Size and Shape Parameters

Transcription

1 Defied i the At the momet there is miimal stadardizatio for defiig particle size shape whe usig automated image aalsis. Although particle size distributio calculatios are defied i several stadards (1, ), few compaies curretl used the ASTM stadards for particle shape calculatios (3). This documet defies the various particle size ad shape parameters calculated i the software. Aisotrop A estimate of the extet to which a bitplae ca be said to be elogated: Mea ertical Chord Mea Horizotal Chord Average Area (of Objects) The mea area covered b objects belogig to a selected bitplae: Total Area Cout Cetroids The cetroid of a field is the poit o which it would be possible to balace a bitplae o the tip of a eedle. The cetroid of a set of pixels belogig to a object at positio i is: Circular Diameter Estimate of a object's circularit: Mea chord Desit Desit of objects withi a give area. Cout Field Area Itesit Average gra value of pixels belogig to a selected bitplae:

2 pixel gra itesit values Total umber of pixels i the processig frame Mea Horizotal Chord Approximates the width of objects: horizotal detected test lie legths horizotal itercepts Spherical Diameter Estimate of the size of a object as if it was a sphere: Mea chord Aspect Ratio Ratio of legth over width. Legth of logest feret Legth of shortest feret Legth Width Momet The Biar momet measures provide a geometrical descriptio of the object. ) Bitplae alue at positio or Y (0or 1) 1 st order momet i & Y ( x xavg) ( Avg) m ) 11 d order momet i ( x xavg) m ) 11 d order momet i Y ( Avg) m ) 11 Ceter of Mass i The cetroid of a field (or ceter of mass) is the poit o which it would be possible to balace a field o the tip of a eedle. The cetroid of a set of pixels belogig to a object at positio i is:

3 _ 1i x i Ceter of Mass i Y The cetroid of a field (or ceter of mass) is the poit o which it would be possible to balace a field o the tip of a eedle. The cetroid of a set of pixels belogig to a object at positio Y i is: _ Y 1i i Circular Diameter Diameter estimate (as if the feature was a two dimesioal object). area π Compactess Ratio of area over covex perimeter: 4π A Covex perimeter Covex Perimeter Lie joiig feret taget poits: π ferets (ta) (umber of ferets Fractal Dimesio Numerical characterizatio of irregular cotours through fractal geometr. P PE δ 1 D D is the Fractal Dimesio, δ is the uit legth of the scale used for the measuremet ad P is the perimeter of the object (1<D<). Itesit Average gra value of pixels belogig to a object (scaled from 0-100). pixel gra values Total umber of pixels

4 Itesit Stadard Deviatio Stadard deviatio of gra level itesit iside each object (scaled from 0-100). Isd sqrt{ sum object pixels [( pixel It. avg object It.) pixel It.]} Mai Legth Legth of the feret perpedicular to the shortest feret. Roughess A shape measure that quatifies the jaggedess of a object's edges: Covex perimeter Perimeter Roudess A shape measure that quatifies the roudess of a object's edges: 4 Area ( π L L) Spherical Diameter Estimate equivalet to the diameter of a three dimesioal object: 1.47 area π Sphericit Estimate of the sphericit of a object: 4π A p Strig Aspect Ratio Shape factor of a thi curved object, expressig how ma times it is loger tha wider:

5 S trig Aspect Ratio Strig Legth Strig Width Strig Legth Legth of a thi curved object, measured alog its medial axis. Strig legth is approximated b: perimeter + Strig Legth perimeter 4 - ( 16 area) Strig Width Width of a thi curved object, measured across its medial axis. The object is assumed to have a costat width. Strig width is approximated b: perimeter Strig Width olume, Clidrical perimeter 4 - ( 16 area) Estimated volume of a clider based o its side view i a D image (rectagle). Clidricit is assumed b kowledge of the sample. cl π Area 4 Mai legth olume, Ellipsoidal Estimated volume of a prolate spheroid based o its side view i a D image (ellipse). Cross-sectio of the solid is assumed to be a circle. ell π Mai legth Width 6 Left ad ceter: 3D assumptio; Right: D view.

6 olume, Spherical Estimated volume of a sphere based o its view i a D image (circle). Sphericit is assumed b kowledge of the sample. sph π Circular diameter 6 olume, Tetragoal 3 Estimated volume of a rectagular prism based o its side view i a D image (rectagle). Cross-sectio of the solid is assumed to be a square. tetr Area Mai legth Area Percet Area Percet measuremets are total area measuremets ot based o stereolog. The express size as a percetage of a referece area ad are cumulative for a ru. Area of a bitplae relative to the total process frame or referece bitplae: Area of bitplae x 100 Total area of process or referece bitplae isual Referece Roudess (left), Covex Perimeter (ceter), Roughess (right). Feret 0º (left), Feret 90º (ceter), Aspect Ratio (right). Boudig Rectagle, Extreme Coordiates, Paret/Child. Distace (left), Ier Distace (ceter), Outer Distace (right). Perimeter (left), Ferets (ceter), Object Cout Poit (right). Projectio (left), Y Projectio (ceter), Area (right).

7 Legth (left), Breadth (ceter), Width (right). The 1. ASTM E Stadard Practice for Calculatio of Mea Sizes/Parameters ad Stadard Deviatios of Particle Size Distributios. ISO 976- Represetatio of results of particle size aalsis -- Part : Calculatio of average particle sizes/diameters ad momets from particle size distributios 3. ASTM F 1877 Stadard Practice for Characterizatio of Particles Copright 008, HORIBA Istrumets, Ic. For further iformatio o this documet or our products, please cotact: Horiba Istrumets, Ic Armstrog Ave. Irvie, CA 9614 USA (949)