FR2629233A1 - Method of reconstituting the spatial coordinates of each of the points of a set of points sampling a three-dimensional surface, and method of producing a three-dimensional image of this surface from the said coordinates - Google Patents

Abstract

The method is applicable especially to video sculpture. By means of cameras 13a, 13b and of video recorders 14a, 14b a series of images are recorded of the three-dimensional surface illuminated by a plane beam of laser light generated by a laser 12. The method includes a phase of passing from the coordinates of the image points recorded by the vision system to the spatial coordinates employed by the module 17, a phase of reconstituting the points possibly badly recorded by the vision system, implemented by the module 16, and a phase of determining the axis of a tool 18 sculpting the three-dimensional image in a material such as wood or aluminium, the latter phase being implemented by the module 19.

Description

The present invention relates generally to the problem of making a three-dimensional image of any surface from two-dimensional images of said surface. It finds an important, but not exclusive, application in the field of "video sculpture,
The invention aims in particular at a method for determining the spatial coordinates of each of a set of points belonging to said trimensional surface and sampling the latter from said prerecorded images. Using the data thus provided, the invention makes it possible to control optimal of a numerically controlled machine tool for machining said three-dimensional image in a material, as part of its application to "video sculpture.

 Such a method is known which makes it possible, in the prior art, to produce the three-dimensional image of a bust from a series of video images. The subject sits on a rotating chair and his bust is illuminated by a laser providing a lamellar flat beam.

The intersection of the flat beam with the bust of the subject gives a curve (or profile) that is sampled, the spatial coordinates of the source points of the samples being determined by means of a known type of process, such as that taught in the French patent 81.24418. The chair on which the subject sits rotates step by step and each time a curve is scanned. In one complete rotation, a predetermined number of curves (for example 512) each sampled in a predetermined number of points (for example 512) are thus obtained. The bust is thus digitized in the form of the X-Y-Z coordinates of each of the stored points (262.144 in the example above).

 The next step is to process the digitized points thus obtained so as to generate orders for controlling the machine tool, so that it sculpts in a solid material such as aluminum or wood the three-dimensional image of the bust.

 The present invention provides in particular an improvement to the process described above.

 The method known up to now has, in fact, a certain number of disadvantages, particularly in the information processing phase and in the generation of electrical signals capable of controlling the machine tool, this phase being commonly called in specialized environments, phase CAD / CAM (Computer Aided Design and Manufacturing).

 Thus, the method of illuminating the bust is not perfect in that the skin or the hair of the subject reflects the light emitted by the laser in a variable manner, which can result in over-lit spots or sub-points. enlightened. In some circumstances, the subject's skin or hair may have a low albebo, which means that the illuminated point does not reflect light. In such a case, the track recorded by the video camera includes missing points creating breaks in the continuity of the trace. It is then considered that there are "missing" points that should have filled gaps or breaks in continuity. These "missing" points correspond to the bust points with a low albedo.

 On the other hand, strong albedo points can reflect light very strongly and diffract light from other parts of the bust, the recorded trace not being continuous and having in fact various points outside the normal trace. In such a case, it is a question of what are termed "aberrant" points.

 In both cases, the machining, under the control of CAD / CAM, lacks precision, which generates errors that are detrimental to the quality of the finished product.

 Another series of drawbacks is also due to the fact that the method used to determine the spatial coordinates from the coordinates of the image points recorded by the video, uses trigonometric formulas such as those described in the patent 81.24418 mentioned above. It follows a lack of precision. It is therefore desirable to have a method for determining the spatial coordinates of the points considered, more precise and more reliable.

 Moreover, the Applicant has found that it is desirable to orient the tool so that it attacks the material at an angle corresponding to the normal to the surface to be made, which makes it possible to obtain a better finish. and a better rendering of the piece. The prior art does not provide such a hypothesis since the machine which is used is controlled only by three degrees of freedom, which only makes it possible to correctly position the cutter attacking the material, but does not make it possible to position the machine. angle of attack of this mill compared to the material. It is therefore desirable to have a method of controlling and controlling as far as possible the angle of attack of the tool relative to the material.

 Finally, the Applicant has found that in certain areas such as the eyes or the mouth, If the angle of attack of the cutter is normal to the surface to be machined, there is a risk of a collision between the tool shaft and the machined material. Consequently, in these hypotheses, it is necessary to be able to rectify, automatically as far as possible, the position of the tool-holding shaft so that the tool attacks the material in a favorable angle but that one avoids, as much as possible, collisions between the tool shaft and the material. In this respect, it is therefore desirable to have in the CAD / CAM a phase for determining the optimum direction of the tool holder shaft.

 The present invention solves all of these problems.

In particular, it aims at a method for determining spatial coordinates of each of the points of a set of source points belonging to a surface comprising a data acquisition step in which the surface of the light is illuminated with a plane of light. with at least one camera at least one image of the trace left by the plane beam on the surface, the trace left by the light plane beam on the surface being said "source profile", the image of this trace in an image plane of the camera being called "image profile", the plane beam and the surface are relatively moved and recorded with said camera & new at least one image of the trace left by the plane beam on the surface, the relative displacement operations are repeated , lighting and recording so that a plurality of image profiles constituting a sampling of the image of the entire surface is recorded, the process comprising a processing step during which, in particular, the column-line coordinates (Col, Lig) of a set of image points sampling each profile image in the image plane of said camera are considered, characterized in that, implementing considerations that
in the plane of the light beam, a direction axis is selected and "spatial" coordinates (R, H) are assigned to each point of said plane, R being the distance between the point considered and the director axis, H being the ordinate of this point on this axis; ;
the following formulas for transforming the coordinates (Col, Lig) of each of the points of the image plane of the camera into spatial coordinates (R, H) of the corresponding source point are taken into account
a1Lig + a2col + a3 a4tig + a5col + a6 (1) R
a7Lig + a8col + l a7Lig + a8col + l the coefficients ai being called "transformation coefficients" and being determined for points of the image plane of said camera, from so-called interpolation coefficients (bit) themselves calculated during a previous phase of calibration of the image plane of the camera during which
we record the image of juxtaposed series
four reference source points located
in the plane of light and whose
spatial coordinates (R, H) in this plane
are known; we find the coordinates
images (col, Lig) of the image of each of these
points for each set of four points
source of reference and we solve the formula
of transformation (1), which gives eight
transformation coefficient values ai
by series of four reference points; we
consider the center of gravity of each series
of four reference points and we assign to
the latter the transformation coefficients
Qi thus determined; we consider zones
triangular Tk interpolation
bounded by straight segments
joining said series centroids
neighboring regions, these centroids constituting the
vertices of said triangular zones Tk; we
uses the following interpolation formula
for each transformation coefficient ai:
(2) ai = sil Col + 8i2 Lig + Big
twenty-four coefficients are determined
Interpolation (piu) by triangular area
interpolation (Tk) solving the formula
Interpolation (2) for each of the coefficients
transformation teeth (ai) assigned to a
triangular zone top of interpolation
Tk ;; this method furthermore consists, in said processing phase, in determining the spatial coordinates (R, H) of a source point whose image coordinates (Col, Lig) of its image are known to perform the following operations
searching, in a search operation, the interpolation zone (Tk) to which the point belongs, as well as the interpolation coefficients (piu) associated with this zone.

 calculating, in a calculation operation, the spatial coordinates (R, H) by concomitant application of said transform (1) and interpolation (2) formulas.

 According to another aspect of the invention, a homogenization phase is implemented in which, for each of the points treated (Pi, n), year considers a predetermined number of neighboring points, the average coordinates of these points, if the treated point is absent, or if at least one of its coordinates differs from the corresponding average coordinate by a difference greater than a predetermined value (E), the said average coordinates are assigned to the point treated.

 Thus, thanks to these provisions, there is a reliable and accurate method for determining and / or reconstructing the spatial coordinates of a set of points from their coordinates in the image plane of the camera.

 In addition, thanks to the homogenization phase, it overcomes the disadvantages associated with points of low or too strong albedo on the surface & reproduce.

The present invention also aims at a method of video sculpture, particularly of the type as briefly described above, which can, advantageously, implement the method for determining and / or reconstructing the spatial coordinates stated above, in particular characterized in that that it implements a machine tool adapted to control a tool with five degrees of freedom, namely three degrees of freedom allowing the positioning of this tool in space, taking into account said spatial coordinates and two degrees of freedom determining a angle of attack of the tool so that the tool is generally directed according to the normal to the surface to be achieved and in that one proceeds to a detection of the concave portions of the surface, to correct the angle of attack of the tool to avoid ~ as much as possible an interaction between the tool and the machined material, during which
- the trace left by the said
surface in a plane perpendicular to a director axis
and passing through the point being processed (Pi, n),
this trace being called secant (Si),
- we also consider a source profile in
to which belongs the treated point (Ri, Hi, en)
the concave parts of the profile are detected
performing the following operations
. we consider a normal vector (DN, iI '
ri + l) at each of the two points
neighbors (Ri ~ l, Hi l, en) and (Risl, Hi + lten)
of the treated point (Ri, Hi, # n)
. the vector product of said normal vectors (Dt en, i-1, DR en, i + 1) is calculated
profile at points close to the point
a coefficient of
convexity QDi associated with the point in process
(Ri, Hi, en),
If the convexity coefficient is negative,
the source profile is concave to the point
treated, and we calculate the sum (E # en, i)
said normal vectors to the profile,
two points close to the point
(DNen, i-1, DNen, i + 1),
. this sum vector is stored (ED in i)
. we then consider all the points
treaties belonging to the same profile
we associate with each of these points the
normal vector to cone profile
stunned, when the coefficient of convexity
QD considered is positive, the vector
sum, when the coefficient of convexity
(QD) is negative,
. when all the points belonging to
the same profile is processed, we start again
predetermined number of times the treatment
profile using the vectors
effectively associated (DZ en, i, ED
at the point treated (Ri, Hi, en).

- a similar treatment is carried out for
each of the secant traces (Si) and we associate with
each of the points treated (Ri, Hi, en) a vector
corresponding to the normal to said secant trace
If at the point treated SN in i, or at a vector sum,
(ES in, i) vectors actually associated with
neighboring points (Ri, Hif en-l) (Ri, Hi, en + l) at the point
treated (Ri, Hi, en).

and, for each point, the tool is directed according to the direction of the vectors effectively associated with said point, in the place of its profile (in) and in that of the secant trace (Si) to which it belongs.

 Thanks to these provisions, it optimally controls the tool, while automatically avoiding, most often, any interference between the tool and the material.

The features and advantages will emerge from the following description with reference to the accompanying drawings, in which:
FIG. 1 is a schematic view of the means implementing a video sculpture method according to the invention,
FIG. 2 is a schematic view illustrating the relative position of the laser and the cameras illustrated in FIG. 1;
FIGS. 2a and 2b illustrate an alternative embodiment,
FIG. 3 is a schematic view of a three-dimensional surface to be reproduced;
FIG. 4 schematically illustrates an image profile as recorded by each of the cameras of FIG. 1,
FIG. 5 illustrates the source profile corresponding to the image profile of FIG. 4,
FIG. 6 is a schematic view of a calibration chart of the vision system,
FIG. 7 is a schematic view of another calibration pattern allowing a more precise calibration of each of the cameras,
FIG. 8 is a block diagram of the principal means implemented in the embodiment described and represented,
FIG. 9 is a simplified flow diagram of transformation carrying out one of the steps illustrated in FIG. 8,
FIG. 10 is an illustration of five source profiles of the subject illustrated in FIG. 3,
FIGS. 11 to 13 illustrate a source profile having a concave portion and steps for correcting the direction of the tool to avoid a tool-material interaction and
- Figures 14 and 15 illustrate a "secant" trace having a concave portion.

 We will first briefly describe an embodiment of the method according to the invention and the means implementing it to have a general view. Then will be described in more detail certain phases of the process.

1. General
FIG. 1 generally illustrates means implementing a video sculpture method comprising the method of producing a three-dimensional image according to the present invention.

The illustrated video sculpture method comprises, in a conventional manner, three main steps implemented by sets of means
the set A allows the acquisition of the information,
the set B allows the processing of the information,
the set C is a use of the information, in this case the machining of the object copied by means of a machine tool 18.

 The acquisition of information is done by placing the object to be copied to a table 10 or the subject whose bust is to be modeled on a seat 10 '. The table 10 and the seat 10 'are rotatable and driven for this purpose by a stepper motor not shown. The subject or object is illuminated by means of a laser 12. In the embodiment chosen and shown, a single laser illuminates the subject or the object. Two cameras 13a, 13b film the object or the subject while the table 10 or the seat 10 'performs a complete turn. The angular steps of the table or seat are here so that two video recorders 14a, 14b respectively connected to the cameras 13a, 13b each record 360 p-images of the object or subject illuminated by the laser 12 (see FIG. ).

 FIG. 3 illustrates a subject 20 and two traces p left by the laser 12. The double data acquisition system 13a, 14a and 13b, 14b thus records a plurality of traces or profiles p realizing, thereby , a sampling of the image of the entire surface of the bust 20 of the subject.

Before continuing this description, the following definitions are given:
- point source ": point belonging to the
outer surface of the object or subject that
we want to reproduce,
- "source profile": trace p left by the
laser on the bust 20 or the object to repro
reduce,
- "image point": image of a source point
recorded by the camera 13a and / or the camera
13b, in an "image plane" belonging to the
camera considered. The image point is carac
by its coordinates (Col, Lig) in the
image plan as well as will stand out from the rest of
the description,
- "image profile": image of the source profile in
the image plane of the considered camera.

 FIG. 2 schematically illustrates the relative arrangement of the two cameras 13a, 13b and the laser 12. The assembly is seen from above, the head of the subject bearing the reference 20, the axis 120 of the laser 12 and the axis 130a, 130b ) of each of the cameras 13a, 13b is intersected on a vertical axis Z corresponding to the axis of rotation of the seat 10 'on which the subject sits. The Z axis is said, in the following description, "axis director". It is observed that the Z axis opens out of the head 20 substantially in the middle of the latter. The axes 130a, 130b are inclined at an angle e of 30 relative to the axis 120 of the laser 12. The latter emits a plane light beam which leaves a trace, also called a profile and referenced in FIG. , on the subject's head and bust.

We choose one of the two cameras, the camera 13a in this case, as the director camera. As a rule, the latter permanently and in its entirety traces the laser beam on the subject's head and bust. However, in some areas, the trace p is partially hidden, and can not be seen from the director camera 13a (see for example Figure 2: at the nose, the trace p is, for a portion of its extent at least , masked). Also, in such a case, we will use the data from the secondary camera 13b, which, with respect to the example illustrated in Figure 2 at least, sees the masked portion of the trace p. Further, in the description, it will be explained how a master file
FIa, associated with the director camera 13a, is completed by the data from the secondary camera 13b.

 It should be noted here that the data acquisition mode is particularly well adapted to a surface having a variable shape on the 360 of its periphery.

 However, such a provision is not imperative. Indeed, instead of placing the object to be reproduced on a turntable, it may, for example, be arranged on a moving plate with a translational movement so that the traces will then be parallel to each other and parallel to a director axis integral with the object, this axis moving parallel to itself. This may be the case when the object to be reproduced is for example a relief map whose mathematical representation is of the form: z = f (x, y) and of which only one face is to be reproduced. On the other hand, when the object has to be reproduced as a whole, the method of the turntable described above will be used.

 With regard to the illustrated embodiment, it will be noted moreover that, advantageously, taking into account the shape of the object, or the morphology of the subject, it is possible to parameterize the angular displacements to obtain more images on the zones. the subject's subject whose surface is subject to abrupt variations (eg the subject's nose) and fewer images in areas where the surface is more even (for example, the nape of the subject).

 In the illustrated example, the data is recorded on a first set of video recorders 14a, 14b, another set of video recorders 14'a, 14'b being used for information processing. This makes it possible to decentralize the processing phase relative to the acquisition phase.

 In Figure 2a, there is illustrated an alternative embodiment of the data acquisition assembly implementing a single camera 13c and two lasers 12a, 12b.

This figure schematically illustrates the relative arrangement of the two lasers and the camera. The set is seen from above, the subject's head also bearing the reference 20.

The axis 130c of the camera and that (120a, 120b) of each of the lasers 12a, 12b intersect on a vertical axis Z corresponding to the axis of rotation of the seat 10 'on which the subject is seated. The axes 120a, 120b are inclined 30- with respect to the axis 130c of the camera. The lasers 12a, 12b each emit a beam of light. This beam leaves on the head of the subject and his bust a trace, referenced in Figure 2a in p (trace left by the left laser 12a) and p '(trace left by the right laser 12b).

 As a general rule, the camera constantly sees both traces of lasers on the person's head. These two traces are completely separated because they can not have anything in common except on the axis of rotation Z. The electronic means take into consideration only one of the traces, in this case the trace p ', left by the laser right 12b. However, as previously, in some areas, the right trace will be hidden (masked area by the subject's nose, for example). Also, in such a case, the camera 13c can not see this trace or at least the portion thereof that is hidden by the nose.

In this case, the electronic means take into account the left trace seen by the camera when the head has rotated 60 as shown in Figure 2b. Indeed, the trace p left by the left laser 12a (of Figure 2b) is identical to that (p ') left by the right laser 12b of Figure 2a. With this arrangement, it is possible to compensate and find the areas masked by the nose or ears, for example.

 This variant embodiment has the advantages of significantly lightening the data acquisition device since the economy of a second camera and two video recorders. However, this embodiment variant has, with respect to the preferred embodiment chosen, two disadvantages: firstly, the implementation of the taking into account of the offset 60 substantially complicates the processing and, secondly, the mechanical stresses are such that the profile p '(Figure 2a) does not coincide perfectly with the profile p (Figure 2b) once the head has rotated 60': effect, the subject is unable to remain perfectly immobile during this time Therefore, in the end, the Applicant has preferred to implement the embodiment described in support of Figures 1 and 2. However, the variant illustrated in support of Figures 2a and 2b demonstrates that there is various methods for registering the entire surface to be reproduced, including hidden parts. Also, the present invention encompasses in this respect any variants likely to achieve this result.

 The analog signal from the cameras 13a, 13b recorded in the video recorders 14a, 14b and delivered by the video recorders 14'a, 14'b is in the form of a series of curves (the profiles p). The curves are substantially continuous and have very bright spots and dimly lit spots.

 Each of these curves is digitized in the electronic means 15, in a manner known per se, by means of an analog-digital converter which delivers the image (line, column) coordinates of a series of samples representative of each of the curves. . French patent 81.24418 describes a preferred embodiment for performing this digitization, and therefore the converter 15 will not be described in more detail here.

 However, the Applicant has found that for technical and economic reasons, the object or the subject to be reproduced being placed on a rotating support, the most easily usable and most economical coordinates from the point of view memory size to use are the so-called "cylindrical" coordinates (R, H, @), where R is the distance between a point on the surface and the Z axis, while H is the ordinate along the Z and e axis corresponds to the angular coordinate of the source profile (intersection of an axis X 'belonging to a reference integral with the bust 20, FIG. 3, with the axis X in the fixed XY plane).

 The coordinate. e corresponds in fact to the pitch (or to a predetermined number of steps and parameterizable) of the motor controlling the rotation of the seat 10 '. A pulse is recorded in the soundtrack of the video recorders 14a, 14b at each step of the motor; as otherwise, the soundtrack is synchronized with the image, we know the position of the motor (and therefore the angle e) at each image.

 The processing means B of the invention comprise, in addition to the video recorders 14a, 14'b and the converter 15 means 17 performing a reconstruction of the cylindrical coordinates of the source points from the image coordinates of each of the samples comprising the profiles. The reconstitution process implemented by the transformation means 17 is described below.

 At the output of the transformation means 17, information is available relating to the cylindrical coordinates of a predetermined number of points representative of the three-dimensional surface, here that of the bust 20 to be reproduced.

 The information processing means B comprise a set of CAD / CAM composed of two modules 16 and 19 connected to the transformation means 17. This set processes the coordinates coming from the means 17 and makes it possible to control a machine tool 18. set implements, including by computer means, a method described in detail below.

The means of transformation 17, and the set
16, 19 are, in the presently preferred embodiment described herein, constituted by a microcomputer 21 performing the functions of the means 17, 16 and 19 described below and controlling, in addition, the converter 15.

The microcomputer 21 is here an IBM computer, model marketed under the reference AT3.

 Finally, the machine tool 18, which here is of the NC-TRIAX-R6-2-TWIST type, manufactured by the Italian company CMS, makes it possible to carve in a material such as wood, resin or aluminum. , a form substantially reproducing that of the bust of the subject sitting in the seat 10 'or that of the object to be reproduced disposed on the table 10.

In summary, in the presently described embodiment, the process processing data from the converter 15 has three phases.
a phase of passing the image coordinates of the image points recorded at the cylindrical coordinates of their source points. This is the function of the transformation means 17,
a phase of homogenization of the points, (function of the module 16),
- a phase of determination of the normal to the surface and correction of this normal, to determine the direction of the tool (function of the module 19).

 In the description that follows, we will describe in detail each of these three phases. We will begin by explaining first the structure of the data provided by the vision system constituted here by the cameras, the laser beams, the video recorders and the converter.

2. Structure of the output data of the conver
weaver 15
Each of the 360 recorded images corresponds to a source profile, characterized by the angle formed between the X 'axis and the X axis in the XY plane.

 It will be noted in the remainder of the description that e designates all at once the angular coordinate of a source profile, the plane containing this source profile characterized by its angular coordinate e, and the image profile corresponding to the source profile e. e is indexed in particular according to n, n corresponding to the sequence number of the source or image profile considered.

Each video camera 13a, 13b is a camera for example THONSON type TAV-1033-NEWICON delivering 316 lines per image and 1024 pixels per line. Also, the image profiles are in fact constituted by a succession of points characterized by their coordinate in the recorded video image, the latter actually corresponding to those of the pixel. Indeed, for a given pixel, we know the line on which it is arranged (coordinated
Lig ranging from 0 to 315) and the position of the pixel in this line (Col coordinates varying from 0 to 1023).

 Any point of the image profile is therefore defined by its coordinates: (Col, Lig, en).

 In Figure 4, there is schematically illustrated an image profile as recorded by the video camera. We have schematized by a cross the pixel illuminated on the occasion of the taking of images. Each image consists of 316 rows ordered from 0 to 315, 1024 pixels being capable of being lit on a line. As an indication, for the profile illustrated, the number of the illuminated pixel above the cross schematically this pixel has been indicated.

Thus, in the example illustrated in line 1, the pixel n 480 is illuminated, in line 3, the pixel n 500 is illuminated, etc.

 For each point of the profile in, one thus has its coordinates image (Col, Lig, in). By way of example, those of the point situated on the sixth line of FIG. 4 are: (502.6, in).

The transformation means 15 implement an image file FI in which the image coordinates of the points constituting the various profiles are stored as follows
the image file sequentially contains the ordinates of the pixels of the profile, on a line considered,
each coordinate is coded on a 16-bit word.

The code of an image point is as follows
TABIEAU I
N of the Comment bit
Bit 15 0 profile separator
1 profile point in progress
Bit 14 0 no point in the
current line
1 presence of a point in
the current line
Bit 13-Bit 10 0 # these bits are not used
Bits 9 - O Position of the illuminated pixel
in the line coded on 10
bit
Each image profile corresponds to a sequential set of 316 words. The profiles are separated by the word: 0 0 0000 0000000000. The number of the profile being read is entered in a counter.

 Table II below illustrates the profile in the structure of the IF file in Figure 4.

BOARD
O 0 0000 0000000000 Profile separator
Profile in 1 0 0000 0000000000 Lig 0, no point
1 1 0000 0111100000 Lig 1, col 480
1 0 0000 0000000000 Lig 2, no point
1 1 0000 0111110100 Lig 3, col 500
1 1 0000 0111101010 Lig 4, pass 490
1 1 OÒoO 1011010000 Lig 5, col 720
1 1 0000 0111110110 Lig 6, pass 502
1 1 0000 0111010110 Lig 7, pass 470
1 1 0000 0111100110 Lig 308, pass 486
1 1 0000 0111110101 Li # g 309, pass 501
1 0 0000 0000000000 Lig 310, no point
1 1 0000 0111100101 Lig 311, col 485
1 1 0000 0011111010 Lig 312, col 250
1 1 0000 0111100110 Lig 313, pass 486
1 1 0000 0111110100 Lig 314, pass 500
1 1 0000 0111101111 Lig 315, pass 495
O 0 0000 0000000000 Profile separator
Profile in + 1 1 0000 0111100011 Lig 0, col 483
Referring to Figure 4 and Table II, it can be seen that each line may have either
- 1 point in a median area a,
- 1 point in lateral zones b,
- no points in these areas. This is in
made of insufficiently illuminated points for
the reasons explained below.

 Thus, in lines 2 and 310, no pixel is illuminated. On the other hand, in lines 5 and 312, respectively 720 and 250 pixels are located in the lateral zones b. These points are called aberrant.

 Indeed, the vision system used is such that it is possible that some points of the object or subject do not sufficiently reflect the laser light and, on the contrary, absorb it. These points are so-called "low albedo" points. In such a case, the reflected light being insufficient, the pixel concerned is not lit. This is why in lines 2 and 310, in the example illustrated in FIG. 4, no pixel is illuminated.

 On the other hand, it is possible that some pixels are illuminated, these pixels not corresponding to points of the subject belonging to the illuminated profile are here the "aberrant" points of the lines 5 and 312 (for example because of reflection of the light laser in the subject's hair).

 A feature of the invention is described below which makes it possible to reconstruct the missing points and to detect the aberrant points.

 Finally, it will be observed that at the output of the converter 15 and at the input of the transforming means 17, a file summarizing sequentially the coordinates (Col, Lig, e) of sets of 31 points belonging to 360 is available. profiles.

3. Reconstruction of spatial coordinates of
point source of each point imaa
enrecristrés
The problem posed is that of allowing 1 passage of the image coordinates of a point (Col, Lig, e> to the spatial coordinates of its source point, these spatial coordinates being in this case selected of cylindrical type (R, H, e) .

 This problem is not simple because it involves moving from a coordinate system in a particularly small plane, that of the cell of the camera, & spatial coordinates, in three dimensions.

 A first method consists in determining, mathematically, for each point of the image plane the cylindrical coordinates (R, H, e) of the corresponding source point, it being understood that the angle e is the one defined above, these coordinates being stored in a file and image coordinate transformation (Col, Lig, e) in cylindrical coordinates (R, H and @) being done by simply reading the file.

 This method, although it comes within the general scope of the present invention, is not technically and economically satisfactory at the time of filing of the present application because it requires a particularly large memory size. However, it is possible that it is technically and economically feasible in the near future and that the present invention encompasses such a method.

 The Applicant has therefore used and improved a technique for transforming image coordinates into cylindrical coordinates using a relatively small memory size.

 In fact, with regard to the cylindrical coordinates (R, H, e), the problem arises essentially for the determination of the coordinates R and H, the angle e being the angle between the axis of X 'and the axis X (Figure 2), this angle being given by the position of the stepper motor animating the seat 10 '.

The following mathematical model is used
a1tig + a2Col + a3 a4Lig + a5Col + a6 (1) R = H =
a7Lig + a8Col + l a7Lig + a8Col + l
The problem that arises here therefore is to determine the transformation coefficients vi i apply to the line-column coordinates of all the points in the space likely to be filmed by the cameras 13a, 13b, to obtain the corresponding cylindrical coordinates for each of these points.

 For this purpose, there is proceeded to a "calibration" step of each of the cameras 13a, b, in situ. This is the subject of the calibration phase described below in section 3.1.

 Once these conversion factors are determined as will be described below, the equations given under (1) above can be used for the actual transformation of the linecolumn coordinates of the points delivered by the converter 15 for each of the vision systems. 13a, 13b. Two so-called "spatial" files FSa and FSb are thus generated (see section 3.2 below).

3.1 Calibration phase
The basic method used for calibration is as follows
We use a calibration chart as shown in Figure 6, comprising a rectangular plate 41 of height H and width R in the example considered R = H = 50 cm) and thickness e (1 cm here). The plate 41 is provided with four pins formed by metal cylinders (referenced A, B, C, D in the example) of radius r and height h predetermined (d, in the example considered r = 1 mm and h = 2 cm). The spatial position of the A-D rods and, in particular, their coordinates (RA, HA), (RB, HB), (RC, HC) and (RD, HD) are known. FIG. 6 illustrates the Z axis, along which the H coordinates are measured and an R axis, perpendicular to the Z axis, along which the R coordinates can be measured. In this figure, the coordinates (RA, HA) of the A peg have also been illustrated.

 The pattern thus constituted is filmed by means of each of the cameras 13. This figure, under the reference 42, illustrates the axis of vision of the camera 13a and under reference 43, the lamellar plane of light from the laser. This lamellar plane is parallel to the plate 41, while the axis of vision 42 of the camera 13 tilts 30 'with respect to the lamellar plane of light and intercepts the plate 41 at the centroid 0 of the four pins A - D.

 The vision system thus records the image coordinates corresponding to the four pins (ColA, LigA), (ColB, LigB), (ColC, LigC) and (ColD, LigD).

 From equations (1) above, it is possible to form a system of eight equations with eight unknowns (the ai) and as among the four points A there is no subset of three points aligned, the system of equations admits a solution that is both unique and non-aberrant.

 The mathematical model (1) above used with the thus determined gives an obvious solution for the four points A-D. However, because of the optical nonlinearities of the vision system, the accuracy of the RH coordinates for the other points is degraded. It has been observed that the error is in fact minimal at the center of the other A-D points.

 To minimize this error, according to one characteristic of this aspect of the invention, the procedure is as follows. A calibration pattern is used in the form of a square plate 53 whose dimensions correspond to the largest dimension of the object or subject that it wishes to reproduce in three dimensions (see FIG. 7). In the example considered, the pattern has a height and a width of 1 m. A plurality of pins 51 are arranged in-line and in column so as to define a plurality of squares 52. In the embodiment chosen and shown, the calibration plate 53 is thus divided into 25 squares on each of the corners. of which a calibration pin 51 is disposed. Each freelancer is characterized by its line - column coordinates (i, j). Thus, the freelancer (i, j) is the freelance of the linear film and the jth column.

 The calibration target 50 is set up as shown in FIG. 6. FIG. 7 shows an axis Z and a R axis respectively parallel to two perpendicular sides of the calibration target 51. Knowing the coordinates (R, H) for each of the squares 51, it is possible to determine, for each of the barycentres 54 of each of the squares 52, the coefficients ai relating to the square considered, by applying the equations (1) above. Each of the centers of gravity 54 is then assigned the corresponding coefficients a 1.

 We then consider the triangles Tk whose vertices are constituted by the baryentres 54 of neighboring squares. These triangles Tk are illustrated in FIG. 7 in phantom. The triangles Tk are here 32 in number and are numbered (k varying from 1 to 32).

To ensure a continuity of the mathematical model used, it is considered that the coefficients ai are polynomials of degree 1 in Col, Lig on each of the triangles Tk. Thus, the coefficients eri are of the form (2) ai = ssilol + ssi2Lig + Pi3
For each of the triangles Tk, we know the coefficients ai for determining the coordinates R,
H of each of its summits.

 We therefore have, for each triangle Tk, and for each ai of a vertex, a system of three equations with three unknowns (the Pij) that we can solve to determine these unknowns.

In summary, the method is as follows
for each of the centers of gravity 54, the coefficients a1 are determined for determining the spatial coordinates (R, H), taking into account the image coordinates (Col, Lig) recorded by the vision system, and taking into account the fact that lton knows the spatial coordinates (R, H) of the pins 51 viewed by the vision system,
from the coefficients ai assigned to each of the barycentres, the coefficients Pij for the triangles Tk considered are determined.

 Consequently, there is thus an interpolation method making it possible to continuously vary the coefficients a 1, taking into account the position of the points arranged inside a given triangle Tk and, in particular, their approximation or their distance. of a summit considered.

 With each of the cameras 13a, 13b, the test pattern 50 is filmed once and for all, and the coefficients Pij relating to each of the cameras are calculated.

Once the Pij coefficients have been determined for the two cameras, they are then "calibrated" and we can transform the coordinates (Col,
Lig) from the converter 15 in spatial coordinates (R, H).

3.2. Constitution of files associated with
each camera
As explained above, each camera 13a, 13b films a series of source profiles, each of the resulting image profiles being sampled by the converter 15 so that at the output of this converter, the coordinates (Col, Lig) of a set of samples to reconstitute each of the profiles considered.

 Figure 8 is a block diagram of the main means implemented here. The function of the cameras 13a, 13b and that of their associated video recorders 14a, 14'a, 14b, 14'b have been shown schematically. This figure also schematically shows the main functions performed by the converter 15 and the transformation means 17.

The converter 15 essentially comprises analog-digital conversion means operating according to the principle described in the French patent 81.24418 cited above. These conversion means carry the reference 151. The coordinates (Col, Lig) for each of the points of the image profiles delivered by each of the cameras are in fact recorded in two image files FIa,
FIb. The file FIa is associated with the vision system comprising the camera 13a, the video recorder 14a and the video recorder 14'a, while the file FIb is associated with the second vision system (camera 13b, video recorders 14b and 14'b). Thus, only the coordinates of the points from this second vision system are recorded in the FIb file, while only the coordinates of the points from the first vision system are recorded in the FIa file.

The transformation means 17 comprise a transformation file 171a (171b) associated with each of the cameras 13a, 13b. Each file 171a (171b) maintains a number of records equal to the number of triangles Tk considered (here 32). Each record includes
the number of the triangle Tk considered,
the coordinates of each of the vertices of this triangle (centroids 54),
the coefficients Pij associated with this triangle for the camera considered 13a (13b) (obtained during the calibration of these cameras). As explained above, the calibration of each camera is done in situ prior to any commercial operation of the process. In FIG. 8, the calibration of the cameras, making it possible to constitute the files 171a, 171b, is schematized in Ca and Cb).

 The transformation means 17 also comprise, on the one hand, a spatial file FSa constituted by the cylindrical coordinates obtained after transformation of the image coordinates contained in the image file FIa and, on the other hand, a file FSb constituted by the cylindrical coordinates obtained after transformation of the images. image coordinates in the FIb image file.

 From the image coordinates of any point contained in one of the FIa or FIb files, it is calculated, by means of an iterative method, the spatial coordinates R, H corresponding to this point.

 In FIG. 8, the iterative transformation step has been schematized in 172a, for the coordinates coming from the file FIa, and in 172b for the coordinates coming from the file FIb. Fig. 9 shows a simplified flow chart of transformation, performing step 172a or 172b. Only step 172a will be described, step 172b being identical.

 Each of the points contained in the FIa file is processed sequentially. The treatment of a given point, having coordinates (Lig, Col) comprises a reading in the file FIa, and an inscription in memory, as schematized in 180. The transformation step described aims to calculate the coordinates (R, H ) corresponding to the coordinates (Lig, Col). To do this, during a first initialization step 181, initialization of each processing of a given image point is initialized, putting the memory which must contain the coordinates of the source point (R, H) to zero. The iterative process is then as follows: in 182, during a second initialization step, two intermediate variables (Rot Ho) are initialized by putting these intermediate variables equal to the contents of the memory (R, H). The variable K, which corresponds to the number of the triangle, is also initialized to zero. In 183, this variable k is incremented. In 184, we read in the file 171a the coordinates of the triangle Tk, and the set of coefficient Pij associated with the triangle Tk considered.

 In 185, a membership test is carried out to determine whether the point whose coordinates are the intermediate variables (roof Ho) belongs to the triangle Tk or not. To do this, we do com tests.

successive parisons of coordinates according to a conventional search method well known to those skilled in the art who knows, knowing the coordinates of a point in a given plane, to which region of this plane belongs this point.

If the test 185 is negative, it returns to 183 where the variable k is incremented. When the test is positive, that is to say that the triangle Tk to which the point having the intermediate coordinates (#, Ho) has been determined, we pass to a transformation step 186.

 In 186, the coordinates (R, H) contained in memory are assigned new values corresponding to the coordinate transform (Col, Lig), by means of the equations (1) and (2) written above, making it possible to calculate from coefficients Pij read at 184 the coordinates (R, H) considered.

 In 187, the test consisting in determining whether the coordinates (R, H) are respectively equal or not to the intermediate coordinates (Rot Ho) is carried out. In the negative, step 182 is returned; if the test 187 is positive, it means that the coordinates (R, H) in memory are actually those of the source point of the image point (Lig, Col) processed.

 These coordinates (R, H) are written in the spatial file FSa.

In summary, during the iterative transformation step, the following operations are performed:
a search operation during which the search-zone Tk at which the source point belongs is searched, as well as the interpolation coefficients Pij associated with this zone. It will be observed that instead of performing this search in the source space, as in the embodiment described, it is possible, without departing from the scope of the invention, to perform it in the image plane of the camera 13a. or 13b,
a calculation operation during which the spatial coordinates (R, H) are calculated by concurrent application of the transform (1) and interpolation (2) formulas.

 One likewise constitutes a spatial file FSb from the coordinates contained in the FIb file.

 It should be noted that for the same spatial point, the cylindrical coordinates determined from the image coordinates in the FIa file and in the FIb file should be the same. In practice, they will be identical to optical errors and rounding up.

It will be observed that the transformation method described above uses little memory since in this case, it is sufficient to memorize by triangle Tk
- his -numble; ro (information),
- the spatial coordinates of its vertices (six pieces of information),
- The associated Pij (24 pieces of information), ie thirty-one pieces of information per triangle. There is therefore a total of 992 pieces of information to be memorized, which is relatively small compared to the information that should be stored if the transformed coordinates for each of the 1024 pixels of each of the 316 lines of the cameras were to be stored in a single memory. , totaling 323,584 pieces of information).

 The spatial coordinates contained in the FSa and FSb files are merged into 173 into a single FS file. This merge allows to complete with the coordinates of the points of the no files the coordinates absent in the other.

 It is at this level of the process that the problem of the points that could not be filmed by the two cameras (hidden parts) was solved: - the hidden parts for one camera could be filmed by the other (see figure 2).

By merging the -FSa and FSb files, a single FS file is created in which in theory the entire area of the bust is sampled (subject to missing or aberrant points in both files for the reasons mentioned above). ).

 The merge takes place using one of the files, the FSa file, as a pilot file and completing the missing coordinates in this file by those possibly existing in the FSb file.

4. Homogenization of the points of a profile
As explained above, in support of #figure 4, each profile can
- present missing points,
--it include aberrant points.

 The purpose of the presently described step, which is called homogenization, is to eliminate the outliers and reconstruct the coordinates of the missing points. This step comprises an operation called "integration", a "filtering" operation and a so-called "reconstitution" operation.

4.1 Integration operation
In Figure 10, there are five source profiles (8 r in # 1, en, enalr in + 2). It can be seen that these profiles concern five successive positions of the seat 10 '.

They have been illustrated in the reference associated with the bust 20 (X ', Y', Z).

The source profile being processed is the profile in. For each of the points treated
Pi, n = (Ri, Hui, 8,), the following operations are carried out
- First determine the neighboring points of the point (Ri, Hi, en) considered. In this respect, we consider the 2p + 1 profiles ranging from # p å to + p. In the example illustrated in FIG. 10, p = 2 and consequently, the five profiles ranging from en-2 to + 2 are considered.

 On each source profile ej thus considered, one selects the 2k + 1 points going from (Ri-k Hi # k, e;) a (Ri + k, Hi + k, e;). In the example under consideration, in FIG. 10, k = k = 2 was chosen.

 This thus determines (2p + 1) x (2k + 1) points close to (Ri, Hi, en) including this point being processed.

 In the embodiment shown, there is therefore a theoretical total of 25 neighboring points at the point Pi, n being processed, including the latter.

 The average R of the ordinates in R and the average H of the ordinates in Z of each of these 25 points are then calculated.

 In the event that points are missing, the average is done by decreasing the common divisor (25 in a normal case), with as many units as there are points missing.

 If the point "processes" Pi n is not missing (bit 14 to 1 in Table I), the filtering operation is carried out.

4.2 Filtering operation
The purpose of filtering is to allow the elimination of outliers. For each of the treated points, the absolute value 1R1 - R 1 is calculated.

 If this value is greater than a given error value E, parameterizable, the point (R1, H11 #n) is eliminated.

 The given value E is determined by the experiment, considering the object that one seeks to reproduce. For example, with regard to the face of a person, for certain areas, it is known that the risk of obtaining aberrant points is particularly high and that these aberrant points may be arranged at a relatively large distance from the profile. In such a case, one will choose for value E, a value of a few centimeters, 3 cm for example.

 On the other hand, in other cases, errors and outliers will be few and in any case relatively close to the profile. In such a case, we will choose as a value E, a low value of the order of a few millimeters, 3 mm for example.

 In addition, according to a characteristic of the invention, it will be observed that said given value E can be parameterizable taking into account the profile analyzed. Thus, in certain areas of the face, such as the nose, a relatively large value E will be chosen, since the profile is likely to have significant variations in its R-coordinate, whereas, for the profiles relating to the nape, one will choose a relatively low value E, since the profile only has variations in its low amplitude coordinate R.

4.3 Reconstitution operation
In the case where the point (Ri, Hi, en) is missing (bit 14 to 0, see Table I), or if it is filtered, as explained above, the so-called reconstitution operation is carried out at during which the calculated mean values R, H are determined at the point (Ri, Hi, on) during the initialization step.

 FIG. 5 is a view corresponding to FIG. 4, in which the points represented are the source points in cylindrical coordinates, and in which the aberrant and missing points have been reconstructed, as explained above (points Pr).

 The file FS, is completed as the processing of the points (Ri, Hi, on) by the coordinates of all the points Pr reconstituted.

 It will be noted that the step of homogenizing a profile that has just been described implements the cylindrical coordinates, after reconstitution of the cylindrical coordinates of the source point from the coordinates of its image.

 In another embodiment of the present invention, it is quite possible to invert the steps of reconstitution and homogenization and proceed to the homogenization step in image coordinates and then proceed to a transformat. ion or the reconstitution of the cylindrical coordinates of all the source points from the original image points or reconstituted "image" points. In fact, it will be observed that, in general, the homogenization phase is a phase during which for each treated point (that it is considered in the source space or in the image plane), we consider a predetermined number of neighboring points, we calculate the average coordinates of these points, if the treated point is absent, or if at least one of its co-ordinates differs from the corresponding mean coordinate by a difference greater than a predetermined value (E), the point average data.

5. Determination of the direction of the tree
Torte tool
The tool used is essentially in the form of a cutter disposed at the end of a tree belonging to a robot that can control the position of this tree in space.

 It is conceivable that the position of the cutter must be determined by at least three coordinates. In this case, the coordinates (R, H, e) will be used.

 But it is necessary, moreover, that the shaft bearing the cutter is disposed in a direction substantially normal to the surface to be reproduced, so that the material is attacked at a favorable angle.

 To do this, the robot must be able to determine not only the position of the cutter along the three cylindrical coordinates, but in addition the general direction of the shaft (two additional degrees of freedom).

The tool shaft will be oriented in a direction normal to the surface if two conditions are found together
- on the one hand, it is necessary that the projection of the tree in the plane in which belongs the treated point:
Pi, n: (Ri, Hi, en) is normal to the profile to which this point belongs,
and, on the other hand, that the projection of the tree in a secant perpendicular plane Si passing through the treated point Pi, n is also normal to the trace of the surface to be reproduced in this secant plane. In the following, we will call "trace secant the trace left in the plane
If by the surface to reproduce.

 In FIG. 11, the projection in the plane of the normal to the surface at the point Pi, n is illustrated under the reference DNe> n, whereas in FIG. 15, the reference SNe> n is represented, i the projection of the normal to this surface at the point Pi n in the plane Si.

 Thus, in addition to the three degrees of freedom needed to control the position of the tool axis, the robot that controls this position, as well as the position of the shaft, must be able to control two additional degrees of freedom. The two additional coordinates that the robot must control are rotations.

One around the Z axis (perpendicular to the Si plane), the other around an axis perpendicular to the Z axis, the Y axis in this case.

The robot and the tool used are here of the type
NC-TRIAX-R6-2-TWIST, manufactured by the Italian company CMS.

 A problem arises when the surface to be machined has several concave parts, one of which is shown in FIGS. 12 and 14. Indeed, in such a concave part, there is a risk of a tool-material collision. Thus, in Figure 12, at the critical point Pc, the direction of projection of the normal is D. Now, this direction intercepts the profile not only at the point Pc but also at the point Pin so that if the tool shaft took such a direction, there would be collision with matter.

 The same problem arises in the Si plane, figure 14.

To overcome this disadvantage, it is necessary to determine a so-called "normal rectified" direction to avoid this collision and, for this purpose, deviating from the normal. This direction has been illustrated for the point Pc in FIG. 13, under the reference # E # en, i and in FIG. 14 (in the plane Si) under the reference ESen, i. As a result, the step of determining the direction of the tool is broken down into three sub-steps
- estimate of normal Nen ix
detection of the concave parts in the plane and calculation of the direction of projection of the rectified normals in the plane in
- detection of concave parts in the plane
If and calculation of the direction of the projection of the normals rectified in the plane Si.

5.1. Estimate of normal
The determination of the normal of the treated point Pi n will be done, taking into account the four closest points P2-P5, figure 10. To determine this normal one proceeds to the computation of the following vector products:
Nl = Pt P2 PtP4
N2 = PtP4> PtP3
N3 = PtP3
N4 = PtP # PtP2
The vectors N1 - N4 are standard, which gives the
Wi> NM1 - 4 vectors (NRi =
liNili
The sum of the four normed vectors is calculated: NM; + NM2 + NM3- + NM4 which makes it possible to obtain a mean direction vector to the four preceding normed vectors The direction of the resulting vector is considered to be the "normal" at the surface at the point being processed Pi, n.

The resulting vector is then normalized, giving the vector N in, i
The above processing is done for each of the points (Ri, Hi, #n) of the FS file.

An FN file is created, with, for each of the points Pi, t, the coordinates of the associated vector at, i
5.2 Determination of Concave Darties in
and calculating the projection of the normal
rectified in this Plan
We consider the following vectors and coordinates
- DN in i: normalized projection of N # n, i in the
plan in,
- RNi and #Ni: - the components of this vector
in the plane in (Figure 11).

 We consider the two neighboring points of (Ri, Hi, en) respectively (Ri-lt 8,) en) and (Ri + 1 Hi + lr en) on the profile en and the normed projection DNen, i-1 and DNe> n, i + i associated with these points.

The following vector product is calculated (DNe> n, 1 + 1 in, il) which makes it possible to obtain a convexity coefficient QDi associated with the point in treatment (Ri, Hi, en);
QDi = (RNi + 1 * HN i-1) - (RNi # 1 * HNi * F1) (3.1)
If the coefficient QDi is positive, it means that the meridian is convex at the point being treated. If it is negative, it means that the meridian is concave.

 If the meridian is convex, write in the FS file the coordinates of the vector DN> in, i- associated with the treated point (Ri, Hi, en).

If the coefficient QDi is negative, the vector is calculated:
DN in, il + DN in, i + l (3.2)
This vector is standard, which gives the vector
Ex envi
The coordinates of the vector ED # in, i, are written in the file FS.

 We treat all the points Pi n of the FS file.

At that moment, an FS file is available, comprising, on the one hand, the spatial coordinates of each of the points Pi n and, on the other hand, associated with each of the points considered, the coordinates
either of the projection DN> in, i of the normal in i in the plane in,
or the vector ED i which is an estimate of the direction of the projection of the direction of the tool-holder shaft in the plane, to minimize the risk of interference between tool holder and material, mentioned above. . ED> en, 1 is called "normal rectified in the plane to".

When the set of points is processed, the above treatment is repeated, using, in the formulas (3.1) and (3.2) above, the coordinates of the vector DN # n, i or E in i associated with each of the points and we modify, in the file FS, the values of the vectors
EPen, i.

 This process is repeated a predetermined number of times (three in this example) In reality, the direction Eten, i, estimated at the point considered after three iterations, is such that the risk of collision toolmatière mentioned above, due to the concavity of the meridian at the point considered, is minimized.

5.3 Determination of concave narties in Si
and calculating the protection of the normal
rectified in this plan
It is recalled first of all that the plane Si is a plane perpendicular to the various planes and intercepting the Z axis at the coordinate Hi, FIGS. 14 and 15. This plane is parallel to the plane XY illustrated in FIG.

 We also consider the secant trace left by the surface of the bust 20 in the plane Si: Si thus designating either the plane or the secant trace.

We consider the following vectors and coordinates
- SNen: normalized projection-of i in the
If,
- RSi and Y51 the components of this vector in
the Si plan.

Consider a treated point (Ri, Hi, en). We consider the two neighboring points of this point respectively (Ri, Hi, 8n-1) and (Ri, Hi, On + 1) on the secant trace
If and the normed projection SNen ~ l, i and SNen + l, i associated with these points.

The following vector product is calculated
SN, e, + l which makes it possible to obtain a coefficient QSi associated with the point in treatment Ri, Hi, in
Qsi = (RSi-1 * YS1 + 1) - (RSi + l * YSi, l) (4.1)
If the QSi coefficient is positive, that is; means that the secant trace is convex to the treated point.

If it is negative, it means that the trace is concave.

 If the trace is convex, the coordinates of the vector Su envi associated with the treated point (Rn, Hi, en) are written in the file FS.

If the QSi coefficient is negative, we calculate the vector
SNC8n-1, i + SN in + 1, i
We call this vector, which gives the vector ES in, i
We write in the file FS the coordinates of the vector
We treat all the points Pi n of the FS file.

At that moment, an FS file is available, comprising, on the one hand, the spatial coordinates of each of the points, and the coordinates of the projection in the plane of the real or rectified normal, (respectively DNen, i and EDenti, and, on the other hand, the coordinates
- the projectior; SN in i of the normal of in i in the plane Si,
or of the vector ES #, i which is an estimate of the direction of projection of the direction of the tool-holder shaft in the plane Si minimizing the risk of interference between the tool-holder and the material mentioned above . ES at i is called "normal rectified in the Si plane".

 As before, this process is restarted a predetermined number of times (three in this example).

Thus, the direction ESen i estimated at the point considered, after three iterations, is such that the risk of tool-material collision mentioned above is minimized.

5.4 Final determination of the direction of
the tool shaft
When the step defined in the preceding paragraph 5.3 is finished, the file FS finally includes for each point Pc n:
- the three coordinates of the point
PI, n (Ri, Hi, in)
the two coordinates in the plane of the vector DNen, i or of the rectified vector EDe> n, i. These two coordinates define the direction of the tool in the plane in.

 the two coordinates in the plane Si of the vector SNen i or the corrected vector E7e> n, i. These two coordinates define the direction of the tool in the plane Si.

 This file is then transferred to machine tool 18.

 The machine tool 18 will therefore be driven from the three coordinates (Ri, Hi, On) and the two directions mentioned above. It should be noted that the CMS machine tool used here is entirely adapted to be driven automatically when the above coordinates are delivered to it in an equivalent and appropriate format well known to those skilled in the art. , especially the familiar post-processor.

 With these features, the tool will attack the material at the most favorable angle while avoiding, or, at the very least, minimizing the risk of toolholder-material collisions mentioned above.

 It should be noted, however, that in some cases (rare) of high concavity, the QDi and QSi coefficients calculated after three iterations will not be positive, and that in such cases a tool-matter collision is likely to occur. The Applicant has found that these cases are rare, and in practice, in the case of video sculpture of a face, nonexistent. However, for the reproduction of very tormented volumes, it is possible to provide an alarm with manual intervention to correct the direction of the tool shaft in case of very high concavity (case of a cavity for example). Nevertheless, thanks to the invention, these cases of manual intervention remain highly minimized.

 The set of calculation steps described in paragraph 3 above, as well as, in general, the management of the entire process and in particular the control and control of the functions and processes described in Figures 8 and 9, as well as those of the machine tool, are provided by the microcomputer 21.

This control and management are of a conventional nature, although adapted to the process just described. Therefore, they will not be described in more detail here.

 Of course, the present invention is not limited to the embodiments described and shown. On the contrary, in addition to the variants already indicated, it encompasses any other variant within the reach of those skilled in the art.

Claims (8)

 A method of reconstructing the spatial coordinates of each of the points of a set of source points belonging to a surface having a data acquisition step in which a light plane beam is illuminated; the surface, at least one image of the trace (p, p, en) left by the plane beam on the surface (20), the trace left by the light plane beam is recorded with at least one camera (13a, 13b). on the surface being said "source profile", the image of this trace in an image plane of the camera being said "image profile", we move relatively the plane beam and the surface and we record with the lad-ite camera again at less an image of the trace left by the plane beam on the surface, the relative displacement, lighting and recording operations are restarted so that a plurality of image profiles constituting a sampling of the image are thus recorded; of the entire surface, the method being characterized in that it comprises a processing step during which, in particular, the column-column coordinates (Col, Lig) of a set of sampled image points are considered. each image profile in the image plane of said camera and the spatial coordinates of the source points corresponding to each of the points of the image plane, this processing step comprising a homogenization phase during which, for each of the treated points (Pi, n), a predetermined number of neighboring points, the average coordinates of these points are calculated, and if the treated point is absent, or if at least one of its coordinates differs from the corresponding mean coordinate by a difference greater than a predetermined value (E), then assigns the treated point to said average coordinates.  2. Method according to claim 1, characterized in that during the homogenization phase, for each treated source point, whose spatial coordinates (Ri, Hi, #n) have been determined, the following operations are carried out:  we determine the neighboring points of the point (Ri, Hi, en) considered, we consider the 2p + 1 source profiles ranging from # p to + p,  - on each source profile e ;; thus considered, one selects the 2k + l points going from (Ri-k, Hi-krBj) to (Ri + k, Hi + k, eu),  the average R and the mean H of the coordinates (R, H) of each of the points are calculated,  if the "processed" point actually exists, a filtering operation is performed during which for each of the points treated, an absolute value (irai -R I) | is calculated; if this value is greater than a given error value E, parameterizable, said treated point (Ri, Hi, en) is eliminated,  if the point (Ri, Hi, en) "treated" does not exist or if it is eliminated, a so-called reconstitution operation is carried out during which the calculated average values are assigned to the point (Ri, Hi, en) (R, H).  3. Method according to any one of claims 1, 2, characterized in that for the acquisition of the spatial coordinates of the source points on the one hand, it implements the considerations that  in the plane of the light beam, a director axis (Z) is chosen and assigned coordinates known as "spatial" (R, H) at each point of said plane, R being the distance between the point considered and the director axis; , H being the ordinate of this point on this axis:  the following formulas for transforming the coordinates (Col, Lig) of each of the points of the image plane of the camera into spatial coordinates (R, H) of the corresponding source point are taken into account:  t1 Lig + a2col + a3 a4Lig + a5Col + a6 (1) R = ~~~~~~~~~~~~ H = - ----------  a7Ig + a8Col + l a7Lig + a8col + 1 the coefficients ai being said transforming coefficients "and being determined for all the points of the image plane of said camera, from so-called" interpolation coefficients "(ssij), they -measures calculated during a previous phase of calibration of the image plane of the camera during which  we record the image of juxtaposed series  four point reference source (51)  located in the plane of light and whose  spatial coordinates (R, H) in this plane  are known; we find the coordinates  images (Col, Lig) of the image of each of these  points for each set of four points  reference source (51) and solves the  transformation formula (1), which gives  eight values of transform coefficients  in a series of four points of  reference (51); we consider the center of gravity  (54) of each series of four points  reference (51) and is assigned to the latter  the transformation coefficients ai as well  determined 5 we consider areas of inter  polation (Tk) of delimited triangular  joined by straight line segments  said centroids (54) of neighboring series,  these barycentres constituting the summits  said triangular areas (Tk); we  uses the following interpolation formula  for each transformation coefficient ai: (2) ai = Biicol + ssi2Lig + Pi3  we thus determine twenty-four coefficients  Interpolation (bit) by triangular area  interpolation (Tk) solving the formula  Interpolation (2) for each of the coefficients  transformation teeth (ai) assigned to a  triangular zone top of interpolation  (tek) and, on the other hand, this method furthermore consists, in said processing phase, in determining the spatial coordinates (R, H) of a source point whose image coordinates (Col, Lig) are known from its image, to do the following  searching, in a search operation, the interpolation zone (Tk) to which the point belongs, as well as the interpolation coefficients (bit) associated with this zone,  calculating, in a calculation operation, the spatial coordinates (R, H) by concomitant application of said transform (1) and interpolation (2) formulas.  4. Method according to claim 3, characterized in that said search and calculation operations comprise the following steps, for each treated image point  a first initialization step (181), during which arbitrary values (O, O) are assigned and stored to the variables (R, H) that one seeks to determine knowing the image coordinates. (Col, Lig) of the treated point (Pi n).  a conformity test (187) during which the equality of the coordinates calculated in the transformation step (186) with the intermediate variables (%, Ho) is checked; in the negative, the intermediate variables (Rot Ho) are set equal to those calculated during the transformation step and we return to the second initialization step (182).  when the membership test (185) is positive, during a transformation step (186), the picture coordinates (Col, Lig) of the treated point (Pi n) are read in an image file (Fia) and the transformation (1) and interpolation (2) formulas are applied simultaneously from the interpolation coefficients (bit) read during the membership test (185), to calculate the spatial coordinates (R, H),  a membership test (185) in which it is searched whether the point having as coordinates said intermediate variables (Rot Ho) belongs to the interpolation zone bearing the number k (triangle Tk) ;; in the negative, the value k is incremented and this test is repeated;  a step (184) for reading the interpolation coefficients (piu) associated with the interpolation zone Tkt  an incrementing step (183) during which the variable k is incremented,  a second initialization step (182), during which two intermediate variables (Rot Ho) are initialized by putting these intermediate values equal to the last known value of the variables (R, H), a variable k is set to zero; corresponding to the number of the interpolation zone (Tk),  5. Method according to any one of claims 1 to 4, characterized in that said director axis (Z) is an axis of rotation, whereas said relative displacemant is a rotation about this axis, a third spatial coordinate (e) being determined by the angular coordinate of the trace of the light beam leaving in a plane perpendicular (X, Y) to said director axis, this third spatial coordinate being assigned to each profile recorded by the camera (13a, 13b).  6. A method of producing a three-dimensional image of a three-dimensional surface comprising the steps of the method according to any one of claims 1 to 5 applied to the determination of the spatial coordinates of a set of points belonging to said surface, characterized in in addition that it implements a machine tool adapted to control a tool with five degrees of freedom, namely three degrees of freedom allowing the positioning of this tool in space, taking into account said spatial coordinates and two degrees of freedom determining an angle of attack of the tool.  7. Method according to claim 6, characterized in that said angle of attack is such that the tool is generally directed according to the normal to the image surface to be achieved and in that one proceeds to a detection of concave parts of the surface to correct the angle of attack of the tool to avoid as much as possible an interaction between the tool and the machined material.  8. Method according to claim 7, characterized in that for detecting the concave portions of the surface  - the trace left by the said  surface (20) in a plane perpendicular to an axis  director (Z) and passing through. the current point of  treatment (Pi, n), this trace being called secant  (Yes),  - we also consider the source profile in  to which belongs the treated point (Ri, Hi, en),  the concave parts of the profile are detected  performing the following operations we consider a normal vector (DN (DN,  DN> in, i + i) at each of the two points  neighbors (Ri, lrHi, lrB,) and (Ri + ltHi + lwen)  from the point trait; (Ri, Hi, # n)  the vector product of the said  normal vectors (DN in, i-1 Dt in, i + 1) at  profile at the points adjacent to the point treated;  a coefficient of  convexity QDi associated with the point in process  (Ri, .Hi, en),  . spi the coefficient of convexity is negative,  the source profile is concave to the point  treated, and calculate the sum (ES in, i)  said normal vectors to the profile,  two points close to the point  at the point treated (Ri, Hi, en).  actually associated  profile using the vectors  predetermined number of times the treatment  the same profile is processed, we start again  when all the points belonging to  (QD) is negative,  sum, when the coefficient of convexity  (QD) considered is positive, the vector  stunned, when the coefficient of convexity  normal vector to cone profile  we associate with each of these points the  treaties belonging to the same profile (@n),  we then consider all the points  this sum vector (ED> in, I) is stored,  treated (Ri, Hi, #n).  neighboring points (Ri, Hi, en-l) (Ri, Hi, en + 1) at the point  (ES> en, I) vectors actually associated with  If the treated point (SNen i) is a sum vector,  corresponding to the normal to said secant trace  each of the points treated (Ri, Hi, en) a vector  each of the secant traces (Si) and we associate with  - a similar treatment is carried out for and for each point, the tool is directed according to the direction of the vectors effectively associated with said point, in the plane of its profile (#n) and in that of the secant trace (Si) to which it belongs.