Computers & Geosciences 60 (2013) 98–108

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Computers & Geosciences

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Form From Projected Shadow (FFPS): An algorithm for 3D shapeanalysis of sedimentary particles

Anibal Montenegro Ríos a,n, Damiano Sarocchi b,1, Yuri Nahmad-Molinari c,2,Lorenzo Borselli b

a Doctorado Institucional en Ingeniería y Ciencias de Materiales, c/o Instituto de Geología UASLP, Av. Dr. M. Nava No 5, Zona Universitaria,78290 San Luis Potosí, Mexicob Instituto de Geología/Fac.de Ingeniería UASLP, Av. Dr. M. Nava No 5, Zona Universitaria, 78290 San Luis Potosí, Mexicoc Instituto de Física, UASLP, Av. Manuel Nava 6, Zona Universitaria, 78290 San Luis Potosí, Mexico

a r t i c l e i n f o

Article history:Received 7 May 2013Received in revised form9 July 2013Accepted 12 July 2013Available online 23 July 2013

Keywords:Clastic sedimentologyClast shape analysisTexture analysisSedimentary depositsImage analysis

04/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.cageo.2013.07.008

esponding author. Tel.: +52 444 8171039x109ail addresses: anibal_mr_1@hotmail.com (A. Mi@gmail.com (D. Sarocchi), yuri@ifisica.uaslp.mi@gmail.com (L. Borselli).l.: +52 444 8171039x109; fax: +52 444 81117l.: +52 444 8262362x145; fax: +52 444 8133

a b s t r a c t

In this paper we present a simple and effective method based on measuring the projected shadow ofsedimentary particles by means of a digital image processing algorithm that enables the three principalaxes of the particle to be determined from a single 2D color image. The method consists in projecting theshadow of the particle when it is resting on the maximum projection area (“c” axis pointing almostvertical, since in this configuration minimal distance from the center of mass to the floor is achievedminimizing the gravitational potential energy), by means of an oblique incident illumination system.Using HSL (hue-saturation-lightness) color space segmentation, two axes of the particle are measureddirectly from the maximum projected area. The length of the shadow provides the third axis of theparticle. Multiple textured and colored sedimentary particles can be easily segmented from a greenbackground and their corresponding shadows by means of a single space color transformation. Thissimple method enables the lengths of the three main axes of several particles to be determined at thesame time without expensive equipment (the software is provided free by the authors). The axis lengthscan span a broad range of sizes, and are measured with low experimental error (less than 5%).

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1. Introduction

The analysis of sedimentary particles is of great importance forthe study of geological processes because it provides informationrelated to the genesis, material transport, formation, depositionand fabric of rocks and sediments. Texture analysis of sediments iscorrelated with features such as density, water conductivity,hardness and porosity.

Shape analysis provides important information about the clastsgeological history. Clasts geological history can be divided in threemain developmental stages (Wohletz, 1987) such: (1) formation ofmajor grain shape, (2) modification by transport abrasion and (3)alteration by post emplacement processes. This concept can beapplied to different geological topic, from volcanology to classicalsedimentological study (Shepard and Young, 1961; Allen, 1982;Mazzullo et al., 1984; Wohletz, 1987; Maria and Carey, 2007;

ll rights reserved.

; fax: +52 444 8111741.ontenegro Ríos),x (Y. Nahmad-Molinari),

41.874.

Manga et al., 2011; Sarocchi et al., 2011; Caballero et al., 2012)among others. Clast morphology depends from genetical mechan-isms (e.g. magma fragmentation style, rocks breakage, comminut-ing and dissolution mechanisms) and it can change due toabrasion or comminuting related with particle interactions insidesediment transport processes. Particle shape affects how geo-morphic processes and sediment interact, because particles areusually deposited with arrangement or alignment to flow givinginformation about paleoflows direction (Capaccioni and Sarocchi,1996; Capaccioni et al., 1997; Valentini et al., 2008; Bullard, 2013).

According to Barrett (1980), particle shape can be described bythree independent features in hierarchical order: (1) general form,which reflects variations in the proportions of the particle; (2)roundness; the second-order property which reflects variations inthe angles of the profile; and (3) texture, a third-order propertysuperimposed on general shape, and referring to surface rough-ness. The use of three main axes length obtained for each particleto shape classification purpose has been also reviewed by Blottand Pye (2008).

Methods of measurement grain shape have been described inliterature; Waddell (1933) defined the sphericity as an expressionof the extent to which the form of a particle approaches theshape of a sphere. Zingg (1935) proposed a classification overall

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geometrical shape, based on the relationships obtained by the threeaxes of a particle, the general form is classified quantitatively usinga diagram. Krumbein (1941) expressed the grain shape as the ratio ofgrain surface area to surface volume. Sneed and Folk (1958) definethe sphericity for studying particle settling velocities. Blatt et al.(1980)expressed sedimentation velocity of the particles in a fluid as acharacteristic of the general form. Kaye (1999) presents a method foranalyzing the general form of a set of particles, the particles arecharacterized by a standardized size in all three axes, using atriangular diagram is possible to classify the particles by means ofthe form. A new classification scheme based on particles three axeslength was provided by Blott and Pye (2008).

A suitable technique for measuring a large number of particlesis required for evaluating parameters of sedimentary deposits(Fitzsimmons et al., 2009). At present there are several instru-ments for particle characterization based on different physicalprinciples; for example the Coulter counter (Deblois and Bean,1970), Sympatec QicPic (Altuhafi and Baudet, 2011), Retsch Cam-sizer (Pilarczyk et al., 2011), Technolog, X-ray diffraction (Reiekeret al., 1998), laser diffraction size analysis (Syvitski,1991), elutria-tion (Tillery and Buchan, 2002), light scattering (Ozaky et al.,1994), sedigraph technique (Syvitski, 1991), and liquid sedimenta-tion balance method (Yoshida et al., 2001). These instrumentshave small particle size detection limits and high accuracy, andprovide particle size distributions that can be expressed in particlevolume or mass. However, most of these methods approximate theparticle by a sphere and consequently other aspects as elongation,or fine and coarse irregularities, are not considered.

Image analysis has been widely used as a method for obtainingthe physical characteristics of granular particles, such as size(Persson, 1998; Komabayashi et al., 2009; Montenegro Rios et al.,2011), morphology (Drevin, 2007; Bowman et al., 2011; Pons et al.,2002; Sarocchi et al., 2011), texture (Pirard et al., 2007), mineralcomposition (Griffin et al., 2012), porosity (Prêt et al., 2004),wettability (Susana et al., 2012), and fractures (Lee et al., 2009).The use of optical instruments (macro objective lenses, opticalmicroscope, scanning electron microscope, transmission electronmicroscope, among others) enables the original sample to bemagnified up to several orders of magnitude. In addition, imageanalysis enables the development of software designed to simulta-neously measure a large number of particles for various purposes indifferent fields such as engineering, biology, physics, and geology,among others (Russ, 2011; Gonzalez et al., 2002; Jahne, 2004).

Currently there are several methods to study the three-dimensional morphology of particles in sedimentological applications:x-ray tomography (Ghorbani et al., 2011), magnetic resonance (Rypl,2010), optical scanning and confocal microscopy (Peng, 2002), stereo-scopy and laser line (Thurley, 2011; Vilaca et al. (2010)), and terrestriallaser scanning (Heritage and Milan, 2009).

Although these methods allow digital modeling of particlesurface topography, in many cases such accuracy is not needed.Samples generally contain a large number of particles, but it is notnecessary to characterize each particle in detail. In many cases isbetter to obtain a parameter that describes the sample in a simplerway in order to reduce costs and time, and improve the statisticalrepresentativeness of the sample size.

In particle shape analysis by image processing, the choice ofillumination systems such as background (Fernlund, 2005a),fluorescent light (Kwan et al., 1999) or laser diode (Gao et al.,2012), determines whether the segmentation is carried out ingrayscale or RGB color space. These methods allow only a two-dimensional analysis and are limited by the color of the sample;for example, transparent or translucent particles (e.g. quartz)cannot be analyzed accurately because of the difficulty in distin-guishing the particle from its background (reflection can generateproblems in optical measurements). The task of segmentation can

be difficult when particle color and intensity values are close to thebackground values.

The main innovative characteristics of Form From ProjectedShadow (FFPS) method, presented in this paper, allows 3D form tobe obtained from a single 2D color image through an appropriateimage segmentation process, treating the image in different colorspaces (Hanbury, 2008). The lengths of the major and intermediateaxes are obtained directly from the maximum projected area,while the minor axis is determined from the shadow profileproduced by a single illumination source (Kaye, 1999; Sarocchiet al., 2008). In this paper we analyzed particles in a size range(100 μm–60 mm) designing the appropriate optical systems. Thissize range could be extended using appropriate scaled opticalsystems. On the other hand, there is no upper limit to thescalability of the method since it has been used in measuringmountains and central peaks in moon craters (Schröter, 1791).

Other innovative characteristic of FFPS segmentation method isthat the algorithm works both on the hue plane, enablingsegmentation of the maximum 2D projected area, and using theHSL (hue-saturation-lightness) color space, enabling the projectedshadow to be segmented in efficient and reliable way. Themeasurement method and setup are inexpensive and easy toimplement. The software is provided free by the authors. Thebasic equipment consists of a common Digital Single Lens Reflex(DSRL) camera with appropriate optical accessories (i.e., 50 mmobjective lens, macro objective lens; microscope) depending onthe sizes to be measured. The method is completely automatic,after the initial calibration step (consisting of measuring a refer-ence object), tens of particles can be analyzed simultaneously.The software can analyze images with a resolution of 15 mega-pixels. In addition to the three main axes of each particle, thesoftware provides the morphological parameters of Zingg (1935),Kaye (1999), Sneed and Folk (1958) and Blatt et al. (1980):perimeters, areas, equivalent ellipse geometry, Feret diameters,and up to ten classical 2D image analysis form factors.

2. Materials and methods

2.1. Materials

A white light source is used to obliquely illuminate the sample,producing the shadow that will be measured (Fig. 1); the lightbeam must be collimated (using Fresnel lens or high intensity LEDlight) in order to preserve the aspect ratio of the objects whilemeasuring their shadows and reducing penumbra zones. Anincandescent spot lamp with a 500-watt bulb was used. The lampwas positioned at an angle of 101 from the horizontal surface. Thedistance between the camera and the illumination system wasapproximately 4 m. The distance between the camera and theparticles was fixed according to the particle sizes and the char-acteristics of the lenses used (see Appendix A for more detail).

A digital Canon Eos 50D camera was used to produce the imagesof the particles and their projected shadows. A resolution of 15megapixels is suitable for a correct analysis. The camera sensor hasa 4752�3168 image resolution. Using the standard Canon EF-S18–55 mm zoom lens, it is possible to measure particles larger than1 mm. Using the MP-E 65 mm f/2.8 1–5� Canon Macrolens, it ispossible to analyze particles with sizes larger than 600 μm. A fine-grained green paper was used as a background. The analysis can beextended to microscopy using a uniformly colored green surface.In this case it is necessary to use a surface that does not displayroughness at the microscopic level (see Appendix A for more detail).This roughness would produce shadows which would introducenoise into the image analysis, increasing the error.

Fig. 1. Geometry of the experimental setup: (a) Lateral view and (b) top view.

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Images were acquired and stored in tagged image file (tifformat, with resolution greater than 300 dpi). The material usedfor this study comes from the Colima Volcano (Mexico). Clastcharacterization (three axis measurements) was obtained using aVernier caliper with 70.005 mm precision.

2.2. Geometric overview

The camera is placed above the object (Fig. 1a and b), locatedaccording to the working distance of the lens. L is the length of theobject, l is the length of the object calculated by means of theprojected shadow and θ is the angle between the light beam andthe surface on which the object lies. Although the light source iscollimated, aberrations of the system and the finite size of thesource cause the shadow to widen if the light source is too close tothe object (l will be greater than L); however, if the light source isfar enough (until l≈L), this error is negligible. The angle φ (Fig. 1b)should be as close to 01 as possible so that the shadow cast by theparticle does not widen.

If 2φ is the angle subtended by the object of length L, then thedistance “r” between the light source and the end of the shadow isgiven by:

r¼ L=2 cot ðφÞ ð1Þwith φ close to 0.11 ensuring being different from zero, which wouldmean illumination source at infinity, this condition ensures that L≈l,which allows a precise analysis. Knowing the shadow length h andthe angle θ, it is possible to obtain the object height H.

The proposed method uses the shadow projected by the particleto determine its height (Kaye, 1999; Sarocchi et al., 2008). As shownfrom the top view, H can be approximated through h, and width Wand length L of the object can be measured directly from the proj-ected image.

3. Image processing algorithm

Sedimentary particles have different colors and textures thatmake difficult to distinguish the particles area from their shadow,being therefore necessary to use different color spaces to performthe analysis. The three-axis analysis consists in segmenting andseparating the area of each particle from its projected shadow (seeFigure) and measuring the two main axes of the particle (lying onthe ground plane) and the shadow′s length separately. For thispurpose, particles must be positioned in rows separated by at least

the maximum projected shadow (tan φ times the maximumparticle height). As a first step, a digital image of the particle andits shadow is produced using an oblique, collimated light source.The image is calibrated to real units with an object of known size.The image distortion problem, due to optical aberration of thelenses, is solved using the method proposed by Zhang (2000). Theparticle image is then analyzed in the hue-saturation-lightness(HSL) color space, resulting in a two-dimensional projection of theparticle (generally the area containing the major and the inter-mediate axes), fromwhich the width and length of the particle areobtained. The third axis is determined by the length of theprojected shadow, as geometrically explained in Section 2.2.

The image is usually characterized by differing light conditions dueto the illumination system. While the particle's upper surface facingthe light source is saturated by light, the other part of the surfacepresents low contrast due to the projected shadow. Through the HSLspace segmentation, it is possible to eliminate the noise generated byexcess light as well as the noise generated by particle's texture. Theprojected shadow is segmented in the HSL space. The block diagram(Fig. 2) shows the stages of the proposed algorithm.

3.1. Color extraction

Identifying the appropriate color space representation of theimage is essential when image processing techniques and efficientmeasurement are required. Illumination information must be wellseparated from color information. Most of the segmentationalgorithms work with grayscale images and less frequently inRed–Green–Blue (RGB) color space. RGB representation repro-duces a wide variety of colors, but does not consider the mannerin which the colors are captured and is also highly sensitive tocolor changes. Thus few features of the object can be analyzed inRGB color space, especially when shadows are present in theimages. There is a vast literature concerning HSL segmentation andpattern recognition (Hanbury, 2008; Zhang and Wang, 2000;McCallister and Hung, 2003; Park, 2003), because this color spacesegmentation performs better with images that are not uniformlyilluminated. In this paper, a segmentation algorithm working inHSL space is proposed. Hue is an attribute that describes a purecolor; saturation gives information about how much the color isdiluted by white light and lightness is an important parameter todescribe color sensation.

Most cameras produce digital images in RGB color space that wehave to transform to the HSL color space. In this work this transforma-tion is performed according to the procedure of Gonzalez et al. (2002).

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Selecting a suitable background color allows the complexity of thealgorithms to be decreased considerably, even when there are a largenumber of colors in the objects to be segmented. If a white back-ground surface is used, no significant differences can be detectedbetween the particle area and the background, because sedimentaryparticles generally have a higher intensity in the red and blue planes.

Fig. 2. Block diagram of the algorithm: the algorithm performs segmentation of theshadow and particle individually; then subtracts the two images to obtain thelength of the shadow; finally the three axes of the particle are measured.

Fig. 3. (a) Original image of natural particles; (b) image HSL hue plane; only particles withigh contrast and non-reflective surface can be well differentiated from the backgroundtexture can be well segmented.

Transforming the original RGB image (Fig. 3a) to HSL and extracting ineach of their planes (Fig. 3b–d), no efficient segmentation is obtained.

In this work, a green background is proposed, in order to be ableto efficiently segment the particles from their shadows since itincreases the differences between the particles and the background.Moreover, in these conditions HSL space enables better segmentationof the projected shadow in the HUE plane. With a green surface,particle segmentation is easier since most natural rocks (silicaterocks, carbonate rocks etc.) present higher intensities in red and blueplanes and more rarely green particles are found. In these cases aproper selection of the background color should be made.

Most of the particles can be well segmented in the hue plane as inthe example of Fig. 4b. However, saturation (Fig. 4c), lightness(Fig. 4d), and HSV (hue-saturation-value) space (Fig. 4e) can be noisyor difficult to segment easily. Fig. 4f shows the segmented particlesusing a Niblack threshold (Leedham et al., 2003) which is based oncalculation of the local mean and local standard deviation. Thisexperiment serves to demonstrate the efficiency of this algorithmover a wide range of colors and textures. The proposed methodreadily produces particle segmentation using only a single image.Pixels are represented in the HSL space and the image is evaluated bythe maximum values in the intensity histogram. The remaining areasare assigned to the background surface. By this method, multicoloredobjects can easily be described, and multiple image processing fordifferent colors is not necessary. This is important in order to savecomputing time when many images need to be analyzed.

In the mineral processing plants ore value is frequently associatedwith silicates (gangue) and shows different colors and textures.For this reason it is difficult to segment the particles. Working inthe saturation plane can be helpful for analyzing particles thatcontain different minerals, and to obtain phase content analysisduring mineral processing. The lightness plane allows a textureanalysis in grayscale and phase content analysis is also possible.Similar properties are shown in the HSV plane. Analyzing images ofthe particles in the RGB color space allows segmentation whenparticles have a uniform color and show high contrast with thebackground. The analysis of particles with different phases and

h a reflective surface can be observed; (c) image HSL saturation plane; particles with; and (d) image HSL lightness plane; only particles with high contrast and uniform

Fig. 4. (a) Original image of natural particles with a variety of colors and textures; (b) image HSL hue plane; colors and textures are discriminated; particles show high contrastallowing easy segmentation; only particles with a high reflective surface are similar to the background; (c) image HSL saturation plane; textures and colors can be welldifferentiated in gray scale; particles with different phases can be distinguished; (d) image HSL lightness plane; most of the particles have intensities very close to the background;particles with high contrast can efficiently segmented; (e) image in the HSV color space; particles show a similar property to HSL image; and (f) Image HSL hue plane segmented.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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textures could be more complex working in RGB color space,especially when the image is not uniformly illuminated.

3.2. Shadow segmentation

A particle's shadow is segmented in HSV space, which is aprojection of the RGB color cube onto a non-linear chroma angle,a radial saturation percentage and a luminance-related value(Cuevas et al., 2010). The representation of this model is aninverted pyramid in which white is located in the central part ofpyramid; black is located at the pyramid vertex and the principalcolors are located in the pyramid base.

Fig. 5a shows the image for analysis with particles and relatedshadows. Fig. 5b shows the image in the HSV plane. In the segmenta-tion process, a portion of the particle is added to the shadow lengthdue to particle texture (Fig. 5d); hence it is necessary to subtract thesegmented image particle from the segmented shadow in order toobtain the real length of the shadow (Fig 5f). The segmentationprocess is carried out by a background correction method (Gonzalezet al., 2002). The length measurement is taken from the particle'scenter of mass to the bottom edge of the segmented image of theshadow. Two axes of the particle are obtained from the segmentedimage (Fig. 5e), and the third axis is calculated from the length of theshadow. The system is calibrated using an object of known size.Overlapping between shadows and particles is not considered by thisalgorithm.

In order to determine the uncertainty due to particle irregularityon the “c” axis measure, ten particles was measured by FFPS and

compared with measurements obtained from a lateral view (Fig. 6). Itshould be noted that shadows shapes are irregular (Fig. 6a) but suchirregularity produce a heights variation within a 10%.

3.3. Error analysis

The distance between the particle and the lighting system is animportant aspect to take into account (Fig. 7). Particles A and B withthe same size are placed at distances da and db from the illuminationsource. The angle θB formed by the particle B is greater than θA;The angle θB formed by the particle B is smaller than θA; Due to this,the position of each particle inside of the field of view should beconsidered in order to get an accurate measurement with an errorless than 5%; LB¼LA75% it means that particle B should bepositioned at 5% more the distance dA. This means that particle Bcan be in different positions with respect to particle A. As seen inFig. 7, the light beam passes through a point tangent to the particle′ssurface. It can be seen that particle A is intersected by the light beamat a point lower than particle B and for this reason the projectedshadow provides different particle heights.

4. Example of application

4.1. Test with natural material

To test the efficiency of the method proposed in this paper, wemeasured 80 particles from a pyroclastic deposit of the Colima volcano(Mexico). Each particle was measured on the three axes (major axis,

Fig. 5. (a) Original image with particles illuminated by collimated light, showing how one portion is illuminated and the other shaded; (b) grayscale image in HSV colorspace, where one portion of the particles is illuminated and the other is shaded; (c) image in HSL color space showing high contrast and well-defined particle perimeters.The shadows are removed and the information from illumination is not considered in this plane; (d) segmented shadow and the shaded portion of the particle in HSV colorspace; (e) particle area segmented in the HSL color space; (f) image produced by subtraction of particle (e) perimeters from shadows (d) where shadow perimeters areperfectly delimited. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. (a) Height distribution measuring method with the FFPS. (b) Height distribution measurement by analyzing lateral view.

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minor axis and intermediate axis). For particles larger than 0.5 mm,each axis was measured using a Vernier caliper. For particles smallerthan 0.5 mm, which are difficult to handle, top and lateral viewphotographs were obtained using a digital camera (as shown in Fig. 6a

and b). Analyzing the top view, it is possible to measure the major andintermediate axes (maximum and minimum Feret diameter), and theminor axis can be measured in the lateral view (minimum Feretdiameter).

Fig. 9. Size distribution of 80 particles by FFPS method vs. Vernier caliper (250 μm–

5 cm).

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The data obtained by using Vernier caliper and side view methodswere compared with those obtained by the FFPS method of analysisproposed in this work. In order to show the differences between sizesgenerated by the two methods, the three axes are presented in thechart separately. In Fig. 8, the measurement obtained using Verniercaliper and lateral views are plotted on the x-axis and the measure-ment obtained using FFPS on the y-axis. Ideally the two methodsshould show a good correlation. The height predicted by FFPS isplotted against the height previously measured by Venier caliper. Thisoperation is made with each of the three axes a, b, c of the particle in a1:1 ratio (Fig. 8). The correlation coefficient (r2) is computed withrespect to each predicted value (by FFPS) vs. observed value (Verniercaliper).

The Kolmogorov–Smirnov test shows an error of 4.92% for themajor axis (Fig. 9) and an error of 4.90% for the intermediate axis.For our purposes, it is important to quantify the error for theminor axis, determined using the FFPS method. In this case, theKolmogorov–Smirnov test shows an error of 6.5%.

In the plot shown in Fig. 10, the distribution of heights obtainedby FFPS method along a particle′s transect (the particle shown inFig. 6 was used) is shown vs. the distribution of heights obtainedby lateral view measurements. The maximum difference obtainedby Kolmogorov–Smirnov test for this particle was 7.1%. Weperformed this experiment with a total of 10 natural particles, in

Fig. 8. Measurement of 80 particles by FFPS vs. Vernier caliper and lateral view (LV) (250 μm–5 cm).

Fig. 10. Height size distribution by FFPS method vs. lateral view for the singleparticle shown in Fig. 6 (100 μm–1.3 mm).Fig. 7. The shadow shows a nonlinear behavior due to variations of the surface.

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order to study the dispersion of the measurements around themaximum height. It was found that 50% of the heights were asclose as 10% from the maximum height.

4.2. Test using artificial material

In order to test the accuracy of FFPS, a monodispersed sample(∅170.005 mm) of 100 spheres was analyzed. The spheres were useddue to their isotropic shape, which allows an easier comparison. Theaverage projected area for the spheres was 8000 pixels. The actualdiameter of each sphere was compared with the major (a) andintermediate (b) axes obtained by means of direct optical measure-ment and the minor axis (c) measured by the FFPS method. Theabsolute mean error was 1.99% of the sphere size for the major (a) axis,2.01% for the intermediate axis (b), and 2.21% for the (c) axis. Thelarger error in the vertical diameter measured by FFPS is due to thedifferent distance of the particles from the light source.

4.3. Error related to the angle of the incident light

A set of experiments was performed to determine the optimumangle of the lighting system with respect to the plane where theparticles are positioned. According to the results obtained (Fig. 11),the error related to the angle of incidence is lower when lightstrikes at low angle (approximately 101).

The error was calculated for three sets of 30 natural particles withsizes of 2, 4 and 8 mm. The actual size of each particle for the smallerclass (2 mm) had been previously measured by image analysis of theprojected area and in lateral view, while the 4 and 8 mm size classes

Fig. 11. Estimated error rate d

were measured by a Vernier caliper. The axes “a”, “b” and “c” weremeasured at incident light angles of 101, 151, 201, 301 and 451.

The error for the direct optical measures of the “a” and “b” axes(Fig. 11) is quite constant and in the order of 2–8% of the particlesize, while the error of the “c” axis, measured by the FFPS method,increases progressively from a minimum of 6–7% at 101 of incidentlight angle, to a maximum of 35–40% at 451. For this reason usingthe FFPS method is recommended to measure the “c” axes ofparticles using angles of at most 10–151. This angle ensures thatthe particle is intercepted at the top tangentially by the light beam.Experiments performed show that with light inclinations around10–151, the error is between 5% and 9%.

5. The FFPS analyzer software

The FFPS program, release 1.3, supported by Windows XP ormore recent Windows versions, has been developed by means ofLabView software (National Instruments Inc.). The programapplies the FFPS method and measures the three axes of eachparticle from a 2D photograph, geometric parameters (perimeters,areas etc.) of projected areas and shadows, as well as a series ofform parameters obtained by the ratios between axis lengths,perimeters and areas (Fig. 12). The executable stand-alone versionof the software FFPS is available as freeware for the scientificcommunity on the website: http://www.laima-uaslp.org/ffps.

The first step in using FFPS program consists in scaling theimage by means of a reference object positioned in the middle ofthe field of view. After this it is possible to analyze the entireimage or select a Region of Interest (ROI) of irregular or geometric

ue to illumination angle.

Fig. 12. Front panel of FFPS analyzer software.

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shape. Particles and shadows with a small size (o15 pixels) areautomatically removed.

The front panel of the program contains the browser addresspath to select the image file, the buttons for image calibration andthe windows to enter the real size of the reference object. Theimage to be analyzed is shown at the left of the front panel. Twosmaller windows at the right show y the projected areas and thesegmented shadows. At the bottom of the panel, a table lists alldata measured.

The software calculates the area (A), convex hull area (Ach),perimeter (P), circularity (Fcirc), compactness (Fcomp), Waddeldiameter (Wd), Heywood circularity (Hcirc) (Allen, 1997), ellipseequivalent major axis of particle projected area (Eemax), ellipseequivalent minor axis of particle projected area (Eemin), majorFeret diameter in projected area (Femax), minor Feret diameter inprojected area (Femin), ellipse equivalent major axis of particleprojected shadow (EemaxS), Major Feret diameter in projectedshadow (FemaxS), b/a ratio (b/az) (Zingg, 1935), c/b ratio (c/bz)(Zingg, 1935), Sneed and Folk (S&F) (Sneed and Folk, (1958)),Blatt (B) (Blatt et al. (1980)), Kaye A (KA), Kaye B (KB), and Kaye C(KC) parameters (Kaye (1999)). All the calculated parameters canbe automatically exported to a spreadsheet.

6. Conclusive remarks

The FFPS is a non invasive method which enables the measure-ment of the three axes of particles from the maximum particleprojected area in a digital image with good accuracy. The algo-rithms used in the FFPS method do not represent a challenge forresearchers of disciplines outside image processing. The methodcan be applied to particles with crystalline or reflective surfacesthat are generally difficult to analyze using other methods(Sinecen et al., 2011). The proposed method provides informationsimilar to the methods proposed by Arasan et al., 2011 andFernlund, 2005b, but with the advantage that only a single image

is needed. This method does not require a special conveyor ormachinery. Errors related to reflectance and segmentation are notsignificant compared with the advantages. The main advantages ofthe method are the wide size range and the variety of particletextures and colors that can be analyzed.

The error related with the FFPS method is due mainly to thedistance of the particle from the light source as described inSection 2.2, but it can be reduced by placing the set of particles atthe same distance from the lighting system. The light inclinationadopted (10–151) is obtained both by empirical results andtheoretical considerations (see Section 4.3) and it corresponds tooptimal balance between small angles and the sharpness of theshadow.

In summary, in this paper a new simple optical method formeasuring the three main axes of particles is presented. The paperdescribes the details of the method and the program, and thededicated software is freely available. The equipment is very cheapand common in most laboratories. The program uses effectivesegmentation algorithms that, with the suggested analytical setup,enable particles to be analyzed with error lower than 5 percent.The size of the objects to be measured depends on the optics usedand works equally well with objects of few microns in a microscopeas with large objects photographed by a common camera. Allparticles in an image can be measured simultaneously and with veryshort execution times. By means of the FFPS method, the 3D particleshape analysis can be performed easily, quickly, at low cost and witha good accuracy, which makes the program a very useful instrumentin various fields where a general study of particle shape is needed.

Acknowledgments

We wish to thank Jose Rafael Hernandez Martinez for the helpduring the experimental work and Luis Angel Rodriguez Sedanofor the useful discussions. We also are grateful with MargaretSchroeder Urrutia for her observation about the English form.

A. Montenegro-Ríos et al. / Computers & Geosciences 60 (2013) 98–108 107

The authors thank Roberto Sulpizio, Karoly Nemeth and ananonymous reviewer whose suggestions have greatly improvedthe original manuscript.

This work was partially supported by Ciencias BásicaCONACyT project (SEP-83301) and PROMEP (UASLP-PTC-241 Project)funds. JAMR acknowledges to the CONACYT for the PhD grant(No. 42642).

Appendix A. FFPS: Sample preparation, image acquisitionand processing steps

�

Take 1 kg sample of loose material by scraping the surface ofthe deposit outcrop.

�

Process the sample by the sieving method where granulometricclasses are splitted by mesh in the range from �4φ to 4φ, with 1φsize step. Shaking time varies depending on the fragility of thematerial. From 2 min by hand shaking for very brittle material upto 15 min by Tyler Rotap shaking for very hard rocks.

�

Apply the FFPS method to different classes because generallyshape is size dependent. Moreover the use of one class at timeallows: (1) to prevent that shade of larger particles overlapwith smaller particles and (2) the camera lens objective can bechosen as a function of the resolution required.

�

Sustain Camera by a photographic stand. A DSLR Camera withgood resolution (8–20 megapixels) is required. The objectiveused varies between a standard 50 mm lenses for coarse sizeclasses to dedicated photomacrography objectives for size ofhundreds microns. An optical microscopy can be used for fewtenth microns clasts. High resolution images of particlesprovide higher precision in the analysis. TIF images formatand resolution higher than 8 megapixels are recommended.

�

Use a flat green surface as background where the particles lie.The surface can be “American” or “bond” paper or very smoothcardboard. The use of a rough surfaces is not recommendedbecause it could generate small shadows that increase theerrors. If particles are greenish it is necessary to use paper orcardboard with contrasting colors.

�

Place separated particles on the green surface forming diagonallines; this geometry allows to the algorithm to locate easily theparticle's position and its corresponding shadow, and finallythe measurement of the three axes. The use of antistatic liquidis recommended during the analysis of fine particles; thisallows handling small particles easily, avoiding the problemsdue to the electrostatic charges. The use of a hair dryer, withdeionizer device, in order to eliminate electrostatic charges.

�

Use an object of well-known size, in order to scale the pixelssize to real units. The size of such object depends from the scaleat which the analysis is done.

�

Place the camera for a top view of the surface where theparticles are placed. Ii is important to choose the field ofphotography with slanted light lit because the particles, thereference object and the shadows assembly must be inside ofthe camera field of view. The particles or shades that lie on theboundary are not considered by the algorithm.

�

Use coherent light source to produce the particles shadows. Anincandescent lamp with a Fresnel lens in front or a highintensity LED lamp can be used. The light source must beplaced at more than 4 m distance from the camera andparticles assembly, with and inclination angle of 10–151.

�

Take one or two digital images of particles assembly and thereference object over the green surface.

�

Transfer the images from the camera to a PC for processing byFFPS software. The software manual explains in detail FFPS use.

�

The updated software, manuals and examples can be down-loaded from: http://www.laima-uaslp.org/ffps.

�

The analytical results will be provided from FFPS software in anExcel spreadsheet (.XLS format).

Appendix B. Supporting information

Supplementary data associated with this article can be found inthe online version at http://dx.doi.org/10.1016/j.cageo.2013.07.008.

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