CN101620060B - Automatic detection method of particle size distribution - Google Patents

Abstract

The invention relates to an automatic detection method of particle size distribution, which is characterized by comprising the following steps: step one, preprocessing images, converting images to be detected into HSV space from RGB space, acquiring chroma, brightness and saturation components of the images to be detected, carrying out Gaussian smoothing filter and histogram equalization to all components and automatically enhancing the brightness, the color and the contrast of the images; step two, carrying out morphological smoothing of color images so as to avoid images caused by the effect of shadow and reflected light; step three, judging a particle area and a centroid thereof and eliminating pseudo-boundary points positioned on the surfaces of particles after completing the process of boundary extraction operation, wherein the pseudo-boundary points have the characteristics of boundary points but are not boundary points ; step four, expanding particles maximumly and carrying out maximum expansion operation of the particle area, i.e. dividing the whole material surface into a plurality of parts according to the principle of proximity to one of the particles; step five, calculating particle size by a double-circle method; and step six, calculating particle size distribution. Accordingly, the invention provides direct information reference of particle size distribution for follow-up decision operation of industrial process control.

Description

Automatic detection method of particle size distribution

Technical field

What the present invention relates to is the method in a kind of detection technique field, specifically is a kind of automatic detection method of particle size distribution.

Background technology

The starting material major part of industrial processes is to belong to irregularly shaped body, as the ore of ironmaking processes, and its volume, yardstick and pattern thousand strange different expressions.These starting material participate in chemical reaction process, and the size particles that yardstick is differed can be accomplished even distribution, will be one of quality assurance condition of chemical reaction.The automatic detection of particle size distribution method commonly used is: one, by the particle centrifugal force field, measure associated change parameter measurement particle size distribution by a kind of optical unit; Two, utilize laser and polarising means thereof, the variation by the observation light beam realizes measurement to particle size distribution; Three, based on the method for graphical analysis.With regard to preceding two class technology, mechanism is very complicated, and can't realize that online in real time detects; The 3rd class methods then are the non-contact detection technology that occurs in the recent period, and still, from the available data that can consult, this type of technology is still immature and perfect.

Find through further retrieval the prior art document, the paper " application of Flame Image Process in the powder size on-line detecting system " that suffering is passed the civil service examinations etc. (" computer engineering and design " 2008 the 29th the 13rd phases of volume), this article has been introduced based on the principle of work of the online granularity Detection of the electrostatic powder of image processing techniques system, hardware and has been formed and software design.This system has adopted at the characteristics of electrostatic powder image that adaptive threshold is cut apart, the boundary chain code image processing techniques.Researched and developed a cover sreen analysis software on this basis, this software can export the cumulative percentage that reaches 30 grades, software is exported the result and the actual grain size distribution compares, and the result proves that the statistical correction rate of this software reaches more than 90.1%.Color grains bitmap images institute's time spent of analyzing one 1600 * 1200 size is less than 5s.

But, the weak point that the described technical method of this article exists: (1) " adopted adaptive threshold is cut apart, boundary chain code image processing techniques ", certainly will cause the processor calculating amount big, analysis time is long; (2) system and device is comparatively complicated.

Also find by retrieval again, the true paper that waits of Li Su " image analytical method is measured polyvinyl chloride resin particle grain size size and distributed " (" Shandong petrochemical complex " 2006 the 34th the 4th phases of volume), this article utilizes image analyzer to pass through transmission light microscopic treatment of picture, introduce parameters such as number average particle diameter, volume average particle size and particle diameter distribution width simultaneously, the characterizing method of having set up PVC grain diameter size and having distributed utilizes this method that the particle size and the distribution of two PVC samples of different manufacturers are compared.

But, the same weak point that exists of the described technical method of this article: (1) " is provided with the gray-scale value threshold value; binaryzation; separate the image of the particle that contacts with each other, the measurement content is set, sensing range; detect etc.; the measurement data of multiple image is forwarded to carry out accumulation calculating among the Excel5.0 again, obtain mean grain size and particle diameter distribution width, draw size distribution figure " and shows the whole computation process whole-course automation that still is unrealized; (2) " measure the area of all particles, and be scaled equivalent diameter of a circle (because the grain size of Contact Boundary is uncertain, so do not consider) " and certainly will expend a large amount of processor calculating time.

Summary of the invention

The objective of the invention is to overcome above-mentioned deficiency of the prior art, a kind of automatic detection method of particle size distribution is provided, can carry out robotization processing and computing to the image that contains particle, the final distribution situation that is observed ore particles in the zone of obtaining exactly, therefore the follow-up decision operation for industrial process control provides direct information reference of particle size distribution.

The present invention is achieved by the following technical solutions, the present invention includes following steps:

Step 1, the image pre-service

To being converted to the HSV space from rgb space by altimetric image, obtain colourity, brightness and the saturation degree component of former figure thus, again each component is carried out Gauss's smothing filtering and histogram equalization, automatically promote brightness, color and the contrast of image, avoid occurring making each component obtain good equilibrium because of the sudden change white noise produces pseudo-border.

Described rgb space, promptly the RGB color space is a kind of color representation method of coloured image.Coloured image is at the vector [R G B] of RGB color space ^TNot only represent the color of red R, green G and blue B three primary colours, also represent the brightness of three primary colours simultaneously, exist very big correlativity between RGB three looks.In other words, by [R G B] ^TThe different values of element can form different color effects.

Described HSV space, promptly the HSV color space also is the color representation method of coloured image.HSV color space model is a kind of three-dimensional colour spatial model that comprises tone H, saturation degree S and brightness V of creating according to the characteristic directly perceived of color, also claims the hexagonal pyramid model.

Describedly be converted to the HSV space from rgb space, because the storage of color digital image and the general rgb color space model that adopts of demonstration, so, every need handle and analyze the color characteristics of coloured image by human vision property the time, must carry out the color space conversion of coloured image.Theoretical verified with experiment: with RGB color space model conversion is that HSV color space model surmounts other conversion regime in the superiority aspect color characteristics processing and the analysis.From RGB to HSV, conversion between them can be divided into four kinds of the conversion of cylinder conversion, single hexagonal awl, spheroid conversion and triangle conversion, the geometric space feature of triangle conversion and the resulting fused images of cylinder conversion is better than other conversion, quantity of information and standard deviation after the conversion, the triangle conversion is better than cylinder conversion.

With the digital picture of digital camera output from the RGB color space conversion to the HSV color space, tone H, saturation degree S and brightness V after the conversion are expressed as follows respectively:

V=max (R, G, B) (formula one)

(formula two)

(formula three)

Described Gauss's smothing filtering is belong to the index low-pass filtering a kind of, and its basic thought is that gaussian kernel function and original signal are carried out obtaining the signal that filtering is exported after the convolution.

Described histogram equalization is a kind of of image histogram correction algorithm, and this is that original image is passed through certain conversion, and obtaining a width of cloth grey level histogram is the method for equally distributed new images.

Step 2, coloured image morphology is level and smooth,

The image that causes because of shade and reflective influence in order to overcome further adopts the coloured image filtering method on the HSV color space that image is carried out smoothing processing, and the regional structure of being correlated with in the combined diagram picture is effectively separated particle.

Step 3, particle zone and barycenter thereof are judged

Adopt the Canny algorithm to locate the border of color lump, the color lump figure that second step was obtained carries out Boundary Extraction, after the Boundary Extraction calculating process is finished, these is in that particle surface has the frontier point feature but not the pseudo-frontier point of frontier point is rejected.In order to reach the purpose of rejecting " pseudo-frontier point ", can adopt this moment window traversal method that particle is carried out region projection.

Described window travels through method, promptly sets the window of an adjustable size, and the size of window has determined the detection yardstick of particle, gets greater than the particle gap less than the value of smallest particles yardstick.Sweep entire image with this window, counted in the border in the window and add up:

$s(m,n)=\underset{x=m-s/2}{\overset{m+s/2}{\mathrm{\Σ}}}\underset{y=n-s/2}{\overset{n+s/2}{\mathrm{\Σ}}}f(x,y)$ (formula four)

In the formula: f (x, y) the binaryzation boundary image that extracts for the Canny algorithm, frontier point value 1, non-border value 0; The horizontal ordinate of x, y presentation video and ordinate; S is adjustable window size, and m, n are the central point of cycling among windows, and (m n) is the frontier point statistics to s.

With s (m, n) compare with the statistical threshold of setting in advance, if the frontier point sum in the window is less than this threshold value, think that then these " frontier points " of being confined by window are " pseudo-frontier point ", the i.e. pseudo-border that causes because of the fold or the shade of particle surface, should be rejected, be thought that simultaneously the center of this window is the part of the view field of particle own.

Step 4, the maximum extension of particle

Divide the result in conjunction with the plane, the maximum extension computing is carried out in its zone, promptly, whole charge level is divided into all many parts according to the principle nearest with certain particle point.

In the 5th step, two circule methods are asked for particle scale

Described pair of circule method promptly to the particle smeared out boundary that two dimensional image presented, at first carried out expanding outwardly separately, reappears each particle by the border of dust or adjacent particles institute shield portions with maximum possible; Then each particle is asked for two circles automatically: minimum circumscribed circle after the granule boundary maximum extension and maximum inscribed circle; At last, utilize two radius of circles to automatically identify corresponding particle scale.

Two circule method manners of execution are as follows:

The first, on particle maximum extension zone, determine that with " three contacts " method of circle seeks " minimum circumscribed circle " in this particle maximum extension zone, this circle has comprised regional whole pixel;

The second, on particle maximum extension zone, determine that with " three point of contacts " method of circle seeks " maximum inscribed circle " in this particle maximum extension zone, this circle is inclusion region partial pixel point only;

The 3rd, the computing formula of particle scale is

$d=R\·T[\frac{R}{r},2]$

In the formula, R, r are respectively the radius of " granule boundary maximum extension zone " minimum external and maximum inscribed circle, T[] any class T-norm operator of expression in the fuzzy logic, thereby the supremum of determining particle scale d is the minimum circumscribed circle diameter in " granule boundary maximum extension zone ", i.e. d≤2R.

In the 6th step, particle size distribution is calculated

Particle size distribution can adopt following formula to calculate:

${\mathrm{\η}}_{\mathrm{ij}}=\frac{{\mathrm{\α}}_{\mathrm{ij}}}{{\mathrm{\β}}_i}\×100\%$ (formula five)

In the formula: η _IjBe statistics scale-up factor, α _IjBe the i subregion (i=1,2, K, M), j class yardstick (j=1,2, K, granule number N), β _iIt is the N class total number of particles in the i subregion.

The present invention finally can obtain the distribution situation that is observed ore particles in the zone exactly by above-mentioned processing and computing to particle image, and therefore the follow-up decision operation for industrial process control provides direct information reference of particle size distribution.Whole calculating realizes whole-course automation, and compared with prior art obviously shorten computing time.

Description of drawings

Fig. 1 is an embodiment particle size distribution synoptic diagram

Fig. 2 is the pretreated particle size distribution synoptic diagram of process

Fig. 3 is through the particle size distribution design sketch behind the morphology smothing filtering

Fig. 4 is the image behind extraction border and the regional determination

Fig. 5 is a particle centroid position synoptic diagram

Fig. 6 is a particle maximum extension synoptic diagram

Fig. 7 is two circle synoptic diagram of asking for the maximum extension zone

Embodiment

Below in conjunction with accompanying drawing embodiments of the invention are elaborated: present embodiment is being to implement under the prerequisite with the technical solution of the present invention, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Among the embodiment, automatic detection method of particle size distribution comprises the steps:

The first step, the image pre-service

To being converted to the HSV space from rgb space by altimetric image, obtain colourity, brightness and the saturation degree component of former figure thus, again each component is carried out Gauss's smothing filtering and histogram equalization.

To the former usefulness of desiring to make money or profit (formula one～three) that collects as Fig. 1, the rgb space of image color expressed converting the HSV space expression to.

The detailed process of H, S, V component being carried out Gauss's smothing filtering is as follows:

If the one dimension Gaussian function is

$g(\mathrm{\τ},\mathrm{\σ})=\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}\exp (-\frac{{\mathrm{\τ}}^2}{2{\mathrm{\σ}}^2})$ (formula six)

Its first order derivative is

$g^{\left(1\right)}(\mathrm{\τ},\mathrm{\σ})=\frac{-\mathrm{\τ}}{\sqrt{2\mathrm{\π}}{\mathrm{\σ}}^3}\exp (-\frac{{\mathrm{\τ}}^2}{2{\mathrm{\σ}}^2})$ (formula seven)

Wherein, g ⁽¹⁾(τ σ) is called Gaussian filter.Function f (τ) is by g ⁽¹⁾(τ, σ) F as a result of filtering (τ σ) is:

F (τ, σ)=f (τ) * g ⁽¹⁾(τ, σ) (formula eight)

In the formula: * is the convolution algorithm symbol; τ is selected threshold value, and σ is the standard variance of Gaussian function.The smoothing effect of Gaussian filter can be controlled by σ, promptly can adjust the level and smooth degree of signal by the value that changes Gauss's standard variance σ, and the σ value is big more, and level and smooth effect is good more.

With each pixel on the image (u, v) pairing H, S, V component, promptly H (u, v), S (u, v), V (u, v) try to achieve through smoothed image behind the gaussian filtering by substitution (formula eight) under the condition that τ, σ determine respectively.

The process of H, S, V component being carried out histogram equalization is as follows:

If f (i, j) and g (i, j) respectively the remarked pixel coordinate (i, j) normalization the original image gray scale and the gradation of image after histogram modification, (i, j) (promptly the represents pixel coordinates gray level from 0 to 255 for i, j) ∈ [0,255] for ∈ [0,255], g for f.For any f (i, j) value, all can produce a g (i, j) value, and

G (i, j)=G (f (i, j)) (formula nine)

In the formula: transforming function transformation function G () satisfies following condition: G () at 0≤f (i, j)≤255 in is monotonically increasing function, and guarantees gray level from black constant to white order, and 0≤g (i is arranged, j)≤255, promptly guarantee after the mapping transformation pixel grey scale in allowed limits.

According to probability theory, when f (i, j) and g (i, probability density j) is respectively P _f(f) and P _g(g) time, stochastic variable g (i, distribution function F j) _g(g) relation is arranged

$F_g\left(g\right)={\∫}_{-\∞}^g{P}_g\left(g\right)\mathrm{dg}={\∫}_{-\∞}^f{P}_f\left(f\right)\mathrm{df}$ (formula ten)

Utilizing density function is the relation of the derivative of distribution function, and both members gets the g differentiate:

$P_g\left(g\right)=\frac{d}{\mathrm{dg}}\left[{\∫}_{-\∞}^f{P}_f\left(f\right)\mathrm{df}\right]=P_f\left(f\right)\frac{\mathrm{df}}{\mathrm{dg}}=P_f\left(f\right)\frac{d}{\mathrm{dg}}\left[G^{-1}\left(g\right)\right]$ (formula 11)

In the formula, G ^-1(g) expression is to the inverse operation of formula (formula nine).

This shows that the probability density function of output image can obtain by the probability density function of transforming function transformation function G () control original image gray level, thereby improves the gray-level of original image, the Fundamentals of Mathematics of histogram modification technology that Here it is.

The order, f (i, j) and g (i, discrete function j) is respectively r _kAnd S _k, then the discretize expression of formula (formula nine) is

(formula 12)

In the formula: T () is a transforming function transformation function, r _kRepresent the gray level of original image, S _kRepresent r _kGray level behind histogram equalization, k=1,2 ... L, L are current statistics gray level, and L ∈ [0,255], n are sum of all pixels in the image, n _lIt is the number of times that l gray level occurs;

For rounding, promptly get less-than operation result's maximum integer downwards.

In actual operation, can be according to the mapping value of desiring in formula (the formula 12) computed image after each gray-level pixels of equalization region is put pairing equalization, and with the pixel value before alternative this gray-level pixels point equalization of mapping value, thereby obtain the brand-new gray balance image of a width of cloth, and then make image obtain significantly to strengthen.

As shown in Figure 2, be the pretreated result of image.

In second step, coloured image morphology is level and smooth

The image that causes because of shade and reflective influence in order to overcome further adopts the coloured image mathematical morphology filter method on the HSV color space that image is carried out smoothing processing.

Coloured image mathematical morphology filter concrete operation process is as follows:

Process one, the circular operator of choosing radius and be 5 pixels as structural element B=B (s, t)

Process two, adopt structural element to the chromatic diagram picture of HSV color space in that (x, (x y) carries out the tone dilation operation to brightness value H=H y)

Promptly

$(H\⊕B)(x,y)=\max \{H(s-x,t-y)+B(s,t)|(s-x,t-y)\∈D_H\mathrm{and}(s,t)\∈D_B\}$

Structural element with B carries out tone erosion operation H Θ B again, promptly

(H Θ B) (x, y)=min{H (x+s, y+t)-B (s, t) | (s+x, t+y) ∈ D _HAnd (s, t) ∈ D _BD in the formula _H, D _BIt is respectively the field of definition of H and B.

Process three is carried out opening operation and closed operation in conjunction with expansion operator and erosion operator, wherein,

ON operation $H\⊗B=(H\⊗B)\mathrm{\ΘB}$

Closed operation $H\⊕B=\left(\mathrm{H\ΘB}\right)\⊗B$

Repeat the mathematical morphology smothing filtering that said process two, three continues to finish luminance component S and saturation degree component V.

As shown in Figure 3, be the level and smooth result of coloured image morphology.

In the 3rd step, particle zone and barycenter thereof are judged

Adopt the Canny algorithm to locate the border of color lump, the color lump figure that second step was obtained carries out Boundary Extraction, so that the position of clear and definite cut zone.

And adopt window traversal method to carry out region projection by four pairs of particles of formula, these are in that particle surface has the frontier point feature but not " the pseudo-frontier point " of frontier point rejected.

As shown in Figure 4, for border and regional determination result are extracted in the level and smooth back of morphological image.

The concrete grammar that barycenter is judged is as follows:

In view of particle projection regional determination operation result might comprise a plurality of particles, be referred to as " particle agglomerate " (i.e. " connected domain " shown in the figure), so also must use two-value extracted region algorithm, the multiply connected domain that these " particle agglomerates " form is cut apart again, carried out the particle barycenter according to formula (formula 13) then and seek.

$\left\{\begin{array}{c}x=\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}\frac{x\·f(x,y)}{f(x,y)}\\ y=\underset{x}{\mathrm{\Σ}}\underset{y}{\mathrm{\Σ}}\frac{y\·f(x,y)}{f(x,y)}\end{array}\right.$ (formula 13)

In the formula: (x y) is the binaryzation area image to f, the some value 1 in the zone, extra-regional some value 0; X, y represent the centre coordinate value in zone.

As shown in Figure 5, on this basis, to calculation level filter with reject lean on each other too near calculation level, thereby obtain the analysis result of particle point centroid position.

The 4th step, the maximum extension of particle

Divide the result in conjunction with the plane, the maximum extension computing is carried out in its zone, promptly, whole charge level is divided into all many parts according to the principle nearest with certain particle point.

Particle point centroid position with Fig. 5 is an example, and the principle according to nearest with certain particle point is divided into all many parts with whole charge level.Expand the result as shown in Figure 6, each stain is represented the centroid position of particle point among the figure, and the colored color lump around the stain represents to center on the maximum extension result that center of mass point " covers the minimum distance point that belongs to this barycenter together ".

In the 5th step, two circule methods are asked for particle scale

As shown in Figure 7, two circule method implementations are as follows:

Process one on particle maximum extension zone, determines that with " three contacts " method of circle seeks " minimum circumscribed circle " in this particle maximum extension zone, and this circle has comprised all pixels of particle maximum extension zone, round O _AbcBe " minimum circumscribed circle " on the present granule maximum extension zone, a wherein, b, c are " three contacts " that minimum circumscribed circle searches out on this particle maximum extension zone;

Described " circumscribed circle ", be meant the circle that does not intersect with any limit through particle maximum extension zone three angle points of polygon and circumference, according to the plane geometry theorem: determine circles at 3, the circumscribed circle that has a least radius in the circumscribed circle set by any three angle points of particle maximum extension zone polygon, because the circumscribed circle of this least radius can comprise whole pixels in corresponding particle maximum extension zone and the pixel count of the adjacent particles extended region that comprised reaches minimum, so be referred to as " minimum circumscribed circle ";

Process two on particle maximum extension zone, determines that with " three point of contacts " method of circle seeks " maximum inscribed circle " in this particle maximum extension zone, and this circle only comprises particle maximum extension area part pixel, justifies O _EfgBe " maximum inscribed circle " on the present granule maximum extension zone, e wherein, f, g are " three point of contacts " that maximum inscribed circle searches out on this particle maximum extension zone;

Described " incircle ", be meant the circle that with three limits of polygon, particle maximum extension zone tangent and circumference does not intersect with any limit, according to the plane geometry theorem: an incircle is determined on three limits, the incircle that has a maximum radius in the incircle set by any three limits of polygon, particle maximum extension zone, because the incircle of this maximum radius only comprises the partial pixel point in corresponding particle maximum extension zone, promptly do not comprise the pixel of any adjacent particles extended region, so be referred to as " maximum inscribed circle ";

Process three, the computing formula of particle scale is

$d=R\·T[\frac{R}{r},2]$ (formula 14)

In the formula: R, r are respectively the radius of " granule boundary maximum extension zone " minimum external and maximum inscribed circle, T[] any class T-norm operator of expression in the fuzzy logic, thereby the supremum of determining particle scale d is the minimum circumscribed circle diameter in " granule boundary maximum extension zone ", i.e. d≤2R.

With the particle minimum circumscribed circle that obtained and the radius R and the r substitution formula (formula 14) of maximum inscribed circle, ask for particle scale d.

By aforementioned calculation, can carry out again filtration to the distribution of particles zone, get rid of some irrational zones, such as: get rid of the too small dust gap area of some particle radius, space, noise or border burr etc.; Simultaneously, filter too huge " plate ", the shelter of similar bulk, check thing or scene such as reflective.The last measuring and calculating of finishing automatically all detected particle scales.

In the 6th step, particle size distribution is calculated

Utilize (formula five) count particles size distribution.

By above-mentioned processing and computing to particle image, finally can obtain the distribution situation that is observed ore particles in the zone exactly, therefore the follow-up decision operation for industrial process control provides direct information reference of particle size distribution.

Compared with prior art, present embodiment has following beneficial effect: whole calculating realizes whole-course automation, and computing time is short, is example with 1024 * 768 pixel images, whole computing time＜2.6s.

Claims (1)

1. an automatic detection method of particle size distribution is characterized in that, may further comprise the steps:

Step 1, the image pre-service, to being converted to the HSV space from rgb space by altimetric image, obtain colourity, brightness and the saturation degree component of former figure thus, again each component is carried out Gauss's smothing filtering and histogram equalization, automatically promote brightness, color and the contrast of image, avoid occurring making each component obtain good equilibrium because of the sudden change white noise produces pseudo-border;

Step 2, coloured image morphology is level and smooth, further adopts the coloured image filtering method on the HSV color space that image is carried out smoothing processing, and the regional structure of being correlated with in the combined diagram picture is effectively separated particle;

Step 3, particle zone and barycenter thereof are judged, the border of location color lump, and the color lump figure that second step was obtained carries out Boundary Extraction, after the Boundary Extraction calculating process is finished, these are in that particle surface has the frontier point feature but not the pseudo-frontier point of frontier point is rejected;

Described rejecting, adopt window traversal method: set the window of an adjustable size, the size of window has determined the detection yardstick of particle, gets greater than the particle gap less than the value of smallest particles yardstick;

Sweep entire image with this window, counted in the border in the window and add up:

$s(m,n)=\underset{x=m-s/2}{\overset{m+s/2}{\mathrm{\Σ}}}\underset{y=n-s/2}{\overset{n+s/2}{\mathrm{\Σ}}}f(x,y)$

In the formula: f (x, y) the binaryzation boundary image that extracts for the Canny algorithm, frontier point value 1, non-border value 0; The horizontal ordinate of x, y presentation video and ordinate; S is adjustable window size, and m, n are the horizontal ordinate and the ordinate of the central point of cycling among windows, and (m n) is the frontier point statistics to s;

With s (m, n) compare with the statistical threshold of setting in advance, if the frontier point sum in the window is less than this threshold value, think that then these frontier points of being confined by window are pseudo-frontier point, the i.e. pseudo-border that causes because of the fold or the shade of particle surface, should be rejected, be thought that simultaneously the center of this window is the part of the view field of particle own;

Step 4, the maximum extension of particle is divided the result in conjunction with the plane, and the maximum extension computing is carried out in its zone, promptly according to the principle nearest with certain particle point, whole charge level is divided into all many parts;

Step 5, two circule methods are asked for particle scale, promptly to the particle smeared out boundary that two dimensional image presented, at first carry out expanding outwardly separately, reappear each particle by the border of dust or adjacent particles institute shield portions with maximum possible; Then each particle is asked for two circles automatically: minimum circumscribed circle after the granule boundary maximum extension and maximum inscribed circle; At last, utilize two radius of circles to automatically identify corresponding particle scale, the specific implementation process is:

The first, on particle maximum extension zone, determine that with three contacts the method for circle seeks the minimum circumscribed circle in this particle maximum extension zone, this circle has comprised regional whole pixel;

The second, on particle maximum extension zone, determine that with three point of contacts the method for circle seeks the maximum inscribed circle in this particle maximum extension zone, this circle is inclusion region partial pixel point only;

The 3rd, the computing formula of particle scale is

$d=R\·T[\frac{R}{r},2]$

In the formula, R, r are respectively the radius of minimum external and maximum inscribed circle of granule boundary maximum extension zone, T[] any class T-norm operator of expression in the fuzzy logic, thereby the supremum of determining particle scale d is the minimum circumscribed circle diameter in granule boundary maximum extension zone, be d≤2R, with the particle minimum circumscribed circle that obtained and the radius R and the r substitution particle scale computing formula of maximum inscribed circle, ask for particle scale d;

Step 6, particle size distribution is calculated.

Images