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WO2003071367A1 - Systeme et procede d'usinage d'un objet - Google Patents

Systeme et procede d'usinage d'un objet Download PDF

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Publication number
WO2003071367A1
WO2003071367A1 PCT/AU2003/000232 AU0300232W WO03071367A1 WO 2003071367 A1 WO2003071367 A1 WO 2003071367A1 AU 0300232 W AU0300232 W AU 0300232W WO 03071367 A1 WO03071367 A1 WO 03071367A1
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WO
WIPO (PCT)
Prior art keywords
edge
profile
filter
machining
image
Prior art date
Application number
PCT/AU2003/000232
Other languages
English (en)
Inventor
Jayantha Katupitiya
Original Assignee
Unisearch Limited
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Unisearch Limited filed Critical Unisearch Limited
Priority to AU2003205429A priority Critical patent/AU2003205429A1/en
Publication of WO2003071367A1 publication Critical patent/WO2003071367A1/fr

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Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/26—Optical coupling means
    • G02B6/262—Optical details of coupling light into, or out of, or between fibre ends, e.g. special fibre end shapes or associated optical elements
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/182—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by the machine tool function, e.g. thread cutting, cam making, tool direction control
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45157—Grind optical lens
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/49—Nc machine tool, till multiple
    • G05B2219/49338—Micromachining, workpieces small, around 1-mm or less

Definitions

  • the present invention relates generally to a system and method for machining an object.
  • the invention has been designed especially, but not exclusively, for micro-machining .
  • Micro-machining involves machining an extremely- minute object (for example, an optical fibre) such that it has a required profile. Because the minute objects are so small, it is not possible to effectively machine minute objects using traditional machining techniques.
  • an extremely- minute object for example, an optical fibre
  • dimensional accuracy is very important in micro-machining because it provides accurate machining, which in turn ensures that the minute object is machined as required.
  • dimensional accuracy is very important when machining a lens on the end of an optical fibre. Being able to provide dimensional accuracy ensures that the machining produces the desired lens. Significant dimensional accuracy is likely to result in an incorrect lens being machined on the end of the optical fibre.
  • a system for machining an object including: an obtaining means for obtaining a desired profile of the object, and obtaining information about an edge of a shaping tool; and a processor for processing the desired profile of the object and the information about the edge in order to determine a path for the object and/or edge to be moved along.
  • the system further includes an assembly for providing a relative movement between the object and the edge such that a portion of the object is removed when the object and edge come into contact with each other.
  • the system further includes an apparatus for moving the object and/or edge along the path whilst the relative movement is being provided, to thereby effect machining of the object into the desired profile.
  • the obtaining means includes a camera for obtaining an image of the edge, the image being the information about the edge.
  • the camera has a resolution of about
  • the obtaining means includes a terminal for allowing a user of the system to enter a function which defines the desired profile.
  • the processor is preferably arranged to identify parts of the edge of the shaping tool which are suited to cutting parts of the desired profile of the object.
  • the processor processes the information about the edge in order to determine a profile thereof; selects a number of parts along the desired profile of the object; for each one of the number of parts, selects a location on the profile of the edge which corresponds to the one of the number of parts; and superimposes the number of parts along the desired profile onto the object, wherein the path is such that when the apparatus moves the object and/or edge along the path, each one of the number of parts superimposed onto the object comes into contact with the corresponding location on the profile of the edge.
  • the processor determines a tangent for each one of the number of parts along the desired profile of the object, the processor selecting the location on the profile of the edge on the basis that it has a tangent that is the same as the tangent for the one of the number of parts along the desired profile.
  • this has the advantage of providing dimensional accuracy when machining the object.
  • the processor includes an image- processing device for determining the outer limits of the edge, the processor using the outer limits to create the profile of the edge.
  • the processor determines the outer limits using an optimal linear operator for step edge detection.
  • the assembly includes a drive motor which is coupled to a member for retaining the shaping tool, the drive motor and member being such that they are capable of rotating the shaping tool in order to provide the relative movement between the object and the edge.
  • the drive motor is coupled to the member via a flexible coupling and the member is mounted to an air bearing such that eccentricities are kept to an acceptable level whilst the shaping tool is being rotated.
  • the drive motor is such that the shaping tool can be rotated at about 10,000 rpm.
  • the acceptable level of eccentricities is about lOnm.
  • the drive motor is driven by compressed air.
  • the apparatus includes a chuck for holding the object, and an actuation means coupled to the chuck, the actuation means being capable of moving the chuck in order to effect movement of the object along the path whilst being held by the chuck.
  • the actuation means includes a feedback circuit capable of producing a signal that can be used by the actuation means to determine a location of the chuck.
  • the actuation means is capable of providing incremental and/or translational movement of the chuck in at least x and z axes.
  • the actuation means is capable of moving the chuck a distance of about 200 microns
  • the actuation means includes a piezoelectric actuator.
  • the feedback circuit includes a capacitive transducer.
  • the apparatus includes a drive motor coupled to an adjustable device capable of holding the object, the drive motor effecting rotation of the adjustable device such that the object can be rotated when held by the device .
  • the device is capable of being adjusted so that the object can be moved into a position such that a rotational axis of the object and a rotational axis of the device coincide.
  • the device includes a chuck for holding the object, a shaft coupled to the chuck, a housing in which the shaft resides, and a plurality of adjustable supports for supporting the shaft in the housing, whereby adjusting the supports allows the fibre to be moved into the position.
  • the system further includes a control circuit capable of detecting whether the rotational axis of the object and the rotational axis of the device coincide, and upon detecting that the rotational axis of the object and the rotational axis of the device do not coincide, adjusting the supports such that the rotational axis of the object and the rotational axis of the device coincide.
  • the control circuit includes a camera for capturing an image of the object whilst being rotated by the apparatus, and a processor for processing the image and in order to determine whether the rotational axis of the object coincides with the rotational axis of the device, the processing also being capable of adjusting the supports .
  • the system is suitable for micro- machining.
  • a method for machining an object including the steps of: obtaining a desired profile of the object; obtaining information about an edge of a shaping tool; and processing the desired profile of the object and the information about the edge in order to determine a path for the object and/or edge to be moved along.
  • the method further includes providing relative movement between the object and the edge such that a portion of the object is removed when the object and edge come into contact with each other.
  • the method further includes the step of moving the object and/or edge along the path whilst the relative movement is being provided, to thereby effect machining of the object into the desired profile.
  • the obtaining step includes using a camera to obtaining an image of the edge, the image being the information about the edge.
  • the obtaining step includes using a terminal to enter a function which defines the desired profile .
  • the processing step includes the steps of: processing the information about the edge in order to determine a profile thereof; selecting a number of parts along the desired profile of the object; for each one of the number of parts, selecting a location on the profile of the edge which corresponds to the one of the number of parts; and superimposing the number of parts along the desired profile onto the object, wherein the path is such that when the object and/or edge move along the path, each one of the number of parts superimposed onto the object comes into contact with the location on the profile of the edge.
  • selecting the location on the profile of the edge includes determining a tangent for each one of the number of parts along the desired profile of the object, the location on the profile of the edge being selected on the basis that it has a tangent that is the same as the tangent for the one of the number of parts along the desired profile.
  • processing the image of the edge includes determining the outer limits of the edge, the step of using the desired profile using outer limits to create the profile of the edge.
  • the outer limits are determined using an optimal linear operator for step edge detection.
  • the step of rotating the shaping tool in order to provide the relative movement between the object and the edge is rotated at about 10,000 rpm.
  • the method further included the step of moving the object along the path.
  • the object is moved incremental and/or translational in at least x and z axes.
  • the movement is about 200 microns
  • the method further included the step of rotating the object.
  • the method is used for micro- machining.
  • a micro-machining apparatus including: a mounting device being adapted to provide mounting for a workpiece to be machined; and a machining head including a grinding element having a peripheral edge portion, the machine head being operatively coupled to the mounting device to permit relative movement between the machining head and the workpiece to provide contact therebetween, the grinding element being rotated and contacted with the workpiece whereby the peripheral edge portion effects machining of the workpiece in a predetermined profile.
  • a micro-machining head including a grinding element having a peripheral edge portion, the grinding element being rotatable about a rotational axis and its peripheral edge portion being configured to contact a workpiece which on rotation of the grinding element is machined in a predetermined profile.
  • a method of micro-machining a work-piece including the steps of:
  • a mounting device to which the workpiece is mounted, and a machining head having a grinding element and being operatively coupled to the mounting device;
  • figure 1 illustrates a system for machining an object in accordance to the preferred embodiment of the present invention
  • figure 2 illustrates an optical fibre which the system shown in figure 1 can machine
  • figure 3 illustrates profile information that is used to calculate a path which the system shown in figure 1 uses to machine the optical fibre;
  • figure 4 illustrates an assembly which forms part of the system shown in figure 1;
  • figure 5 illustrates an apparatus which forms part of the system shown in figure 1;
  • figure 6 illustrates a cross-sectional view of an adjustable device which forms part of the apparatus shown in figure 5;
  • figure 7 illustrates the rotational axis of an optical fibre and a chuck which forms part of the device shown in figure 6.
  • Micro-machining essentially involves machining of minute objects, such as optical fibre.
  • the system 1 has an obtaining means 3 which includes a camera 3a and a terminal 3b.
  • the camera 3a is used to obtain an image of an edge 5 of a shaping tool 7 (which in this embodiment is in the form of a circular grinding wheel) , the edge 5 being used to machine a lens 9 onto the end of an optical fibre 11 (as shown in figure 2) .
  • the camera 3a has a resolution of about 176nm.
  • the image of the edge 5 of the shaping tool 7 is used to determine a profile T U03/00232
  • the obtaining means 3 includes a mount (not shown in the figures) for the camera that enables the camera 3a to be moved.
  • the movement of the camera 3a allows the camera 3a to be moved so that the axis of the camera 3a tracks the tool 7 profile - thereby minimizing parallax error and spherical aberration, which would otherwise result in a profile which is not entirely accurate.
  • the terminal 3b (in the form of a computer terminal) allows a user of the system 1 to input a function which defines a desired profile for the end of an optical fibre 11, which in effect is the profile of the required lens 9.
  • the system 1 also includes a processor 13 which is in the form of computer hardware and software running thereon.
  • the processor 13 is such that it is connected via a link 15 to the camera 3a so that the image of the edge 5 of the shaping tool 7 can be transferred from the camera 3a to the processor 13.
  • the processor 13 also being connected to the terminal 3b via another link 17 so that the function defining the desired profile of the lens 9 of the optical fibre 11 can be transferred from the terminal 3b to the processor 13.
  • the processor 13 is such that it processes the image of the edge 5 of the shaping tool 7 and the function defining the desired profile of the lens 9 of the optical fibre 11 in order to determine a path for the end of the optical fibre 11 and/or edge 5 of the shaping tool 7 to be moved along. Effectively, the path is used to machine the end of the optical fibre 11 into the desired lens 9 profile.
  • the processor 13 In order to determine the path, the processor 13 first determines a profile 19 of the edge 5 of the shaping tool 7 (as shown in figure 3) . This is done by applying an optimal linear operator for step edge detection to the image of the edge 5 of the shaping tool 7. Effectively this allows the processor 13 to determine the edge 5 of the shaping tool 7, and in turn determine the profile 19 thereof.
  • the optimal linear operator is used in the preferred embodiment because it allows sub-pixel edge detection and thereby accurately determine the profile 19 of the edge 5 of the shaping tool 7. Being able to accurately determine the profile 19 is particularly important for machining a lens 9 on the end of an optical fibre 11 because it allows the lens 9 to be accurately machined. It is, however, possible to use other techniques to determine the edge 5 of the shaping tool 7.
  • the next step carried out by the processor 13 in determining the path is to use the function defining the desired profile of the lens 9 of the optical fibre 11 (which was input into the terminal 3b) in order to select a number of parts along the desired profile of the end of the optical fibre 11 (the parts being marked A and B in figure
  • the processor 13 examines the profile 19 of the edge of the shaping tool 7 in order to identify a location on the edge 5 of the shaping tool 7 which corresponds to the spaced apart location on the desired profile of the optical fibre 11. This involves, in this embodiment, determining a tangent for each of the parts along the desired profile of the optical fibre 11 and for each spaced apart location along the desired profile of the optical fibre 11 using the profile 19 of the edge 5 of the shaping tool 7 to identify a location (which are marked A' and B' in figure 3) thereon that the same tangent as the location along the desired profile of the optical figure 11.
  • location A of the desired lens 9 profile has the same tangent as the location A 7 on the profile 19 of the edge 5. The same can also be said for locations B and B .
  • the processor 13 then superimposes the parts along the desired lens 9 profile of the optical fibre 11, onto the optical fibre 11.
  • the processor 13 calculates the path such that each one of the number of parts superimposed onto the optical fibre 11 can come into contact with the corresponding locations on the edge 5 of the shaping tool 7 when the end of the optical fibre 11 and/or edge 5 of the shaping tool 7 is moved along the path.
  • the path is such that locations A and A' will come together, after which locations B and B' will come together.
  • the system 1 also includes an assembly 21 for providing relative movement between the optical fibre 11 and the edge 5 of the shaping tool 7 such that a portion of the optical fibre 11 is removed when the optical fibre 11 and edge 5 of the shaping tool 7 come into contact with each other.
  • the assembly 21 includes drive motor 23 coupled to a member 25 which is capable of retaining the shaping tool 7.
  • the drive motor 23 is in the form of an air driven motor which is controlled by an air regulator, whilst the member 25 is in the form of a chuck.
  • the drive motor 23 and member 25 being such that they cooperate to rotate the shaping tool 7 at about 10,000rpm, thereby providing the relative movement between the edge 5 of the shaping tool 7 and the optical fibre 11.
  • the drive motor 23 is coupled to the member 25 via a flexible coupling 27.
  • the member 25 is also mounted to an air bearing 29 which is fed with filtered compressed air at about 90psi from a compressor 31.
  • the flexible coupling 27 and the air bearing 29 ensuring that eccentricities in the shaping tool 7 (particularly at the edge 5) are kept to about lOnm whilst being rotated.
  • the system 1 also includes an apparatus 33 which is capable of moving the optical fibre 11 and/or edge 5 of the optical fibre 11 along the path, previously determined by the processor 13, whilst the assembly 21 is providing the relative movement between the edge 5 of the shaping tool 7 and the optical fibre 11. This movement effecting the machining of the end of the optical fibre 11 into the desired lens profile entered into the terminal 3b.
  • the apparatus 33 includes a chuck 35 which is capable of holding the optical fibre 11, and an actuation means which is coupled to the chuck 35.
  • the actuation means 37 is such that it can move the chuck 35 in order to effect movement of the end of the optical fibre 11 along the path whilst being held by the chuck 35.
  • the actuation means 37 also includes a feedback circuit (not illustrated) which produces a signal that is used by the actuation means 37 in order to determine the location of the chuck 35, which in turn is used to ascertain the location of the end of the optical fibre 11.
  • the feed back circuit is in the form of a capacitive transducer which is associated with the chuck 11 and a fixed structure.
  • the actuation means 37 being such that it can move, either incrementally and/or transitionally, the chuck a distance up to 200 microns in at least x and z axis.
  • the actuation means 37 is in the form of a number of piezoelectric actuators that are appropriately positioned about the chuck 35 to provide movement in the x and z axis.
  • the apparatus 33 also includes a drive motor 39 and an adjustable device 41 (illustrated in figure 6) , both of which are coupled together.
  • the adjustable device 41 is coupled to the chuck 35, whilst the drive motor 39, which is in the form of an air driven motor, cooperates with the device 41 in order to effect rotation of the chuck 35, which in turn rotates the optical fibre 11.
  • the device 41 includes, a shaft 43 coupled to the chuck 35, a housing 45 in which the shaft resides, and a plurality of adjustable supports 47 that support the shaft 43 in the housing 45.
  • the adjustable supports 47 which include picomotors 49 that can adjust the supports 47, to effect movement of the shaft 43.
  • the device 41 also includes an air bearing 51 to which the shaft 43 is coupled.
  • the air bearing is such that it ensures that eccentricities in the fibre 11 are kept to a minimum whilst being rotated.
  • the air bearing 51 is supported with filtered compressed air at around 90psi from the compressor 31.
  • the movement provided by the device 21 allows the chuck 35 to be moved, and in turn, the optical fibre 11 to be moved.
  • the movement provided by the adjustable device 41 is such that it essentially allows a rotational axis of the optical fibre 11 and a rotational axis of the chuck 35 to coincide.
  • the system 1 also includes a control circuit (not illustrated) which is capable of detecting whether the rotational axis of the optical fibre 11 and the rotational axis of the chuck 35 coincide.
  • the control circuit includes a camera (which could be camera 3a) which captures an image of the end of the optical fibre 11 whilst it is being rotated by the apparatus and includes a sensor which is used to detect the rotational axis of the chuck 35.
  • the control circuit also includes an image processor which is connected to the camera so that a captured image of the end of the optical fibre 11 rotating can be transferred from the camera to the image processor.
  • the image processor is in the form of hardware/software which analzises the images of the rotating fibre 11 in order to determine whether there is an angular and/or positional error in the edge of the optical fibre 11. Essentially, an angular difference will exist if there is an angular difference between the rotational axis of the fibre 11 and the rotational axis of the chuck 35, as shown in figure 7. It can be seen from figure 7 that there exists an angular difference between the two axis because the axis of the fibre 11 is inclined relative to the axis of the chuck 35. A positional error will be considered to exist if the two axis are apart from each other.
  • An angular and/or positional error indicates that the rotational axis of the optical fibre 11 and the rotational axis of the chuck 35 do not coincide.
  • the control circuit uses the angular and/or positional error to generate an electrical control signal which is proportional to the angular and/or positional error.
  • the electrical control signal is fed to the picomotors 49 of the adjustable supports 47 of the device 41, which effects adjustment of the supports 47 such that the rotational axis thereof and the rotational axis of the device 41 coincide.
  • Step edge detection is an important subject in image processing erators are in general of small size. Because the noise in and computer vision and many methods, including some optimal images is generally random, it is difficult to efficiently filters, have been proposed. In. this paper, we propose an optimal remove it from the image data merely in a small window. linear operator of an infinite window size for step edge detection. This operator is at first derived from the well-known mono-step On the contrary, the attributes extracted from a great edge model by use of a signal/noise ratio adapted to edge detecnumber of pixels would be less sensitive to noise, which tion.
  • the Gaussian disThe performance of ISEF is analyzed and compared with that of tribution is a nonzero function from ⁇ to + ⁇ , but in Gaussian and Canny filters, and it is shown that ISEF has a better practice, when one processes an image by Gaussian filperformance in precision of edge localization, insensibility to ters, the Gaussian function is considered to be nonzero noise, and computational complexity.
  • Edge detection based on the optimal filter ISEF is thus presented and the essential difference only in a finite interval [-w/2, +w/2]; i.e., a mask of a between ISEF and some other optimal edge detectors is shown. finite size is used.
  • Edge detection has been an important subject in image distributions in the derivatives at the boundaries of the processing because the edges correspond in general to finite window, which is equivalent to an introduction of important changes in physical or geometrical properties noise in the low-pass and derivative images.
  • the derivatives express well the of filters of infinite window size, the cutoff effect problem changes in the gray value function; edges can therefore can be avoided.
  • ' be detected by the maxima of the gradient or the zero
  • the essential problem for a Gaussian filter is the concrossings of the second derivatives including the Laplac- tradiction between the noise-suppressing effect and the ia ⁇ , calculated by some differential operators. . edge localization precision. As is well known, the larger
  • the optimal kernel we use a filter that is of an infinite size for efficiently reducing develop in the present paper is deduced from mono- and he noise on the one hand and is sharper at the center muitiedge models by use of the criteria determined from than the Gaussian filters for improving the precision for the point of view of signal processing rather than as an edge localization on the other hand.
  • FIG. 1 An edge detector considered as a smoothing filter followed by a differential block.
  • f ⁇ x be the low-pass smoothing filter kernel for removing the noise that we want to find that gives the where ⁇ (x) is the Dirac distribution, we have best results for step edge detection,
  • Nix is the white noise independent of Six) with Another part that corresponds to the noise in the first derivative of the filter output is idldx) ⁇ Nix) *f(x) ⁇ , whose
  • E tf E ⁇ [idldx)Nix) *fix)f ⁇ where E ⁇ - ⁇ indicates the expectation.
  • the energy of the noise in S 0 M can be measured by mum of the first derivative or the zero crossing of the EN, with
  • filters /(x) and C -fix where C is a or the zero crossing of the second derivative, the preciconstant, have essentially the same performance in resion of edge localization can be analyzed from the sign moving the noise, We would like to always take a normalchange and the slope of the second derivative of the filized filter kernel with the amplitude gain 1, i.e., tered image.
  • fix ip/2) ⁇ expi-p ⁇
  • the optimal low-pass linear filter as a preparation id/dx)fix (2.19) for edge detection for removing the noise is a symmetric -a ⁇ In b ⁇ b ⁇ x for x ⁇ 0, exponential filter of an infinite window size, briefly called the infinite size symmetric exponential filter.
  • edges which gives, from Eqs. (2.4) and (2.18) can be detected from the differentiation of the output of this filter, such as by maxima of the first derivative or A • a ⁇ In b ⁇ V- for x > 0, zero crossings of the second derivative or Laplacian.
  • id 2 ldx 2 ) ⁇ Six) *fix) ⁇ -A - a - h b - b-' for x ⁇ 0,
  • SM(x) equal to -A 2 , so we have the autocorrelation of the muitakes values -A or A with A > 0, and a jump of SM(x) tiedge sequence SM(x) as follows, from -A to A (respectively from A to -A) co ⁇ esponds to step edge.
  • (x) is constant:
  • FIG. 5 Muitiedge model.
  • the optimal linear smoothing filter is still a symmetric exponential filter of an infinite and window size, i.e., the same as that found based on the mono-step edge model.
  • ⁇ is the density of (4.3) edge points, i.e., the average number of edge points in an interval of unit length.
  • the optimal filter and Eq. i4.4) can be rewritten as will become planar to effectively remove the noise.
  • the optimal low-pass smoothing filter for removing the noise as a preparation for edge 2 ⁇ a ⁇ exp(-2 ⁇ x) 2 • a ⁇ b x for x ⁇ 0, detection is a symmetric exponential filter of an infinite fiix) window size. Edges can therefore be detected by use of 0, for x ⁇ 0; the first or second derivatives of the smoothed image. (4.7)
  • the scheme in Fig. 1 is convenient for the analysis of the optimal filter for edge detection, but for practical realizaand tion, it is not necessary to realize the low-pass filtering and the differentiating block separately.
  • D U) Yu ⁇ + 1) + Yuii - 1) - XH) - XO), (5.15) to bidimensional cases is to take (D(x, y)).
  • Dix, y) is a distance measure defined for (x, y) such that £>(x, y) nential filters.
  • the filter / e (x, y) is circularly symmetric for Euclidean /X/, ( 0 *J5C/ ) distance, as is desirable in most cases.
  • the filter fi, j) and its derivatives can therefore be to deduce the bidimensional symmetric exponential fildecomposed into the cascade of the one-dimensional ters of which a fast realization is possible.
  • symmetric exponential filters respectively in the dimensions i and; ' ; each can be realized in turn by the combina ⁇
  • UX) [a m ⁇ exp(-/? •
  • FIG. 6 Isovalue surface of a t dime ⁇ sional ISEF. in which * • • ⁇ * e w , because the first which can be easily realized by the cascade of ID expopartial derivative idldx j )f m ixj) in the dimension X j and the nential filters. low-pass exponential filters in the other dimensions can Edges can be detected by the zero crossings of the be realized by the cascade of o ⁇ e-dtme ⁇ sio ⁇ al filters.
  • the partial Laplacian The advantage of the use of partial multidimensional derivative filter is thus realized by the Laplacian is that we can detect and obtain closed edge cascade of them.
  • Laplacian and Partial Laplacian Laplacian image to suppress the noise but does not blur the edges in of an M-dimensional image I(X) filtered by an M-dimen- the subspace in which we are interested, if the complesional exponential filter / m (X) is defined by ment and the subspace are orthogonal to each other, as is the case in many practical images.
  • step edges can be detected by the zero crossings of the second derivatives.
  • Fig. 7 the two
  • the first derivative is negative, which correbetween the output and input of multidimensional filters sponds to a negative zero crossing (i.e., when x is increased to pass through the zero crossing, the second derivative changes its sign from negative to positive).
  • W be a window centered at the pixel P which is a Mix, y) ⁇ Nix, y) zero crossing of the band-limited Laplacian.
  • a linear gradient estimator Mix, y) gives the estimated £ ⁇ [ ) - gr(P)] 2 ⁇ gradient * gr( ) for the pixel P by ix. ⁇ ytex, , y)
  • FIG. 10 Experimental results of ISEF filter for ID noisy edge signals.
  • the optimal gradient estimate is the different regions separately by use of BLI.
  • the ence between the averages of gray values of the regions adaptive gradient gives a stronger response to edge R[ and R , which is evidently not shift-invariant.
  • the estimate error because of the small the less important the estimate error.
  • window size used for adaptive gradient calculation it applications, to make the calculation simple, we take may be more sensitive to noise than the first derivatives window size 5 x 5 or 7 x 7 and experiments show that calculated by ISEF, especially for very noisy images. Of the result is satisfactory.
  • window W contains course, the adaptive gradient can be improved by use of a in general only two regions separated by the zero crosslarger window, but in this case this will imply a greater ings (Fig. 9). These two regions will correspond respeccomputational complexity. tively to zones of values 1 and 0 in W of the binary band- limited Laplacian image (BLI), because the ISEF method 8. EXPERIMENTAL RESULTS detects zero crossings with a good precision [17]. So the optimal gradient estimate can be calculated by the differOur optimal edge detection filter is deduced from one- ence between the gray value averages in the original imand muitiedge models.
  • the adaptive gradient can be mented by the recursive algorithms presented and tested used only when the possible edge distribution in window for different types of images, including computer-generW is known. This is why we propose using it for gradient ated and real ones.
  • the experimental results are very thresholding after the detection of zero crossings. And it satisfactory.
  • ID noisy is the use of the knowledge of zero crossings obtained edge signals are given.
  • the adaptive grain the artificial image we know exactly where we do and his operator separately smoothes the regions of differdo not have the edges with this kind of image, it is conent gray values to remove the noise but at the same time venient and confirmatory to examine and compare the no blurring effect is produced because it processes differperformance of different techniques, such as the sensibil-
  • FIG. 11 Experimental results for a computer-generated noisy image, (a) Original image; (b) edges detected by ISEF filter; (c) best result for edges detected by DOG; (d) best result for edges detected by Canny-Gaussian filter; (e) best result for edges detected by simplified version of Canny by Deriche.
  • Laplacian exhibits the advantage of exedge model, based on a combined signal/noise ratio critetremely little computational complexity and gives closed rion adapted to edge detection, i.e., maximizing the reedge supersurfaces even in high-dimensional cases.
  • edge detection i.e., maximizing the reedge supersurfaces even in high-dimensional cases.
  • We sponse to the step edge and minimizing those to the noise introduced also the partial Laplacian for high-dimenand to the derivative of the noise.
  • an sional cases which shows the advantages of obtaining optimal low-pass filter as a preparation for edge detection closed edge surfaces in some subspaces of interest, and is the infinite symmetric exponential filter.
  • the perforthe smoothing of the complement of the subspace sup- mance of this optimal filter is analyzed and compared presses the noise without blurring the subspace edges.
  • FIG. 12 Edges detected by ISEF methods Top (a) original mage, (b) edges detected by ISEF (gradient threshold 5) Bottom (a) o ⁇ gi ⁇ al image, (b) edges detected by the DRF method (gradient thresholds 5 and 8), (c) edges detected by Laplacian of Gaussian filter (gradient thresholds 5 and 8)
  • edges can therefore be ISEF filters, which confirms the theoretical analysis of detected by the zero crossings of the second derivatives optimization and performance. or Laplacian, or by the maxima of the gradient, always It may be interesting to explain qualitatively the optifiltered by the ISEF filter.
  • the differentiation at a is presented to remove some false zero crossings.
  • the pixel should concern only its very close neighbors; the edge candidates thus detected are then verified by gradicloser a pixel to the pixel of interest the more important ent thresholding with or without hysteresis.
  • This gradient the role that it should play in differential operation. Becan be calculated from the ISEF filter or from the adapcause of. the existence of noise, an additional smoothing tive gradient if non-shift invariant operators are considwill be necessary, but we should always keep in mind the ered.
  • the adaptive gradient can be used only principle that closer pixels should play a more important after the BLI is obtained.
  • the advantage of the adaptive role in the differentiation operation Obviously, in examgradient is that it is more sensitive to weak edges because ining the first derivative of the symmetric exponential regions of different gray values are smoothed separately. filters, we see that this principle is always respected no
  • the optimal linear operator for edge detection promatter how great the smoothing factor b for removing the posed is implemented and tested for computer-generated noise (Fig. 3). So even when one adjusts the smoothing and real images and compared with some other optimal factor b to adapt it to different noisy images, this propoperators such as the Gaussian filter, Canny's filter, and erty is preserved and always gives a Dirac distribution in its simplified version by Deriche.
  • the experimental the second derivative of the filter kernel at the center of results show a significantly better performance by the the kernel, which assures that on the one hand the more
  • Edge localization error x c [17] the center, such as the box difference filters (average difference filters) [28]. But because first the form of this

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Abstract

L'invention concerne un système d'usinage d'un objet, qui comprend un moyen permettant d'obtenir un profil souhaité de l'objet et des informations relatives à une arête d'un outil de façonnage, un processeur destiné à traiter le profil souhaité de cet objet et les informations relatives à ladite arête, afin de déterminer un trajet pour l'objet et/ou l'arête à déplacer le long de ce dernier.
PCT/AU2003/000232 2002-02-25 2003-02-25 Systeme et procede d'usinage d'un objet WO2003071367A1 (fr)

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AU2003205429A AU2003205429A1 (en) 2002-02-25 2003-02-25 A system and method for machining an object

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AUPS0710A AUPS071002A0 (en) 2002-02-25 2002-02-25 Micro-machining

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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4710605A (en) * 1985-04-08 1987-12-01 American Telephone And Telegraph Company, At&T Bell Laboratories Laser nibbling of optical waveguides
US4932989A (en) * 1989-04-05 1990-06-12 At&T Bell Laboratories Method and apparatus for fabricating microlenses on optical fibers
US5011254A (en) * 1989-11-30 1991-04-30 At&T Bell Laboratories Coupling of optical devices to optical fibers by means of microlenses
WO1997034744A2 (fr) * 1996-03-21 1997-09-25 Newnes Machine Ltd. Systeme integre de sciage selon des traces courbes commande par integration des mouvements sur la base des positions
JPH10138100A (ja) * 1996-11-11 1998-05-26 Mori Seiki Co Ltd Ｎｃ工作機械における工具位置測定方法及びその方法のプログラムを記録した媒体
WO2000013848A1 (fr) * 1998-09-03 2000-03-16 Anca Pty. Ltd. Taille d'outils coupants a aretes ondulees

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4710605A (en) * 1985-04-08 1987-12-01 American Telephone And Telegraph Company, At&T Bell Laboratories Laser nibbling of optical waveguides
US4932989A (en) * 1989-04-05 1990-06-12 At&T Bell Laboratories Method and apparatus for fabricating microlenses on optical fibers
US5011254A (en) * 1989-11-30 1991-04-30 At&T Bell Laboratories Coupling of optical devices to optical fibers by means of microlenses
WO1997034744A2 (fr) * 1996-03-21 1997-09-25 Newnes Machine Ltd. Systeme integre de sciage selon des traces courbes commande par integration des mouvements sur la base des positions
JPH10138100A (ja) * 1996-11-11 1998-05-26 Mori Seiki Co Ltd Ｎｃ工作機械における工具位置測定方法及びその方法のプログラムを記録した媒体
WO2000013848A1 (fr) * 1998-09-03 2000-03-16 Anca Pty. Ltd. Taille d'outils coupants a aretes ondulees

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
DATABASE WPI Derwent World Patents Index; Class X25, AN 1998-356053 *

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