CN100354878C - Method of abstracting data from curve function recorded on cooraination peper - Google Patents
Method of abstracting data from curve function recorded on cooraination peper Download PDFInfo
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- CN100354878C CN100354878C CNB2005100227529A CN200510022752A CN100354878C CN 100354878 C CN100354878 C CN 100354878C CN B2005100227529 A CNB2005100227529 A CN B2005100227529A CN 200510022752 A CN200510022752 A CN 200510022752A CN 100354878 C CN100354878 C CN 100354878C
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Abstract
The present invention relates to a method of abstracting data from a curve function recorded on coordinate paper in image processing technology. The coordinate paper of the present invention is coordinate paper which is used on a roller type electric automatic recorder. The method of the present invention is that firstly the coordinate paper for recording a curve is scanned and processed, the chart data of the curve is obtained, a binaryzation process is used to eliminate the figure of a background chart according to the background of the chart data and the figure of a target image, then the curve is processed in a median smooth mode, the start position of a bottom edge of a chart data which is obtained is used as a benchmark to predetermine step length as the length unit of a sample, each section of ordinate value Y on the curve is read step by step, and simultaneously each length position X and a function value Y which is corresponding to the length position are stored in a database.
Description
Technical field
The present invention relates in the image processing techniques, from being recorded in the method for the curvilinear function extraction data on the coordinate paper.Coordinate paper of the present invention is meant the coordinate paper that is used on the electronic self recording instrument of drum-type.
Background technology
Along with the development of computing machine, many traditional paper inking charts all remain to realize digitizing storage data by the process of scanning and image recognition.So not only can increase work efficiency, and can get rid of the error that human factor causes, improve the accuracy that parameter is selected greatly, promote the digital development process of traditional record diagram file, help analysis and research work.But the unique point of paper inking chart is not a standard very, and has been subjected to The noise, makes identification work be subjected to a lot of interference.Theoretic traditional broken line chart normally continuous, the very clear and definite curve of break clearly, but actual chart because hardware record or hand-kept, curve is not a typical curve, it is difficult to face following identification:
(1) image curve is not continuous, and frequent breakpoint, overlapping point, litura, stain and jitter points are arranged, and curve has frequent shake, and the accurate identification of curve is had very big requirement;
(2) because the self recording instrument hardware reason, some architectural features of image are not clearly, and break is a fuzzy transition type camber line, and the standard of recognition data neither standard value, but with near fluctuation up and down standard value, extraction has produced difficulty to data;
In addition, because the live width of the aim curve of image is the width of self recording instrument nib, with respect to the stain noise on the image, the image live width is very little, so must correctly judge aim curve and effectively revise noise.
Present contour extraction method has a lot, comprises method, reptile method and curve-fitting method of Houph or Soble conversion or the like, but adopts traditional contour extraction method to have following shortcoming:
(1) method of employing Hough or Soble conversion:
Handle for the coordinate paper that image is bigger, carry out Hough or Soble conversion to entire image, bigger to the requirement of internal memory, the processing time is also long.In addition, also to remove the operation of making an uproar in the past carrying out Hough or Soble conversion to image.But adopt filtering mode or a lot of useful image informations of meeting filtering, perhaps can not play the effect of filtering.
(2) adopt the reptile method:
There are the following problems for this method: because there is breakpoint in image, after the week of then may circulating, has only found parts of images, and missed most data; To need constantly to produce new starting point in order addressing these problems, to repeat the extraction of profile.Can cause the waste of most of the time.
In addition, adopt Hough or Soble conversion and employing reptile method aircraft pursuit course profile all will carry out refinement to the image information of extracting.But the process of refinement also can filter out effective picture element, produces unnecessary breakpoint.
(3) method of employing curve fitting:
Because for some similar corrugated curves, adopt curve fitting can smoothly fall the right angle flex point of each saltus step later on, view data is changed, and the key point of extracting for similar corrugated graph data is exactly the coordinate position of these right angle flex points, therefore can not adopt the method for curve fitting to handle.
Summary of the invention
The invention provides and a kind ofly be applicable to that processing is recorded on the coordinate paper by self recording instrument, and image is bigger, the figure of figure undulate is to extract the method for related data on the curve.
The method of invention is: at first the coordinate paper to recording curve carries out scan process, obtain the chart data of curve, it is characterized in that: according to the background of chart data and the profile of target image, utilize the binaryzation process to remove the profile of background chart, again curve being carried out median smoothing handles, base reference position with the gained chart data is a benchmark then, with predetermined sample length unit is step-length, read the ordinate value Y of each section on the curve piecemeal, deposit in the database with each extension position X with the corresponding functional value Y of this extension position simultaneously.
Median smoothing of the present invention is handled the median smoothing that preferably adopts five point data and is handled.
The present invention is on reading curve during each point function, earlier according to second function and relatively more definite its monotonicity interval of first point function on the curve, in monotony interval, preferentially on dull direction, look for curvilinear function, as can not find again and look for curvilinear function in the opposite direction of dull direction.Adopt this practice can accelerate the speed of graphics process, also can reduce errors simultaneously.
For the coordinate paper of the electronic self recording instrument of some drum-type, so data of record are images through geometric distortion on it, and the present invention is to be benchmark with its base length when extracting data, can cause result's distortion as blindness calculating.For avoiding this situation, the distortion that figure is removed in each the The data posteriority correction method of reply gained.For example adopt following coordinate conversion equation to carry out curvature correction:
x1：＝x
y1：＝y-(L-sqrt(L
*L-sqr((y-L)
*sin?θ))
In the formula: L is the chord length of circular arc, and θ is the angle of circular arc.
The function extraction data of the comparatively special record coordinate paper upper curve of certain state on the baseline of method only put down in writing to(for) curve map can adopt following method: at first the coordinate paper to recording curve carries out scan process, obtain the chart data of curve, again according to the background of chart data and the profile of target image, utilize the binaryzation process to remove the profile of background chart, roughly determine the position of baseline again according to curve, determine baseline with least square method again, base reference position with the gained chart data is a benchmark then, with predetermined sample length unit is step-length, read the ordinate of each section on the curve piecemeal and be positioned at baseline state up and down, simultaneously with each extension position X and with the corresponding curve of this extension position on the ordinate of each section be arranged in baseline function of state up and down and deposit database in, wherein be positioned at dotted state function that curve is positioned at baseline top for just, be positioned at dotted state function that curve is positioned at baseline below for negative, the dotted state function that is on the curve baseline is zero.
The data that will obtain by the above method, extension position with recording chart is a benchmark, each function with same extension position deposits database respectively in respectively, and foundation retrieval relation, when determining a concrete extension position, can read out in each function numerical value and function of state on this extension position place virgin curve.
For some more special data and curves, can be with the data that obtain by the above method, extension position with recording chart is a benchmark, elder generation is with the combinations of states of non-zero in each function of state, form the combinations of states function, deposit each function of same extension position in database respectively respectively again, and set up the retrieval relation, when determining a concrete extension position, can read out in each function numerical value and combinations of states function on this extension position place virgin curve.
The present invention can overcome the deficiencies in the prior art, can realize being recorded in curvilinear function on the coordinate paper of the electronic self recording instrument of drum-type and become numerical value and deposit in the database, is convenient to carry out the processing again of data, and research work.And use method of the present invention can extract the feature of curve, and reduce even overcome distortion fully, reflect the original appearance of curve truly.
Description of drawings
Fig. 1 is the self-recording paper wind speed inking chart of standard.Fig. 2 is actual wind speed inking chart intercepting segment.Fig. 3 is another actual wind speed inking chart intercepting segment.Fig. 4 is the wind speed inking chart intercepting segment of the 3rd reality.The schematic flow sheet of the meteorological wind speed and direction self-recording of Fig. 5 paper data extract data.Fig. 6 be image space geometry distortion with and the process synoptic diagram proofreaied and correct.Fig. 7 extracts wind speed curve unique point procedure chart for the present invention.Fig. 8 is for removing noise, the effect comparison after the smoothing processing in several prior aries and the method for the present invention.Fig. 9 is the data drawing list cut-away view by the recording wind vane record.Figure 10 is the wind direction inking chart intercepting segment after rough handling of the present invention.Figure 11 is the searching algorithm block diagram of wind direction curve sampled point.The one day wind speed curve cut-away view of Figure 12 after handling with the present invention.Figure 13 is after handling with the present invention, and with the wind direction curve cut-away view of same section of Figure 12.
Embodiment
One embodiment of the present of invention are wind speed, wind direction curves of handling with wind direction and wind velocity self recording instrument record gained, extract wind speed, the wind direction data of corresponding time on the curve.
Fig. 1 is the segment of the self-recording paper wind speed inking chart of a standard.Fig. 2 to Fig. 4 then is the chart of physical record.What anemorumbograph institute horizontal ordinate write down is each sampling moment, and its ordinate record is the distance of wind operation.Design according to anemograph, its recording pointer only is to produce a saltus step the fixing distance back of wind operation one (be actually vane in weathervane rotated default revolution after), and the difference in height of this saltus step is wind and moves a predetermined distance (200m).Therefore, according to determining in Fig. 2 to Fig. 4 curve that wind speed is to be calculated as follows to obtain:
Distance (this distance the is default fixing) time of ÷ two adjacent samples between the moment of wind speed=two adjacent samples wind operation between the moment.
By above calculating as can be known, resulting here wind speed is actually the average velocity of wind in the sampling constantly.What need extract when anemobiagraph is carried out data processing is the mean wind speed of each time.
Fig. 9 is the segment of wind direction recording curve chart intercepting.The wind direction curve one that is write down as can be seen from Figure 9 has four wind direction baselines, be respectively applied for and judge south/north, northeast/southwest, east/west, the southeast/northwest, the wind direction baseline is meant the line of reference of judging wind direction, concrete wind direction constantly is a side that is recorded in baseline, that is to say, this function is the record that certain state is arranged in the both sides of four reference direction axles that provide, for example judge the baseline of north and south wind, if wind direction trace sometime is positioned at the top of this north and south wind direction baseline, just representative is a south wind, be positioned at the below of this north and south wind direction baseline, just representative is a north wind.Real wind direction of a certain moment is to characterize the combination of wind direction on above four baselines and the combinations of states function that forms, south wind trace and southeaster trace for example at a time appear simultaneously, then wind direction is a south-southeast this moment, and this is a concrete combinations of states function.Record by existing self recording instrument can be combined into 16 wind directions at most.Simultaneously also as can be seen, how correctly determining baseline, is to extract the problem that at first will solve in the wind direction data.
Be also shown in from above-mentioned these figure, the image curve of the chart of this class is not totally continuous.Frequent breakpoint, overlapping point, litura, stain and jitter points are arranged in the chart of its physical record, and curve there is frequent shake.In addition, because the self recording instrument hardware reason, some architectural features of image are not clearly, as, its break is a fuzzy transition type camber line on the wind speed curve, the also non-standard value of the standard of its recognition data, but with near fluctuation up and down standard value; And be also shown in by anemobiagraph, the used coordinate record paper coordinate of this figure is a camber line shape, these all should be noted that in carrying out data extract.
By analysis to the wind speed diagram curve, can find that the broken line bar chart image fixes in certain monotonicity in interval, the data that we were concerned about simultaneously are not the edge contours of curve, the more important thing is the position coordinates of the key point of curve, as long as therefore follow the tracks of out the position of the key point of broken line chart, just can accurately extract the data of curve.
The present invention is being undertaken by Fig. 5 institute program in handling wind speed, wind direction curve image, and its concrete practice is:
(1) removes background
After image is scanned, according to the difference of the gray-scale value of background in the self-recording coordinate file and target image, at first utilize the binaryzation process, remove the Background table skeleton, cut out the profile of reference value value image.For guarantee target image accuracy of identification, will not be removed with the background information of its adhesion.Because background image is just in order to provide a benchmark in artificial cognition, thereby its form fixes, and we can break away from background information and can not produce mistake when extracting data based on priori.
(2) dullness according to wind speed curve increases and decreases trend tracking image information
Extract requirement according to self-recording paper wind speed partial data, as long as find the key point of curve saltus step, can be the contour thinning of image curve just, and this curve is undaform, the monotonicity in each from the crest to the trough or from the trough to the crest section interval be all fixed.Utilize this feature,, determine the monotonicity interval according to monotonicity, in monotony interval, preferentially on dull direction, look for effective feature picture element, but because self recording instrument hardware, not every point is all followed this monotonicity in the process of record, thereby in the other direction to search speed also be necessary.This process is referring to Fig. 7.
(3) smoothing processing of curve
Because the quality problems of image itself, the curve of tracking has the hop of a lot of mistakes.In order to remove these wrong hops, guarantee the order of a curve parts of images global feature that jumps again, according to the principle of medium filtering, we have adopted the median smoothing of five point data to handle.The value of any in the principle of medium filtering right the digital picture or in the Serial No. is replaced with the Mesophyticum of each point value in the neighborhood of this point.
Intermediate value is defined as follows:
One group of number x
1, x
2, x
3..., x
n, the n number is arranged following x according to the size order of numerical value
I1≤ x
I2≤ x
I3≤ ... ≤ x
In
Y is exactly sequence x
1, x
2, x
3..., x
nIntermediate value.
In the smoothing processing process in native system, mainly be the target of handling as intermediate value at the coordinate of x axle.
Because what electronic anemorumbograph adopted is the drum-type record, so the data of record are the images through geometric distortion.Because the specification of self recording instrument is fixed, its coordinate is the circular arc of one section fixed angle, therefore can adopt the posteriority correction method.The restoration model of geometric distortion can be determined by calculating.
If f (x y) is undistorted original image, g (x1, y1) be f (x, y) Ji Bian result, then:
g(x1，y1)＝f(x，y)
Arbitrarily geometric distortion can by non-distorted coordinates system (x, y) transform to distorted coordinates system (x1, equation y1) defines, the process of this distortion be always and with function h1 (x, y), h2 (x y) defines, so have:
x1＝h1(x，y)
y1＝h2(x，y)
So the problem of this distortion has just changed into the problem of mapping transformation.
Observe through calculating, the coordinate transformation equation that draws is:
x1：＝x
y1：＝y-(L-sqrt(L
*L-sqr((y-L)
*sinθ))
Wherein, L is the chord length of circular arc, and θ is the angle of circular arc.This process can be referring to Fig. 6.
In the process that air speed data extracts, exist because physical cause does not have the scarce survey data on the record, the white space of bulk has appearred on curve, for speed and the precision that improves computing, need manually in image, to find the data field that lacks survey in case of necessity.In lack surveying the selection course of data field, what at first determine to select is an interval, promptly if only selected interval starting point or end point, then do not think to lack survey interval; If lack to survey interval selection less than ten minutes data interval also think be not to lack survey interval.
For some the glutinousness noises on the wind direction curve, mainly be some manual pencil markings, be in the past the manual extraction data time monotonicity that add and curve be reciprocal, thereby, follow the tracks of in the engineering also by filtering at above curve.For the glutinousness ink marks of some fritters, be to handle in tracing process with invalid unique point, thereby also by filtering.The glutinousness ink marks of those bulks, owing in the process of artificial cognition, also can't discern, thereby need through human intervention, be used as to lack and survey data processing.
Through above processing gained curve, its result is better than the result of prior art.This point can be referring to Fig. 8.
To extracting data by the wind speed curve of above processing gained.Promptly press the base length of coordinate self-recording millimeter paper, read the ordinate value Y of each section on the curve piecemeal by the step-length of prior setting, simultaneously with each extension position X
iWith with the corresponding mean wind speed functional value of this extension position f (Y)=(Y
i-Y
I-1) ÷ (X
i-X
I-1) deposit in the database one by one.Set up the retrieval relation simultaneously, can inquire about each mean wind speed value constantly very easily.
Result is seen accompanying drawing 12.Curve is the wind speed curve to be extracted on the self-recording paper among the figure, and the wind speed curve that has extracted is to be stacked on the wind speed curve to be extracted, because of accompanying drawing 13 is an artwork master, and the not high reason of resolution, be not easy to find out.Elapsed time is corrected and finds out ten minutes wind speed curve sections of integral point, goes out per ten minutes air speed value according to data extract between the sintering of line segment, and deposits database in.Among the figure in the square frame mark be the 17:00 that extracts to interior air speed value of 17:10 time period.As seen from the figure, at 17:00 constantly, its mean wind speed is 2.0 meter per seconds; In the 17:10 moment, its mean wind speed is 1.7 meter per seconds.
The present invention at first carries out scan process to the coordinate paper of recording curve, obtain the chart data of curve, again according to the background of chart data and the profile of target image, utilize the binaryzation process to remove the profile of background chart, these processes are identical with aforementioned way.Figure after above processing is referring to Figure 10.Its handling procedure is referring to Figure 11.
Chart through above processing is carried out choosing of baseline sampling point, and its concrete practice is:
At first determine the baseline on the chart.
(1) owing to the position relative fixed of wind direction baseline,, can try to achieve by following proportionate relationship so can determine the general location of four wind direction baselines earlier:
lineposition[3]：＝round(w*0.47)；
lineposition[2]：＝round(w*0.62)；
lineposition[1]：＝round(w*0.77)；
lineposition[0]：＝round(w*0.91)；
More than various in the width of w representative image, lineposition[x] represent the coordinate of four wind direction baseline X-directions.
(2) can be according to the general location of above four wind direction baselines at this position two-sided search sampled point, 20 points of system's uniform sampling.The searching algorithm block diagram 11 of each sampled point.
By the sampled point that above step obtains, use the least square fitting curvilinear equation of curve fitting, its method and process are as follows:
In the best-fitting of the curve problem, commonly used another kind of yardstick and disposal route thereof are: after setting the function of a certain type, (the parameter a in the example as described above, b c), make deviation at the each point place to determine parameter among the function y=f (x)
r
i＝f(x
i)-y
i (f＝1，2，…，n)
Quadratic sum
Minimum. this condition according to the sum of square of deviations minimum determines that the method for parameter is called least square method. many experimental formulas of utilizing least square method to set up are arranged in engineering and the scientific experiment.
Now use p order polynomial curve y=f (x)=a
px
p+ a
P-1x
P-1+ ... + a
1X+a
0, utilize least square method to carry out match, the minimum problems of the question resolves itself into p+1 meta-function:
Utilize the multivariate function to ask the method for extreme value can be in the hope of one group of unique coefficient a=[a
p, a
P-1..., a
n]
T
Because four wind direction baselines are straight lines,, determine straight slope and intercept according to above method so in native system, only need select polynomial curve for use one time.
According to the wind direction length equation of determining, can search the starting and ending point of image at wind direction baseline two ends.Because coordinate paper that recording wind vane write down is a function of state, therefore the data of extracting can be positioned at the top of baseline or overlap with baseline by image, perhaps are positioned at these three kinds of situations of below of baseline, just are being designated as respectively, zero-sum bears.Make up being not equal to zero function in these function of states of gained again, obtain the combinations of states function, deposit each function of same extension position in database respectively respectively again, and foundation retrieval relation, when determining a concrete extension position, can read out in each function numerical value and combinations of states function on this extension position place virgin curve.
Result is seen accompanying drawing 13.Mark is ten minutes wind direction curves and deal with data in the square frame frame, among Figure 13, vertical square frame the inside respectively mark be four baselines that extract, from left to right each baseline be used for respectively judging northwest/southeast, west/east, southwest/northeast, north/south to.In the oval frame is the wind direction curve of per two minute to be processed half a minute.According to the position of two fen half a minute wind direction curve, extract the wind direction data (broken line partly is the wind direction curve of match) of per two minutes halfs respectively with respect to four baselines.Combination by analysis, per two and half of the interior extraction of horizontal square frame wind direction value is respectively among the figure: ENE (east-northeast), E (east), ESE (east-southeast), ESE (east-southeast), ESE (east-southeast), requirement according to the meteorological observation standard, choose maximum wind directions and represent ten minutes wind directions in these 5 two and half wind directions, wherein ESE is maximum, is 3.So draw ten minutes wind direction values be: ESE (east-southeast), and it is scaled the center angle value and inserts in the database.
Can draw by Figure 12 and Figure 13, in 17: 10 timesharing of one day, its wind speed is 1.7 meter per seconds, and wind direction at that time is an east-southeast.The wind speed and direction function in each moment of pointwise record like this, and with in its input database, set up the relation back of retrieval and just can check in recording period interior each moment corresponding air speed, wind direction value very easily.
Claims (8)
1, a kind of from being recorded in the method for the curvilinear function extraction data on the coordinate paper, at first the coordinate paper to recording curve carries out scan process, obtain the chart data of curve, it is characterized in that: according to the background of chart data and the profile of target image, utilize the binaryzation process to remove the profile of background chart, again curve being carried out median smoothing handles, base reference position with the gained chart data is a benchmark then, base length along coordinate self-recording millimeter paper, by predetermined sample length unit is step-length, read the ordinate value Y of each section on the curve piecemeal, deposit in the database with each extension position X with the corresponding functional value Y of this extension position simultaneously.
2, according to claim 1 from being recorded in the method for the curvilinear function extraction data on the coordinate paper, it is characterized in that adopting the median smoothing of five point data to handle.
3, according to claim 2 from being recorded in the method for the curvilinear function extraction data on the coordinate paper, when it is characterized in that on reading curve each point function, earlier according to second function and relatively more definite its monotonicity interval of first point function on the curve, in monotony interval, preferentially on dull direction, look for curvilinear function, as can not find again and look for curvilinear function in the opposite direction of dull direction.
4, according to claim 3 from being recorded in the method for the curvilinear function extraction data on the coordinate paper, it is characterized in that the distortion that figure is removed in each The data posteriority correction method to gained.
5, according to claim 4 from being recorded in the method for the curvilinear function extraction data on the coordinate paper, it is characterized in that the coordinate conversion equation is:
x1：＝x
y1：＝y-(L-sqrt(L*L-sqr((y-L)*sinθ))
Wherein, L is the chord length of circular arc, and θ is the angle of circular arc.
6, a kind of from being recorded in the method for the curvilinear function extraction data on the coordinate paper, at first the coordinate paper to recording curve carries out scan process, obtain the chart data of curve, it is characterized in that: according to the background of chart data and the profile of target image, utilize the binaryzation process to remove the profile of background chart, determine the position of baseline again according to curve, determine baseline with least square method again, base reference position with the gained chart data is a benchmark then, with predetermined sample length unit is step-length, read the ordinate of each section on the curve piecemeal and be positioned at baseline state up and down, simultaneously with each extension position X and with the corresponding curve of this extension position on the ordinate of each section be arranged in baseline function of state up and down and deposit database in, wherein be positioned at dotted state function that curve is positioned at baseline top for just, be positioned at dotted state function that curve is positioned at baseline below for negative, the dotted state function that is on the curve baseline is zero.
7, described arbitrary according to claim 1 to 6 from being recorded in the method for the curvilinear function extraction data on the coordinate paper, it is characterized in that by extension position be benchmark, each function with same extension position deposits database respectively in respectively, and foundation retrieval relation, when determining a concrete extension position, can read out in each function numerical value and function of state on this extension position place virgin curve.
8, described arbitrary according to claim 1 to 6 from being recorded in the method for the curvilinear function extraction data on the coordinate paper, it is characterized in that by extension position be benchmark, elder generation is with the combinations of states of non-zero in each function of state, form the combinations of states function, deposit each function of same extension position in database respectively respectively again, and set up the retrieval relation, when determining a concrete extension position, can read out in each function numerical value and combinations of states function on this extension position place virgin curve.
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| WO2012113095A1 (en) * | 2011-02-22 | 2012-08-30 | Peng Hsin-Fung | Coordinate information conversion and display system |
| CN102650936B (en) * | 2011-02-23 | 2015-05-20 | 蓝盾信息安全技术股份有限公司 | Method and system for displaying history curves |
| CN102622722A (en) * | 2012-01-10 | 2012-08-01 | 中联重科股份有限公司 | Engine characteristic curve conversion method and device |
| CN105807319B (en) * | 2016-03-11 | 2018-11-09 | 中国海洋石油集团有限公司 | A kind of near-field wavelet bubble period pick-up method and system |
| CN109145857B (en) * | 2018-09-04 | 2024-02-09 | 深圳十沣科技有限公司 | Method for extracting curve data from curve graph |
| CN113359216A (en) * | 2021-06-03 | 2021-09-07 | 山东捷瑞数字科技股份有限公司 | Method, system and storage medium for identification of recorded data of tipping-bucket rain gauge |
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| CN1410941A (en) * | 2001-09-24 | 2003-04-16 | 国枝博昭 | Curve identifying system |
| US6694057B1 (en) * | 1999-01-27 | 2004-02-17 | Washington University | Method and apparatus for processing images with curves |
| CN1581232A (en) * | 2004-05-17 | 2005-02-16 | 上海交通大学 | Method for drawing main curve from complicated picture |
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|---|---|---|---|---|
| WO2000045326A1 (en) * | 1999-01-27 | 2000-08-03 | Washington University | Method and apparatus for processing images with curves |
| US6694057B1 (en) * | 1999-01-27 | 2004-02-17 | Washington University | Method and apparatus for processing images with curves |
| CN1410941A (en) * | 2001-09-24 | 2003-04-16 | 国枝博昭 | Curve identifying system |
| CN1581232A (en) * | 2004-05-17 | 2005-02-16 | 上海交通大学 | Method for drawing main curve from complicated picture |
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