CN102494976A - Method for automatic measurement and morphological classification statistic of ultra-fine grain steel grains - Google Patents

Method for automatic measurement and morphological classification statistic of ultra-fine grain steel grains Download PDF

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CN102494976A
CN102494976A CN201110368047XA CN201110368047A CN102494976A CN 102494976 A CN102494976 A CN 102494976A CN 201110368047X A CN201110368047X A CN 201110368047XA CN 201110368047 A CN201110368047 A CN 201110368047A CN 102494976 A CN102494976 A CN 102494976A
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李新城
朱伟兴
丁飞
赵从光
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Jiangsu University
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Abstract

The invention discloses a method for automatic measurement and morphological classification statistic of ultra-fine grain steel grains. The method provided by the invention comprises the following steps of 1, acquiring an image of an ultra-fine grain steel grain and carrying out pretreatment, 2, carrying out binary segmentation of the pre-treated image by a region division-based self-adaptive threshold segmentation method to obtain a binary image, 3, carrying out grain boundary repair of the binary image by a distance transformation-based modified watershed algorithm, and carrying out grain aperture filling by a modified seed filling algorithm to obtain a repaired image, 4, extracting grain morphology characteristic parameters, and 5, carrying out grading statistic of grain sizes according to diameters, and carrying out grain morphology classification according to roundness, form factors and length-width ratios. Through the method provided by the invention, image repair and accurate and efficient measurement, classification and statistic of an ultra-fine grain steel microstructure (grain) can be realized automatically.

Description

A kind of automatic measurement of ultra-fine grain crystalline grain of steel and typoiogical classification statistical method thereof
Technical field
The present invention relates to the quantitative metallographic analysis field of ferrous materials microstructure, be specifically related to a kind of automatic measurement and typoiogical classification statistical method thereof of ultra-fine grain crystalline grain of steel.
Background technology
Develop rapidly along with ferrous materials science and technology; The research and development of all kinds of steel have been based upon on the basis of composition, structure, tissue and performance quantitative relationship gradually, thereby meaning promptly can be controlled its phase structure and microstructure obtains required performance through preparation and various subsequent technique for steel.Quantitative metallographic analysis is studied the important method that concerns between metal material composition, tissue, technology and the performance just, through the quantitative test to various material metallographic structures, between the microstructure of material and macro property, makes up quantitative relationship.
Ultra-fine grain steel is fast-developing in recent years a kind of new type steel, and its principal feature is that its metallographic structure is the crystal grain of extreme refinement mostly, and its crystallite dimension is usually less than 4 microns, so show very high intensity, hardness, plasticity and toughness.For ultra-fine grain steel, the particle diameter of its crystal grain, form and distribution play decisive influence to the performance of steel.When carrying out quantitative metallographic analysis, in the ultra-fine grain steel metallographic structure a large amount of occur such as image deflects such as crystal boundary disappearance, intracrystalline holes, must carry out image repair, make the original grain boundary true reappearance; Otherwise,, cause the quantitative relationship of composition, structure, tissue and the performance of material to be difficult to accurate foundation with the quantitative metallographic analysis effect that has a strong impact on thereafter.In order to improve the performance of ultra-fine grain steel, need accurately measure, classify and add up the particle diameter of ultra-fine grain crystalline grain of steel, form etc.Therefore, measure how accurately, efficiently and the particle diameter of adding up crystal grain, form distribution, become the major issue that presses for solution in the ultra-fine grain steel microstructure analysis field.
In engineering practice; The main dependence of this work has deep metal material knowledge and the engineering technical personnel that enrich the quantitative metallographic analysis experience, and the mode of operation that adopts the conventional artificial restorative procedure to carry out metallic phase image repair and conventional mesh method manual measurement, calculating and statistics is carried out measurement, the classification of crystal grain.Certainly lead to because this analytical effect depends primarily on people's subjective factor various subjective errors, efficient low, measure the statistic of classification low and problem that takies human cost in a large number of precision as a result; Thereby the quantitative relationship that causes steel product ingredient, structure, tissue and performance is difficult to the accurately consequence of foundation, and this has become " bottleneck " problem that has a strong impact on new material R&D work process.
Summary of the invention
The automatic measurement and the typoiogical classification statistical method thereof that the purpose of this invention is to provide a kind of ultra-fine grain crystalline grain of steel, this method can realize automatically that metallographic structure (crystal grain) image to ultra-fine grain steel repairs and its morphological feature is carried out accurately, measures efficiently, classifies and added up.
Technical scheme of the present invention is: a kind of automatic measurement of ultra-fine grain crystalline grain of steel and typoiogical classification statistical method thereof, and its concrete steps are:
(1) gathers ultra-fine grain crystalline grain of steel image, and carry out pre-service;
(2) adopt adaptive threshold partitioning algorithm based on area dividing that pretreated image is carried out two-value and cut apart, obtain bianry image;
(3) said bianry image is repaired crystal boundary through the correction watershed algorithm based on range conversion, and fill the intracrystalline hole, obtain repairing image with improving seed fill algorithm;
(4) extract the grain form characteristic parameter, its concrete steps are:
(4-1) said reparation image being carried out scale sets and region labeling;
(4-2) extract the grain form characteristic parameter: area, girth, length breadth ratio, diameter, circularity and shape coefficient;
(5) being that criterion is carried out hierarchical statistics to crystallite dimension with said diameter, is that criterion is classified to grain form with said circularity, shape coefficient, length breadth ratio;
Further, the pretreated concrete steps of said step (1) are:
(1-1) utilize the histogram equalization algorithm that can keep image detail to strengthen entire image;
(1-2) utilize the rim detection method of differential operator to extract the edge, the some place that gray scale is suddenlyd change is regarded as corresponding frontier point, and then the point set on definite border;
(1-3) utilize the stretching algorithm to strengthen the contrast of image simultaneously.
Further, said step (2) is based on the adaptive threshold partitioning algorithm of area dividing, and 2500 of the subregion numerical digits of its area dividing adopt big Tianjin method algorithm.
Further, said step (3) the steps include: based on the correction watershed algorithm of range conversion
(3-1) carry out the Euclidean distance conversion, obtain each independent nucleus;
(3-2) successively enlarge each independent nucleus according to correction factor, two independent nucleus adhesions after revising then are regarded as an independent nucleus with it, unified numbering;
(3-3) nucleus after the said numbering is carried out expansion process, nucleus keeps increasing with layer position in the expansion process, is the watershed divide when two nucleus meet, and forms the separatrix of crystal grain this moment.
Further, said correction factor is 2.
Advantage of the present invention is:
1, adopts correction watershed segmentation algorithm and improvement seed fill algorithm can solve image deflects such as crystal boundary disappearance and intracrystalline hole respectively well, can obtain desirable image repair effect based on range conversion.
2, the measuring accuracy of crystal grain image can reach
Figure 257258DEST_PATH_IMAGE001
0.01 μ m, and accomplishes not have omission, do not have heavily inspection.
3, adopt the measurement classification that can carry out the grain properties parameter based on the measuring method of pixel accurately, efficiently, easily, whole measurement assorting process is moved on the computing machine of standard configuration, and the crystal grain measurement classification of accomplishing a visual field only needs a few minutes to get final product.
4, the present invention provides reliable basis for the quantitative micro-analysis of crystal grain in the ultra-fine grain steel.
5, the present invention has excellent universality, can be applied in field of materials, the biological field shot-like particle of all background complicacies and complex shape and measure classification work.
Description of drawings
Below in conjunction with accompanying drawing and embodiment the present invention is done further explain:
Fig. 1 FB(flow block) of the present invention;
Fig. 2 is the hardware synoptic diagram of image capturing system;
Fig. 3 is the original image of embodiment 1;
Fig. 4 is that embodiment 1 is through pretreated image;
Fig. 5 is the image after embodiment 1 two-value is cut apart;
Fig. 6 (a) is the forward direction template; (b) be that the back is to template;
Fig. 7 (a) is the defective crystal grain of crystal boundary to be repaired; (b) be crystal grain after crystal boundary is repaired;
Fig. 8 (a) is an intracrystalline hole image to be filled; (b) be the image of filling behind the intracrystalline hole;
Fig. 9 is the reparation image of embodiment 1;
Figure 10 (a) is the size distribution figure of embodiment 1 crystal grain; (b) be the form distribution plan of embodiment 1 crystal grain;
Figure 11 is the original image of embodiment 2;
The image that Figure 12 is embodiment 2 after pre-service and two-value are cut apart;
Figure 13 is the reparation image of embodiment 2;
Figure 14 (a) is the size distribution figure of embodiment 2 crystal grain; (b) be the form distribution plan of embodiment 2 crystal grain;
Figure 15 is the original image of embodiment 3;
The image that Figure 16 is embodiment 3 after pre-service and two-value are cut apart;
Figure 17 is the reparation image of embodiment 3;
Figure 18 (a) is the size distribution figure of embodiment 3 crystal grain; (b) be the form distribution plan of embodiment 3 crystal grain.
Embodiment
The medium filtering that the present invention relates to, contrast stretching algorithm, its particular content is referring to Yang Shuying.VC++ image processing program design (in January, 2005 second edition). publishing house of Tsing-Hua University, the .ISBNB7-81082-450-3/TP.162.PP98-105 of publishing house of Beijing Jiaotong University, 76-80; The histogram equalization algorithm that can keep image detail is that the present invention is at cold fine jade; Dawn, Zhang Jiashu. the histogram equalization [J] that jointing edge details local auto-adaptive strengthens. the innovation work on microelectronics and the computing machine .2010.1.vol27. No1.PP:38-41. one civilian basis; Adaptive threshold partitioning algorithm based on area dividing is that the present invention is promptly auspicious grandson. graphical analysis (in July, 2005 first published). and the innovation work on the Science Press .ISBN7-03-013850-3/TP.391.41..PP9-10. basis; Correction watershed segmentation algorithm based on range conversion is that the present invention is at J.J. Charles; L.I. Kunchevaa; B. Wells, I.S. Lima.Object segmentation within microscope images of palynofacies [J]. the innovation work on Computers Geosciences .34 (2008) the .PP:688 – 698. one civilian bases.
As shown in Figure 1, the present invention at first utilizes image capturing system to obtain the original image (target crystal grain image) of crystal grain and deposits it in subsidiary image pick-up card.Target crystal grain image is carried out pre-service, be beneficial to the carrying out of subsequent operation.The morphological feature that only relates to crystal grain for purposes of the present invention, and irrelevant with colouring information is so only need are used adaptive thresholding algorithm based on area dividing to carry out two-value to it to cut apart, obtain the black and white template of target image, i.e. the bianry image of crystal grain.Since crystal grain bianry image " successions " problems such as the peculiar crystal boundary disappearance of original image, intracrystalline hole, also must be through repairing the grain boundary based on the correction watershed segmentation algorithm of distance function, improvement seed fill algorithm filling hole.After accomplishing above-mentioned image repair step and setting scale, just can carry out region labeling to each crystal grain.Adopt retroactive method and be measuring unit, target crystal grain is extracted three initial configuration characteristic parameters respectively: chip area, girth and length breadth ratio with the pixel; Utilize area, girth again, then can calculate size of microcrystal, circularity and three characteristic parameters of shape coefficient respectively.
Thus, can carry out the hierarchical statistics analysis of size of microcrystal to target image, obtain corresponding analysis diagram according to size of microcrystal;
Then, according to circularity, shape coefficient and length breadth ratio target image is carried out the typoiogical classification statistics; At last the automatic classification of above size of microcrystal and form, statistic of classification result are filed and show output with the diagram file form.
Through 3 embodiment the present invention is specified again below:
Embodiment 1
Utilize image capturing system to obtain the original grain image of steel, the hardware of image capturing system is as shown in Figure 2: steel sample 1, professional microscope 2, camera (CCD) 3, computing machine (interpolated image capture card) 4, printer 5.The concrete steps of IMAQ are to utilize microscope that image is transferred to proper focal length, when image is the most clear the shooting and store (original image) in the image pick-up card into, can carry out the image pre-service.
The original image of embodiment 1 is as shown in Figure 3.Original image to Fig. 3 carries out pre-service earlier.At first, utilize medium filtering that image is carried out denoising.Then, utilization can keep the histogram equalization algorithm of image detail entire image is carried out enhancement process, with the detailed information of rich image, thus the display effect of reinforcement image.In order further to extract the edge, the present invention utilizes the rim detection method of differential operator to carry out, and its principle mainly is to utilize the effect of grey scale change.Because its Grad of some place of gray scale sudden change is very high, can be considered corresponding frontier point, thereby confirm the point set on border.Utilize the contrast of stretching algorithm increasing image simultaneously, as shown in Figure 4 through pretreated effect.
Also need carry out two-value to Fig. 4 cuts apart to obtain the bianry image of crystal grain.Because diversity, the complicacy of ultra-fine grain crystalline grain of steel image,, the present invention's employing cuts apart so carrying out two-value based on the adaptive threshold partitioning algorithm of area dividing to image.Adaptive threshold partitioning algorithm based on area dividing is promptly pressed the coordinate piecemeal to image, and each sub-piece is obtained optimal threshold Ti respectively automatically.The present invention finds through a large amount of tests, when dividing 2500 sub regions, adopts OTSU (big Tianjin method) algorithm, and its segmentation effect is best, and is as shown in Figure 5.
Target image though its picture quality obtains obviously to improve, but still exists the peculiar defective of ultra-fine grain steel (crystal boundary disappearance, intracrystalline hole etc.) after cutting apart through above-mentioned pre-service and two-value, influence the degree of accuracy that the measurement of target crystal grain is classified.For this reason, the present invention improves traditional watershed segmentation algorithm, has formed the new correction watershed segmentation algorithm based on range conversion.Mainly to obtain the geometric center of each crystal grain be the crystal grain core to this algorithm through target image being carried out range conversion, and each crystal grain core is revised, and to avoid over-segmentation, revised crystal grain image used the watershed segmentation algorithm again repair crystal boundary.
The detailed process of above-mentioned correction watershed segmentation algorithm based on range conversion is: 1. carry out the Euclidean distance conversion; Obtain each independent nucleus; Its process is: the background gray scale is set to 0 in the bianry image earlier; Target (crystal grain) gray scale is set to 255, use then forward direction template (shown in Fig. 6 a), back to template (shown in Fig. 6 b) to its from left to right-from top to bottom and from right to a left side-take turns doing twice scanning from bottom to top, when template center arrives a new target location; Just with the pixel value addition of each element in the template and its correspondence position, minimum and value are promptly as the pixel value of current goal.2. the size according to correction factor successively enlarges each independent nucleus, if two independent nucleus adhesions after revising then are regarded as an independent nucleus with it, and unified numbering.The present invention shows through repetition test that according to the characteristics of image of ultra-fine crystalline substance adopting correction factor is, best results at 2 o'clock.3. the nucleus after the above-mentioned numbering is carried out expansion process, according to the principle that water level rises synchronously, nucleus keeps increasing with layer position in the expansion process, is the watershed divide in case two nucleus meet, and forms the separatrix of crystal grain this moment.Fig. 7 a, Fig. 7 b are respectively the grain form after defective crystal grain and the crystal boundary reparation.
For the intracrystalline hole defect shown in Fig. 8 a, the present invention adopts improved seed fill algorithm to fill processing, and the image after the filling is shown in Fig. 8 b.This filling algorithm sees another patent of invention of the inventor for details: (" the automatic measurement of precipitation particles and typoiogical classification method thereof in a kind of steel ", application number: 200910030216.1).The basic procedure of this seed filling improvement algorithm is following:
⑴ sub pixel is pressed into storehouse.
⑵ release a pixel from storehouse when the storehouse non-NULL, and this pixel is arranged to desired value.
⑶ whether be communicated with or eight connected pixels with four of current pixel adjacency for each, tests, be in the zone and do not visited with the pixel of confirming test point.
⑷ then be pressed into storehouse with this pixel if the pixel of being tested was not filled in the zone.
In sum, target image has been carried out respectively that pre-service, two-value are cut apart, after crystal boundary reparation and hole fill each step process, can obtain the automatic reparation image of view picture target image, as shown in Figure 9.
So far, can carry out measurement, the classification work of crystal grain.At first, extract required grain form characteristic parameter, leaching process is:
(1) set the image scale, i.e. the physical size of each pixel in the uncalibrated image, its algorithm is following:
1. in target image, draw a straight horizontal line segment, write down starting point coordinate (x1, y) (x2 y), and calculates the length L 1=|x1-x2| (unit: micron) of this line segment and the pixel count N1 that is streaked with terminal point coordinate;
2. in target image, draw a vertical line segment, write down starting point coordinate (x, y1) (x y2), and calculates the length L 2=|y1-y2| (unit: micron) of this line segment and the pixel count N2 that is streaked with terminal point coordinate;
3. set the enlargement factor A of this metallic phase image.
Figure 430751DEST_PATH_IMAGE002
Figure 628383DEST_PATH_IMAGE003
Figure 534022DEST_PATH_IMAGE004
In the following formula:
Figure 630154DEST_PATH_IMAGE005
-horizontal direction size factor is each pixel physical size in the horizontal direction;
Figure 528709DEST_PATH_IMAGE006
-vertical direction size factor is the physical size of each pixel in the vertical direction;
Figure 393897DEST_PATH_IMAGE007
-two-dimensional factor is the two-dimentional physical size of each pixel;
(2) each crystal grain in the same image is carried out region labeling, promptly each grained region pixel is identified, and further obtain their characteristic parameters separately.This region labeling algorithm sees another patent of invention of the inventor for details: this region labeling algorithm sees another patent of invention of the inventor for details: (" the automatic measurement of precipitation particles and typoiogical classification method thereof in a kind of steel ", application number: 200910030216.1).This region labeling algorithm is the recursion marking algorithm, the steps include:
1. at first by from left to right, begin scanning with the mode of TV grating from the upper left corner of image from top to bottom.Up to finding 1 pixel that does not have mark.
2. give a new mark NewFlag to this 1 pixel.
3. by the numeral order of figure, 8 adjoint points of this object pixel (shade) point are scanned, just be labeled as NewFlag (it is the NewFlag in 2. just) to it if run into 1 pixel that does not have mark.Scan 8 adjoint points of 1 pixel in 8 adjoint points this moment again by above-mentioned order, as run into 1 pixel that does not have mark, again it is labeled as NewFlag.This process is a recurrence, in adjoint point, runs into 1 pixel that does not have mark, and recursion one deck is exhausted up to 1 pixel that does not have mark, just begins to return, and returning also is to return layer by layer.
4. recurrence finishes, and continues 1 pixel that scanning does not have mark, carries out 2. then, 3. two steps.
5. carry out said process repeatedly up to the lower right corner of raster scanning to image.
(3) the geometric shape characteristic parameter of extraction image, specific as follows:
1. particle area:
Bianry image template array is scanned, and it is total to calculate in the target area ash value and be 255 pixel N i , can draw the target area area A i :
Figure 470437DEST_PATH_IMAGE008
2. crystal grain girth:
Adopt the Freeman chain code that bianry image template array is carried out traverse scanning, the border of tracking target grained region becomes 8 direction chain codes with the frontier point coordinate conversion, and (the zone boundary outline line is linked to each other piecemeal by the short line between the adjacent boundary pixel and forms.The slope of short line only has eight directions, and promptly 0 °, 45 °, 90 °, 135 °, 180 °, 225 °, 270 °, 315 °, represent with 0,1,2,3,4,5,6,7 numbers respectively, be called chain code Ci=0,1,, 7}.) can draw target area crystal grain girth
Figure 53865DEST_PATH_IMAGE009
i :
Figure 490531DEST_PATH_IMAGE010
In the formula: N 1 -horizontal direction chain code number, promptly 0 °, 180 °The borderline pixel sum of direction
N 2 -vertical direction chain code number, promptly 90 °, 270 °The borderline pixel sum of direction
N 3 -oblique chain code number, promptly 45 °, 135 °, 225 °, 315 °The borderline pixel sum of direction.
3. size of microcrystal:
Size of microcrystal D i Be: the diameter of a circle when equating with the contour area of crystal grain in image,
Figure 475805DEST_PATH_IMAGE011
4. crystal grain circularity:
Calculate the crystal grain circularity i :
Figure 793971DEST_PATH_IMAGE013
In the formula: A i -region area; P i -area circumference
5. grain form coefficient:
Grain form coefficient
Figure 847378DEST_PATH_IMAGE014
:
Figure 874108DEST_PATH_IMAGE015
In the formula: ;
Figure 584892DEST_PATH_IMAGE017
-region area
6. crystal grain length breadth ratio:
Get the minimum boundary rectangle of target area, W i -rectangle is wide, L i -rectangle is long, can draw the particle length breadth ratio i:
The present invention is that criterion is carried out hierarchical statistics to crystallite dimension with the size of microcrystal, is that criterion is classified to grain form with circularity, shape coefficient, the length breadth ratio of crystal grain.The statistic of classification result of the crystallite dimension of embodiment 1, grain form is respectively shown in Figure 10 a, 10b.
Embodiment 2
The original metallic phase image of ultra-fine grain steel shown in figure 11, its crystal grain is tiny, and is different.Current series invention to its process of handling is: at first target image is carried out pre-service and carry out two-value based on the adaptive threshold partitioning algorithm of area dividing cutting apart, treatment effect is shown in figure 12; Again bianry image is carried out the processing that repair on the border, the intracrystalline hole is filled, treatment effect is shown in figure 13; Set scale and each crystal grain is carried out region labeling, measure and grain form characteristic parameters such as calculating chip area, girth, length breadth ratio, diameter, circularity and shape coefficient, crystallite dimension and form are carried out statistic of classification.The statistic of classification result of the crystallite dimension of embodiment 2, grain form is respectively shown in Figure 14 a, 14b.
Embodiment 3
The present invention also has fabulous crystal grain measuring and classification effect to a large amount of common irons of crystallite dimension about 20 microns that use in the mechanical engineering, the metallographic original image of ordinary steel shown in figure 15, and its crystal grain is thick.Current series invention to its process of handling is: at first target image is carried out pre-service and carry out two-value based on the adaptive threshold partitioning algorithm of area dividing cutting apart, treatment effect is shown in figure 16; Again bianry image is carried out the processing that repair on the border, the intracrystalline hole is filled, treatment effect is shown in figure 17; Set scale and each crystal grain is carried out region labeling, measure and grain form characteristic parameters such as calculating chip area, girth, length breadth ratio, diameter, circularity and shape coefficient, crystallite dimension and form are carried out statistic of classification.The statistic of classification result of the crystallite dimension of embodiment 3, grain form is respectively shown in Figure 18 a, 18b.

Claims (5)

1. the automatic measurement of a ultra-fine grain crystalline grain of steel and typoiogical classification statistical method thereof is characterized in that adopting the following step:
(1) gathers ultra-fine grain crystalline grain of steel image, and carry out pre-service;
(2) adopt adaptive threshold partitioning algorithm based on area dividing that pretreated image is carried out two-value and cut apart, obtain bianry image;
(3) said bianry image is repaired crystal boundary through the correction watershed algorithm based on range conversion, and fill the intracrystalline hole, obtain repairing image with improving seed fill algorithm;
(4) extract the grain form characteristic parameter, its concrete steps are:
(4-1) said reparation image being carried out scale sets and region labeling;
(4-2) extract the grain form characteristic parameter: area, girth, length breadth ratio, diameter, circularity and shape coefficient;
(5) being that criterion is carried out hierarchical statistics to crystallite dimension with said diameter, is that criterion is classified to grain form with said circularity, shape coefficient, length breadth ratio.
2. the automatic measurement of a kind of ultra-fine grain crystalline grain of steel according to claim 1 and typoiogical classification statistical method thereof is characterized in that: the pretreated concrete steps of said step (1) are:
(1-1) utilize the histogram equalization algorithm that can keep image detail to strengthen entire image;
(1-2) utilize the rim detection method of differential operator to extract the edge, the some place that gray scale is suddenlyd change is regarded as corresponding frontier point, and then the point set on definite border;
(1-3) utilize the stretching algorithm to strengthen the contrast of image simultaneously.
3. the automatic measurement of a kind of ultra-fine grain crystalline grain of steel according to claim 1 and typoiogical classification statistical method thereof; It is characterized in that: said step (2) is based on the adaptive threshold partitioning algorithm of area dividing; 2500 of the subregion numerical digits of its area dividing adopt big Tianjin method algorithm.
4. the automatic measurement of a kind of ultra-fine grain crystalline grain of steel according to claim 1 and typoiogical classification statistical method thereof is characterized in that: said step (3) the steps include: based on the correction watershed algorithm of range conversion
(3-1) carry out the Euclidean distance conversion, obtain each independent nucleus;
(3-2) successively enlarge each independent nucleus according to correction factor, two independent nucleus adhesions after revising then are regarded as an independent nucleus with it, unified numbering;
(3-3) nucleus after the said numbering is carried out expansion process, nucleus keeps increasing with layer position in the expansion process, is the watershed divide when two nucleus meet, and forms the separatrix of crystal grain this moment.
5. the automatic measurement of a kind of ultra-fine grain crystalline grain of steel according to claim 4 and typoiogical classification statistical method thereof is characterized in that: said correction factor is 2.
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