming an image, comprising:
a camera system,
a system for acquisition of the data of a source image distorted by the
camera system,
a system for digitizing said source image including a first image memory
for storing the intensity data of each pixel marked by an address in a
bi-dimensional matrix, and
a system for processing the digital image for constructing a
distortion-corrected target image corresponding to the source image.
The invention also relates to a method of correcting geometrical optical
distortions produced by such a camera device in an image.
The invention is used for correcting digitized images in the field of X-ray
systems or in video systems, or in digital image systems.
Significant geometrical distortions may be introduced by the objective of a
camera in the image produced by this camera, particularly if this
objective is of the wide angle type. These geometrical distortions are
most frequently of the barrel type or of the pincushion type. These
geometrical distortions appear even if the objective of the camera has a
very good quality.
2. Description of the Related Art
A device for compensating optical imperfections in a television camera is
already known in the state of the art from UK Patent Application GB
2,256,989, corresponding to U.S. Pat. No. 5,276,519.
This device comprises a camera registering the image formed by the optical
system and means for digitizing this image, which include storage of the
intensity data of each current pixel.
This device also comprises an error corrector for compensating the
geometrical, registering and chromatic errors and for also compensating
the optical imperfections of the lens system.
This error corrector is controlled by a correction control unit. This
correction control unit receives exterior information components via an
interface, these components being suitable for programming the unit so
that it can apply control signals to the error corrector which take the
parameters of the camera system into account. Under these conditions, the
error corrector is capable of correcting the pixel data.
In the error corrector, a cartographic memory receives these control
signals from the correction control unit in dependence upon the parameters
of the camera system. This cartographic memory is tabulated as a function
of these parameters for defining the cartography which is necessary for
correcting the faults of the optical system with a given lens type and
under given camera conditions.
The output of the cartographic memory is applied to an interpolator used
for enhancing the definition of the output image.
The cartographic memory is calibrated by applying a test pattern to the
pick-up camera having a regular square grating design and by manually
adjusting the stored parameters so that a corrected grating is obtained at
the output of the device. This operation may be realized by displaying,
for example the output signal of the device on a screen provided with a
superimposed graticule.
The device known from U.S. Pat. No. 5,276,519 does not correct the
imperfections of the camera system in an automatic manner. It is necessary
to supply it with data about the focal length of the lens, the camera
distance and the zoom rate used. Moreover, a cartographic memory should
contain tables for each lens type and each camera condition, these tables
including information relating to the new addresses to be assigned to the
pixels of the target image for replacing the original addresses of these
pixels in the source image, that is to say, in the image directly
originating from the camera system and being beset with imperfections. The
target image may thus be corrected from the distortions of the source
image.
No automatic tabulation means for the cartographic memory or automatic
means for computing the correction functions to be applied to the pixels
of the source image for obtaining the pixels of the target image are
described in the document cited hereinbefore. Only means for manual
calibration of the cartographic memory have been described, including the
superposition of the distorted target image of a grating on a reference
graticule and the manual correction of the input parameters of the camera
system.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a device and a method
for calculating correction functions of the optical distortions of a
camera system in order to obtain pixel data with which a corrected target
image can be constructed.
It is another object of the present invention to provide such a device and
a method for automatically computing such correction functions without
having to take the parameters of the camera system into account.
These objects are achieved by means of a device as described in the opening
paragraph, in which the system for processing the image includes:
a first sub-assembly for predetermining, on the basis of image data of a
distorted TEST source image, an optical center and a polynomial function
for correcting radial distortions around said optical center, and
a second sub-assembly including a memory for storing the optical center and
the polynomial function determined by the first sub-assembly, a computing
block applying the polynomial correction function to each pixel address of
the target image for supplying the address of a pixel in the distorted
source image in which an intensity data is present which is to be applied
to the initial address in the target image, and a second image memory for
storing data of the reconstructed target image.
A method of correcting optical distortions produced in an image by a camera
system comprises the preliminary steps of:
a) acquiring data and digitizing a TEST source image, including the storage
of the intensity data of each pixel marked by an address in a
bi-dimensional matrix,
b) estimating an optical center located at best at the optical distortion
center of the TEST source image and the ratio of said optical center
computed in a digital image to be constructed, referenced TEST target
image representing the corrected TEST source image of the optical
distortions, and
c) estimating a polynomial function for causing the address of a
corresponding point denoted reference point in the distorted source image
to correspond to the address of a pixel in the corrected TEST target
image, based on the hypothesis that the geometrical optical distortions in
the source image are radial around the distortion center, so that said
corresponding points are aligned at best with the estimated optical
center.
In the preliminary steps, such a method may also comprise the iterative
steps of:
d) estimating the best polynomial function F.sup.Nopt capable of
minimizing, at an iteration of the order of Nopt, the patterning error
realized at the localization of the pixels of the TEST target image
constructed at a preceding iteration in accordance with the hypothesis of
radial distortions around an optical center OC.sup.n estimated at said
preceding iteration, and
e) estimating, at an iteration of the order of Nlast, an optimized modified
optical center OC.sup.Nlast and re-estimating, under these conditions, a
new polynomial function F.sup.Nopt(Nlast) capable of further minimizing
the patterning error realized at the localization of the pixels of the
reconstructed target image in accordance with the hypothesis of radial
distortions around said best estimated optical center OC.sup.Nlast.
These and other aspects of the invention will be apparent from and
elucidated with reference to the embodiments described hereinafter.
BRIEF DESCRIPTION OF THE DRAWINGS
In the drawings:
FIG. 1A shows a device for forming images including a camera system and two
sub-assemblies of a system for processing digital images, one for
determining and the other for applying the geometrical correction rules
for optical distortions of the camera system;
FIGS. 1B and 1C illustrate the calibration step of acquiring a test pattern
by the camera system;
FIG. 2A shows a block diagram of the first sub-assembly of the image
processing system for performing a method of determining the correction
rules and determining the distortion center for geometrically correcting
the optical distortions produced by the camera system, and FIG. 2B shows a
block diagram of the second sub-assembly of the image processing system;
FIGS. 3A to 3G show source and target images in the different steps of the
method;
FIG. 4A shows an intersection in the source grating and illustrates the
non-linear filtering operation for extracting the reference points;
FIG. 4B shows an intersection in the source grating for determining the
reference point R.sub.k.sup.0 which is nearest to the distortion center,
by way of an alignment criterion;
FIG. 4C shows a horizontal sub-assembly HS.sub.k.sup.0 of reference points
for determining the step of the first grating TG.sup.0 by means of a first
median filtering operation;
FIG. 4D shows a central sub-assembly S.sub.k.sup.0 of reference points for
determining the step of the first theoretical grating TG.sup.0 by means of
a second median filtering operation;
FIG. 4E illustrates the formation of rectangular rings having an increasing
size for forming pairs P.sub.k.sup.0 ;
FIGS. 5A and 5B show source images which are pincushion and
barrel-distorted, respectively;
FIG. 6A illustrates the operation of causing a grating point
TR.sub.g(k.alpha.).sup.0 to correspond to a reference point
R.sub.f(k.alpha.) in a rectangular ring .alpha., and FIG. 6B illustrates
the same operation in an adjacent, larger ring .beta.;
FIG. 7A illustrates the determination of the errors .DELTA..sub.k.sup.n of
aligning the pairs P.sub.k.sup.n with the optical center OC.sup.n, which
errors are due to the distortion;
FIG. 7B illustrates the determination of the pairs of radii X.sub.k.sup.n
and Y.sub.k.sup.n for estimating the polynomial function F.sup.n ;
FIG. 7C represents the points of the pairs P.sub.k.sup.Nlast ideally
aligned with the center OC.sup.Nlast which at best minimizes the
patterning error;
FIG. 8A illustrates the determination of a polynomial F.sup.n for
connecting at best the points formed by the pairs of radii X.sub.k.sup.n
and Y.sub.n.sup.k plotted on the abscissa and the ordinate, respectively,
in a graph in a graduation of original pixels OC.sup.n ;
FIG. 8B illustrates the determination of the first polynomial F.degree. at
the zero iteration in the iterative method and FIG. 8C illustrates the
determination of an improved polynomial F.sup.m at a subsequent n
iteration; and
FIG. 8D shows the points of the pairs P.sub.k.sup.Nlast ideally placed on a
curve which is representative of the best polynomial F.sup.Nlast(Nopt) for
minimizing the patterning error.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
I. DEVICE (FIGS. 1A, 2A, 2B)
A camera system may generally include an optical lens system of the wide
angle type or a zoom lens system which produce geometrical optical
distortions in the image formed by this camera. These distortions appear
even when the optical system has a very good quality.
With reference to FIG. 1A, a device for forming an image comprises a camera
system 1 consisting of an optical lens system which supplies a distorted
image of a scene. This optical lens system 1 is attached to a camera 2
which converts the optical image into electric signals by way of, for
example, a CCD. These electric signals are applied to a digitization
system 3 which is capable of storing the digitized image data, i.e., the
intensity data relating to each address of the pixels of the image, in a
bi-dimensional matrix, in a first picture memory. These digitized image
data relate to the distorted image.
This device for forming images also comprises a system for processing the
digital signal, which system comprises a sub-assembly 47 processing the
digitized image data stored in the picture memory of the digitization
system 3 for supplying data of a corresponding digital image reconstructed
with a correction of distortions, which data are finally stored in a
second picture memory.
The digital image data at the output of the digitization system 3, relating
to an image distorted by the camera system, will hereinafter be referred
to as source image SI, and the digital image data supplied by the
sub-assembly 47 of the image processing system relating to the
distortion-corrected reconstructed image, will be referred to as target
image TI.
The sub-assembly 47 of the image processing system comprises, on a
chip-card or in a look-up table, rules for correcting the distortions for
constructing the corrected target image TI. These rules may be determined
by means of a method comprising preliminary steps. One of the objects of
the invention is to provide such a method for determining these correction
rules in an automatic manner. The correction rules are determined once for
all operations in a first sub-assembly 4 of the processing system.
Subsequently, they are automatically applied by means of the sub-assembly
47 of the image processing system referred to as second sub-assembly 47.
With the switch INT shown in FIG. 1A, the first sub-assembly 4 of the
processing system can be switched off when these rules have been
determined.
The first sub-assembly 4 includes, as shown in FIG. 2A, a block 41 for
extracting reference points (R.sub.k) at the points of intersection of the
bars of the source grating (SG.degree.). The output from block 41 is
connected to an input of block 42 for estimating the first approximate
theoretical grating (TG.sup.0), computing the address of a center
(GC.sup.0) and the step size (GM.sup.0) of said first theoretical grating
(TG.sup.0). The output from block 42 is connected to a first input of
block 43 for estimating a distortion-corrected theoretical grating
(TG.sup.n), computing by way of iteration the address of a center
(GC.sup.n) and the step size (GM.sup.n) of said corrected theoretical
grating (TG.sup.n). A block 44 for computing a correction polynomial of
the radial distortions is connected to the output of block 43. This block
44 provides a transformation rule for passing a point of the corrected
theoretical grating at the iteration n(TG.sup.n) to a reference point
(R.sub.k) of the distorted source grating, this transformation rule
operating at the iteration n. The output from block 44 is connected to a
block 45 for computing a patterning error (E.sup.n) due to the iteration n
transformation rule. The output from block 45 forms the output of the
first sub-assembly 4, and is also connected to a block 46 for computing a
modified address of the optical center (OC.sub.n) which minimizes the
patterning error, which is connected to a second input of block 43.
As shown in FIG. 2B, the second sub-assembly 47 includes a memory 48
connected to the output of the first sub-assembly 4 for storing the
optical center and the polynomial function determined by the first
sub-assembly 4. A computing block 49 then applies the polynomial
correction function to each pixel address of the target image (TI) for
supplying the address of a pixel in the distorted source image (SI),
received from the digitization system and first picture memory 3, in which
an intensity data is present which is to be applied to the initial address
in the target image. A second image memory 50 is then provided for storing
data of the target image.
The method of determining the correction rules performed in the first
sub-assembly 4 of the image processing system will subsequently be
described. This first sub-assembly 4 may also be an extension of the
digitization system 3, or it may be integrated in this digitization system
3.
In the device for forming the image according to the invention, as shown in
FIGS. 1A, 2A and 2B:
(a) in the first sub-assembly 4 of the processing system, computing steps
are carried out for determining once for all operations:
rules for correcting the geometrical distortions produced by the camera
system 1, and
precise localization of the center of the geometrical distortions which is
also the optical center of the lens system of the camera in the majority
of cases; and
(b) in the second sub-assembly 47 of the processing system, computing steps
are carried out for constructing a distortion-corrected target image TI by
means of said rules and the knowledge of the center of distortion for each
distorted source image SI.
This will be continued with a description of:
a method of determining these rules for correcting the geometrical
distortions and for concomitantly determining the precise localization of
the distortion center, carried out in the first sub-assembly 4, and
a method of constructing the target image TI by using this knowledge,
carried out in the second sub-assembly 47.
II. METHOD OF DETERMINING THE CORRECTION RULES AND THE DISTORTION CENTER
(FIG. 1, Block 4; FIG. 2A, Blocks 41 to 46)
A method of concomitantly determining these correction rules and the
precise coordinates of the distortion center will be described hereinafter
with reference to FIG. 2A which shows the different steps by way of a
block diagram.
This method does not require any preliminary measurements, such as the
measurement of the focal length, or the measurement of the camera
distance, or the real measurement of the test pattern pitch.
This method is based on the hypothesis that the geometrical distortions
generated by the camera system are radial, that is to say, in the target
image constructed by the second sub-assembly 47 of the processing system,
a corrected point should be present on a radius determined by the
distorted point and by the distortion center. For this reason, this method
requires, in addition to determining the correction rules, a concomitant
precise determination of the distortion center. Nevertheless, this method
does not require any preliminary precise real measurements. In this
method, the aim is not a precise measurement by means of, for example a
sensor, of the localization of the optical center of the camera, because
only the distortion center of the source image is interesting due to the
fact that the distortions are radial around the distortion center.
With reference to FIG. 2A, this method, performed in the first sub-assembly
4, comprises at least the following steps:
II. A. ACQUISITION OF A PATTERN
This step comprises the following sub-steps:
II.A1. Construction of a Pattern (FIG. 1A)
A test pattern M is realized.
To this end, the design of a grating on a plane, rigid support is
preferably realized. The meshes of this grating may be square-shaped or
rectangular. In one example, this pattern may be a design on a white base
support of 1 m.times.1.50 m representing horizontal and vertical black
bars forming squares as shown at M in FIG. 1A.
II.A2. Calibration of the Camera (FIG. 1B, FIG. 1C, FIG. 3A)
The camera is placed to face the plane of the pattern M for acquisition of
a net image of this pattern. A calibration is realized before pick-up.
This calibration consists of:
rendering the plane support of the pattern M perpendicular to the optical
axis X'x of the pick-up camera, as illustrated in FIG. 1B;
rendering the bars of the grating parallel to the rows and columns of the
CCD element of the camera 2, as illustrated in FIG. 1C; and
placing the plane support of the grating in such a way that the whole image
plane of the camera is covered by the grating squares, as illustrated in
FIG. 3A.
The calibration conditions thus essentially consist of verifying three
conditions of orthogonality, two of which are verified when the optical
axis X'X of the camera is perpendicular to the plane of the pattern and
the third is verified when the bars of the pattern grating are parallel to
the orthogonal rows and columns of the CCD element of the camera.
The calibration operation may be performed by simply using squares. This
calibration is not coercive because it appears that the method according
to the invention can withstand possible imperfections of this calibration.
II.A3. Acquisition of an Image of the Grating, Serving as a Pattern (FIG.
1A and FIG. 3A), Referred to as Source Grating
By means of the camera 2 provided with its optical lens system 1, focusing
and pickup is realized of the pattern grating M. The digitization system 3
provides a digitized image in the form of a grating referred to as source
grating SG.sup.-2 having optical distortions as shown in FIG. 3A.
The distortions may be pincushion-shaped as in FIG. 5A or barrel-shaped as
in FIGS. 5B and 3A.
II.B. EXTRACTION OF THE REFERENCE POINTS R.sub.k (FIG. 2A, Block 41)
An image of the distorted source grating is digitized and stored in the
digitization and storage means 3 shown in FIG. 1.
With reference to FIG. 3A, the points of intersection of the vertical and
horizontal bars of the distorted source grating SG.sup.-2 will hereinafter
be referred to as reference points R.sub.k in the digitized image of the
source grating SG.sup.-2. Horizontal and vertical are understood to mean
parallel to the rows and columns of the CCD element of the camera, as
resulting from the calibration.
As far as the notations are concerned:
for the reference points R.sub.k, k is an index with which the points of
reference of the source grating can be enumerated, for example, from 1 to
500, and
for the images of the source grating, for example, SG.sup.-2, the index
permits of enumerating the image processing step. Here the index (-2)
indicates that this step is the second before that which provides the
source grating image SG.sup.0 which is used for determining the correction
rules and the optical center.
With reference to FIG. 2A, the series of operations constituting the steps
of the method according to the invention comprises a first step performed
in the block 41 consisting of the extraction of reference points R.sub.k
of the image of the source grating SG.sup.-2 by determining their address
in this source image by means of the following sub-steps:
filtering of the source image for increasing the intensity of the zones of
intersection,
thresholding the filtered image intensities; and
labelling the thresholded points for forming zones and extracting the
barycenter of each zone.
II.B1. Raising the Level of Intensity of the Zones of Intersection by Means
of Filtering (FIG. 3b; FIG. 2A, Block 41)
In the case taken as an example, in which the bars of the test pattern
grating are represented in black on a white or bright background, the
zones of intersection of the vertical and horizontal bars are black as
shown in FIG. 3A. In this sub-step, the digitized image of the distorted
pattern SG.sup.-2 is processed for brightening these zones and for
darkening the rest of the image. Subsequently, one obtains the image of a
source grating denoted SG.sup.-1 as shown in FIG. 3B.
This operation may be carried out by means of a first method, known to
those skilled in the art, consisting of a linear filtering operation by
means of linear filters corresponding to correlation masks having the form
of a cross.
Instead of a test pattern in the form of a grating, it is also possible to
choose a test pattern of dots. Experience has proved that camera
registration of a dotted test pattern is less satisfactory than that in
the form of a grating because of glare effects. The registration of a test
pattern in the form of a grating has the additional advantage that more
useful information can be supplied for satisfactorily performing the
method according to the invention.
Here, a method is proposed which uses a non-linear filtering operation
which is more efficient than the known linear filtering operation. The
advantages of this non-linear filtering operation with respect to a
conventional linear filter are that:
it produces no glare,
it can withstand the distortion at the intersection, and
it is easy to carry out.
In the step of extracting the reference points, performed on the digitized
source image SG.sup.-2 of the grating, the increase of the intensities at
the intersections of the grating bars is essential. It is thus important
to realize a very good filtering operation.
An intersection of a horizontal grating bar and a vertical grating bar is
shown diagrammatically in FIG. 4A. The edges of the horizontal bar and the
vertical bar are shown by way of distorted lines in the distorted source
image.
In this step, a filter is used at each point of the source image SG.sup.-2
of FIG. 3A. By way of this filtering operation, one determines:
the center C of the filter,
four cardinal points S, N, E, W, and
four diagonal points SE, SW, NE, NW.
The 8 points surrounding the center C of the filter are entirely defined by
the distances d1 and d2, where d1 is the distance measured in pixels
between the center C and the cardinal points (d1=C-S, C-N, C-E, C-W), and
d2 is the distance measured in pixels between the center C and the
diagonal points (d2=C-SE, C-SW, C-NE, C-NW).
The distance d1 is chosen in such a way that the cardinal points are
situated within the design of the bars of the grating, where the center C
is situated in the zone of intersection. This result is obtained by
choosing d1 to be of the order of 1 to 5 pixels; generally, of the order
of half the thickness of a bar of the grating measured in pixels in the
distorted image.
The distance d2 is chosen in such a way that the corresponding diagonal
points are situated at the bottom of the image, that is, outside the
regions of the grating bars. This effect is obtained by choosing d2,
measured in pixels, to be of the order of half the pitch of the distorted
grating in the digitized image. For example, for a grating having a pitch
of the order of 50 pixels, d2 may be 20 pixels.
By choosing reasonable distances d1 and d2 which those skilled in the art
can determine by means of several routine tests without any precision
being required, this filtering operation may reveal that, when the center
of the filter is within a zone of intersection, the cardinal points S, N,
E, W are within the regions of the bar design of the grating and the
diagonal points are effectively situated at the bottom, even in the
regions of the distorted image where the strongest distortions are found.
In the example of the grating formed from black bars on a white background
before filtering in the image SG.sup.-2, each of these five points
constituted by the center and the four cardinal points has a low
intensity, whereas the four diagonal points have a higher intensity.
By way of the non-linear filtering operation according to the invention, a
measurement is realized which is expressed by the following measurement of
the FILT criterion: FILT=Min(NW,NE,SE,SW)-Max(C,N,S,E,W). In this
criterion, Min(NW,NE,SW,SE) means that the minimum intensity relating to
the diagonal points is evaluated, and Max(C,N,S,E,W) means that the
maximum intensity relating to the cardinal points including the center is
evaluated.
When the filter is correctly centered at an intersection, each diagonal
point normally has a large intensity, so the minimum intensity evaluated
for the intensity of these points is even larger. On the other hand, each
of the five points, the center and the cardinal points normally has a
smaller intensity, so the maximum of the intensity evaluated for the
intensities of these points is even lower. The result is that there is a
large difference between this Min and this Max.
The non-linear filter realizes the evaluation of this FILT criterion at
each point of the distorted image of FIG. 3A. The result of computing the
FILT criterion constitutes the output of the non-linear filter according
to the invention.
The detected regions of intersection are those where the measurement of
this criterion is largest. The obtained image resulting from this
filtering operation is a new source grating SG.sup.-1 and shows, as in
FIG. 3B, that the regions of intersection are increased in intensity and
that other regions of the distorted source image are darkened.
II.B2 Thresholding the Increased Intensities of the Points (FIG. 2A, Block
41; FIG. 3C)
After the sub-step of increasing the intensity of the points of the zones
of intersection, a sub-step of thresholding the intensity of these points
is realized.
Here, a method will be proposed for performing said thresholding sub-step
in order to detect said reference points. In accordance with this method,
said thresholding sub-step is performed in the enhanced image SG.sup.-1 by
selecting a reference number Nb representing the number of points having
the strongest intensity.
Those skilled in the art, who have acquired the image of the distorted
source grating SG.sup.-2, as shown in FIG. 3A, effect:
counting of the number N1 of the intersections in the image,
counting, by taking the digitization into account, of the approximate
number N2 of pixels contained in one zone of intersection: each zone of
intersection has four sides and its surface is given by the product of
thicknesses in pixels of the horizontal and vertical bars of the grating
in the distorted image, as is shown, for example, in FIG. 4A, and
computing the searched number Nb equal to the product of the number of
intersections N1 in the distorted image by the approximate number of
pixels N2 | | |
