The Virtual Point Light Source Model the Practical Realisation of Photometric Stereo for Dynamic Surface Inspection

Transcription

1 The Virtual Poit Light Source Model the Practical Realisatio of Photometric Stereo for Dyamic Surface Ispectio Lydo Smith ad Melvy Smith Machie Visio Laboratory, Faculty of Computig, Egieerig ad Mathematical Scieces (CEMS), Uiversity of the West of Eglad, Bristol, BS16 1QY, UK Telephoe Abstract. The implicatios of usig commercially available o-collimated ad distributed illumiates for the applicatio of photometric stereo to dyamic ispectio tasks are cosidered. A ew form of lightig model, termed the virtual poit light source model, is proposed for modellig real distributed illumiates i relative close proximity. The ew techique has applicatio for the two- ad three-dimesioal ispectio of movig s usig a iovative techique kow as dyamic photometric stereo. Such ispectio tasks have previously bee cosidered difficult or impossible to udertake usig covetioal imagig techiques. Experimetal results are preseted i the paper. 1 Itroductio Previous work [1, 2] has show how photometric stereo (PS) has useful applicatio for the capture ad aalysis of fie texture ad specifically a potetial for the ispectio of complex s possessig cocomitat two- ad three-dimesioal features. The techique eables precisely registered pixel based 2D albedo patters ad 3D topographic features ad textures to be isolated ad subsequetly separately aalysed [3]. It is importat to appreciate that such complex s had previously bee cosidered difficult or impossible to reliably ispect usig covetioal 2D-image capture ad processig techiques. Not surprisigly it has bee realised that this approach may have potetial applicatio across a rage of difficult ispectio ad aalysis tasks, icludig the idustrial ispectio of textiles, leather, ceramics ad wood products [1], as well as ew applicatios i foresic sciece ad medicie [4] usig portable had-held devices. I all cases the richer data set afforded by the utilisatio of the PS method is recogised to potetially offer sigificat theoretical advatage over covetioal 2D image itesity or scalar based imagig techiques [1-3]. Before cosiderig issues relatig to the practical applicatio of PS it is useful to briefly review the basic theory of covetioal 'static' PS. A detailed explaatio will ot be give here; istead the iterested reader is F. Roli ad S. Vitulao (Eds.): ICIAP 2005, LNCS 3617, pp , Spriger-Verlag Berli Heidelberg 2005

2 496 L. Smith ad M. Smith referred to [1]. However, give the importace of achievig practical applicatio, particular cosideratio will be give to those idealised assumptios commoly made i PS literature. 2 Theory of Covetioal Static Photometric Stereo 2.1 Two Light Source Photometric Stereo for Plaar Surface Ispectio Figure 1 shows two distat poit light sources formig a right-agled triagle with a ukow ormal. The is assumed to be Lambertai ad the viewig positio is held to be distat. Assumig the image itesity uder each illumiate to be I 1 ad I 2 respectively, the withi the plae of the triagle: Albedo = (I I 2 2 ) 0.5 (1) Ad, Topography (i.e. ormal sese withi the plae) = Ta -1 (I 1 / I 2 ) (2) light 1 light 2 Fig. 1. Two-light photometric stereo schematic Hece, the method is able to isolate 3D topography ad 2D albedo patters for omially plaar s, commoly ecoutered i umerous idustrial ispectio tasks. (Note that i order fully to defie o-plaar three-dimesioal s a third light/image must be itroduced.) 3 Dyamic Photometric Stereo A ew form of dyamic photometric stereo (DPS) has recetly bee proposed [5] i which the covetioal static form is exteded to allow applicatio to the ispectio of fast movig s, typically ecoutered i idustrial quality cotrol tasks. I order to realise a dyamic applicatio it is ecessary to either use a sigle composite image or to acquire multiple images simultaeously. DPS uses differet forms of multiplexig i order to allow the simultaeous acquisitio of multiple views. Chael isolatio (where the term 'chael' is used here to refer to a separate lightig

3 The Virtual Poit Light Source Model 497 image combiatio) may be achieved usig methods of spectral, spatial or temporal multiplexig. A detailed descriptio of the DPS techique ca be foud i [5, 6]. Figure 2 shows a schematic of the lightig ad camera cofiguratio used for DPS. Fig. 2. Web ispectio usig earby liear illumiatio ad lie sca camera 4 Theoretical Assumptios About Lightig i Photometric Stereo Method Several factors are fudametal to successful lightig for machie visio. These iclude agle of illumiatio, itesity, uiformity, distributio ad spectrum of light. Although these factors may be altered ad arraged to achieve lightig for highly applicatio specific situatios, i all cases the availability of commercial lightig solutios will set a limit o what may be achieved withi practical desig costraits. As with PS the theory of DPS is based o a umber of idealised assumptios. I particular it is assumed that the light sources used are collimated i ature, i.e. take the form of distat poit sources. While this may be reasoably well approximated i the laboratory settig, achievig collimated illumiatio with sufficiet uiformity i itesity, over a suitable area for the practical ispectio of large fast movig, becomes more problematic. 4.1 Real Illumiates Real illumiates have a fiite size ad proximity. I order to achieve the ecessary itesity distributio required for the imagig of movig s at productio rates ofte exceedig 200m/miute it is ofte ecessary to employ distributed sources i relative close proximity, such as the lie lights depicted i Figure 2. Such lights may take the form of florescet tubes, liear arrays of fibre optics or high itesity LED's ad would appear to be far from 'poit source' i ature. Modellig real illumiates. First cosider the problem associated with the earby poit source, as illustrated by Figure 3. As a result of o-collimatio the local positio of the source appears to vary betwee locatios (i.e. a <> b). Although a calibratio may be applied to accommodate this variatio, the distributed ature of a real source would seem to suggest that it would be urealistic to treat it as a poit source.

4 498 L. Smith ad M. Smith ear-by poit source ormal a b Lambertia Fig. 3. A ear-by poit source, where a > b However, i the case of diffuse reflectio, we show here that a earby-distributed illumiate ca i practice always usefully be approximated by a equivalet virtual poit source. The virtual poit light source Cosider a Lambertia illumiated by a cotiuous liear illumiate source, rather like a log strip light, as show by Figure 4, for which it is assumed that the legth of the source (L) is sigificatly greater tha the legth of the (S). L P 1 liear illumiate P 2 P S A A S Fig. 4. Distributed liear illumiatio, where agle A is i Radias This is ot a ureasoable assumptio i practice. Ay two poits, say P 1 ad P 2, o the source that are equally spaced either side of a give poit of iterest, P S, will be at a equal distace ad appear with equal itesity, I 1. For 0 < A < π/2 we may cosider the strip source to be composed of a large umber of such equally spaced sources as L. Now, by aalogy, cosider two poit sources of itesity, I 1, as show by Figure 5(a), for which A is kow where we wish to fid the equivalet sigle virtual poit source P V, located above P S ad with itesity I 2, as show by Figure 5(b). From Figure 5(a), for a rotatio of the θ, where to avoid occlusio θ < ((π/2)-a) the itesity (i) at Ps is give by

5 The Virtual Poit Light Source Model 499 L I 2 I 1 I 1 Y P S A A Y P S S (a) Two poit sources (b) Equivalet virtual poit source S Fig. 5. Virtual poit light source i = I 1 Cos(A+θ) + I 1 Cos(A-θ) (3) i = I 1 [Cos(A+θ) + Cos(A-θ)] (4) i = I 1 [2CosA.Cosθ] (5) i = I 2 Cosθ (6) Where I 2 = 2I 1 CosA (7) This result is iterestig i that, igorig occlusio ad iverse square effects, i.e. for distat sources, ay group of real poit sources may be replaced by a equivalet virtual source, as depicted by Figure 6. Furthermore, i the case of a real distributed source, we may cosider the source to be the superpositio of a large umber of symmetrical poit sources ad as such modelled by a sigle virtual distat poit source. This assumes that the etire illumiate remais visible ad is ot occluded by features or subject to ed effects. The situatio remais much the same for a exteded source, such as a strip light typically used i web ispectio, while i close proximity, as show by Figure 2. For a log (i relatio to the illumiated ) strip light, ad a omially plaar, i which the amplitude of topographic features is relatively small, these assumptios hold, eve if the source is earby. This is essetially because ed-effects may be igored ad by makig assumptios about exteded source as a group of poit sources equivalet virtual poit source ormal ormal θ Lambertia θ Lambertia Fig. 6. Approximatig a exteded source

6 500 L. Smith ad M. Smith symmetry it is possible to igore iverse square effects, as there will always exist symmetrically spaced illumiate poits of equal itesity. Eve for a distributed source for which L α s, at L > 5Y the variatio due to iverse square is foud to be less tha 2%. 4.2 Experimetal Validatio of the Virtual Poit Light Source Figure 7 shows a plot of reflected itesity usig a exteded illumiate i the form of a 122cm log strip light located at a distace of 42cm from a matt. Figure 7(a) shows that the itesity fuctio, where θ is the agle betwee the ormal ad the light source vector, appears to obey Lambert's law ad this is cofirmed by Figure 7(b), where a liear regressio aalysis gives a squared correlatio coefficiet of better tha 99.9% There are importat practical implicatios of these fidigs i terms of applicatio to dyamic PS. I practice LED lie lights are ofte used i web ispectio as they offer good stability ad log life. Such illumiates are composed of may small sources, each emittig a coe of light, as depicted by the schematic Figure 8(a). itesity θ (degs) itesity Cosie (θ) (a) (b) Fig. 7. Matt illumiated by a exteded source LED elemets LED group visible from P S P 1 virtual poit sources P 1 radiat coe agle P S P S1 P S (a) Schematic of real liear array of LEDS (motio of is out of plae) (b) Equivalet virtual poit sources Fig. 8. Modellig a distributed liear source

7 The Virtual Poit Light Source Model 501 At ay give locatio although a differig group of LEDs will be visible, the size of the group will be similar ad will be depedet upo the LED elemet size, spacig ad radiat coe agle. As has bee show, i each case the symmetrical group of LEDS may be replaced by a sigle virtual source immediately above the poit of iterest, as depicted by Figure 8(b). Hece, it is possible to simulate the earby-distributed source i terms of kow idealised virtual poit sources. 5 Dyamic Applicatio Usig Lie Sca Imagig Figure 9 shows the results of applyig dyamic PS usig IR LED lie lights, the virtual poit light source model ad lie sca camera acquisitio. The ceramic was travellig at 30m/miute. (a) Acquired image (b) Redered topography Fig. 9. Dyamic photometric stereo operatig at 30m/miute As ca be see, the albedo is geerally very well removed i Figure 9(b) ad the detail of the topography is clearly visible. 6 Coclusios The implicatios of usig real illumiates have bee cosidered i the cotext of the practical applicatio of photometric stereo (PS) to movig s. A ew form of virtual lightig model has bee proposed, which is able to model real distributed illumiates i close proximity. Experimetal results have validated the theoretical fidigs. The employmet of dyamic photometric stereo for the capture ad aalysis of two- ad three-dimesioal data represets a useful method of eablig quality cotrol for rapidly movig productio lie situatios. The techique also offers ew potetial for the use of free-roamig had-held devices for texture acquisitio i medical, foresic sciece ad other evolvig fields.

8 502 L. Smith ad M. Smith Refereces 1. Smith, M. L., Surface Ispectio Techiques - Usig the itegratio of iovative machie visio ad graphical modellig techiques, Professioal Egieerig Publishig, ISBN , (2000). 2. Smith, M. L., Smith, L. N., publicatio agreed for 2004, 'Polished Stoe Surface Ispectio usig machie visio', i P. S. Midha (ed), Complemetary Techologies for Stoe Processig, OSNET, (2004). 3. Smith, M. L., Farooq, A. R., Smith, L. N., Midha, P. S., Surface texture ispect tio usig covetioal techiques applied to a photometrically acquired bump map, Sesor Review, Vol. 20, No. 4, (2000). 4. Smithwick, Q. Y. L., Seibel, E. J.,Depth ehacemet usig a scaig fiber optical edoscope. Optical Biopsy IV, Ed. Robert R. Alfao, Proc. of SPIE Vol. 4613, , (2002). 5. Smith, M. L., Smith, L. N., Dyamic photometric stereo, submitted to 13 th Iteratioal coferece o image aalysis ad processig, Cagliari, Italy, September 6-8, (2005). 6. Smith M. L., ad Smith L. N., (ivetors), 'Ifra-red photometric stereo', patet applicatio WO03/012412A2, (filed July 2001).