localization of free 3 d surfaces by the mean of photometric

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME

International Conference on Communication Systems (ICCS-2013) October 18-20, 2013 B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India Page 210

Localization of Free 3D Surfaces by the Mean of Photometric Stereovision

M Khoudeir, B Bringier

LaboratoireXlim-SIC, UMR-CNRS n°6172

Université de Poitiers Bvd Marie et Pierre Curie, BP 30179

86962 FuturoscopeCedex, France

[email protected]

ABSTRACT: Within the framework of the analysis of 3D textured surface through image analysis, we approach here the case of the 3D interfaces (fluid-solid) surfaces for the analysis of the local variations of their relief. Generally, the interaction between the light and these local variations of the relief leads to a textured images of these surfaces. Our aim here is to achieve the feasibility of this measurement through a local relief extraction based on photometric stereovision. The proposed approach is an original adaptation stereovision based on photometric model to the case of free surfaces with a high degree of variation and with Lambertian photometric behaviour .The suggested method is presented and the relevance of this approach for that kind of surface is tested on particular shape. The results obtained are the first step of a global study of the displacement of the local variation of this 3D free surface. KEYWORDS: Free Surface, Image Acquisition, Photometry model, 3D map, Stereovision.

I. INTRODUCTION The localization of 3D surfaces and the measurement of their displacements are today a real challenge. In structure, solid and fluid mechanics, the determination in space and in time of 3D interfaces (fluid-solid, fluid-fluid) and 3D surfaces (solid or free-surface) is necessary to the understanding of physical phenomenon and obviously the measurement of the three components of the displacement is wished. Different techniques to localize in space and in time the position of free-surface, waves or textured surface have been developed recently by [1] and [8]. Methods to estimate 3D solid surface have been also quite performed. Fringe projection [7] or photometric model [2], {3], [4], [5] are applied for different applications and particularly for solid surface. Our objective is to adapt our technique of photometric stereovision to the case of free surface obtained at the fluid-solid interface. At this time of our study, we consider only opaque surface that photometric properties can be approximated by Lambertian model. To do that, we suggest to deal with different steps. The first step, which will be presented here consist on extracting

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ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Special Issue (November, 2013), pp. 210-215 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) www.jifactor.com

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International Conference on Communication Systems (ICCS-2013) October 18-20, 2013 B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India 11

the 3D relief of a “static testing surface” in order to put out the relevance of this approach according to the shape of the surface and to its photometric properties. So, we consider a corrugated plastic with a wave length representative of fluid surface variation. Then in a second step, we will extend this approach to the case of dynamic free surface. The proposed approach is based on a photometric model which is function of the nature of the surface and the relative positions between the camera, the light source and the surface. This model leads to a set of three equations including three unknown factors of which two are related to the relief variations that are the two degrees of freedom describing the surface orientation. The third one is related to the colorimetric characteristics of the surface and it represents its reflectance. In a second time, to solve this system of equations, once needs three separate images acquired using under three different lighting configurations. Then, for the studied surface, we can extract its local relief. This technique is applied to measure the different positions and movement of a corrugated plastic. Accuracy of the position and the shape of the considered surface are presented and compared. II. PHOTOMETRIC MODEL BASED METHOD

A. Link between textured surface image and relief Since surfaces are not specular, Lambertian model [6] was used to characterize their photometric behaviour and to set the link between grey level, colour information and relief. Let us consider a rough textured surface composed of Lambertian micro-facets. The surface is lighted under incidence angle i and observed by camera mounted perpendicularly to the surface plane (x, y) (Fig. 1). Definitions of the angles shown in the fig. 1 are the following:

i : Incidence angle related to the surface; : Incidence angle related to the facets; : Angle between the surface normal and the facet normal.

Fig. 1: Configuration for view shot

In case of Lambertian surface, the image intensity I(x, y) represents the energy received by the CCD sensor. It is expressed by the following relation:

Where ),( yxI is the Image intensity, ),( yxL the coefficient representative of surface colorimetric properties, ),( yx the incidence angle related to the facet and r the distance between the lighting source and the facet.

yxr

yxLyxI ,cos,, 2

Y

X

S

i

i N

Z



The distance will be assumed to be constant since relief variations are negligible compared with the distance surface/lighting source. We try then to express the angle ),( yx as a function of Cartesian coordinates (x, y, z) of the current point. The following vectors are defined:

TZ ]100[

, vector normal to the surface plane;

TiiiiiS ]cossinsincos[sin

, the unit vector of the light source direction with i the angle

between the X

axis and the projection of the lighting source vector S

in the plane ),( YX

, ]cossinsincos[sin][ cbaN

, the normal to the facet.

Let us consider a point M from the surface. The relief in the neighbourhood of this point can be considered as a plane defined by the following equation:

0: zcybxaP Combining the equation of N

with the equation of the plane, we obtain finally:

The above expression enables us to differentiate different information included in the image grey level. B. Method to extract information related to relief The previous equation is employed to extract the relief information from the image. This equation comprises three unknowns, two of which are related to relief variations ( x

z

and

yz

) and one to surface colorimetric properties ),( yxL . We have to solve a system with three

equations and three unknowns. To produce the equations, three images are recorded. They correspond to the same surface lighted under three incidence angles. The incidence angles () are low to prevent shadows in the images. Let 1I , 2I et 3I be the images shot successively under the following lighting conditions : 011 and , 3222 and , 3233 and . The 3-equation system is the following:

221

sinsincossincos

2,,

yzxz

iiyz

iixz

i

r

yxLyxI

221

sin2

3sin

2

1cos

,,3

221

sin2

3sin

2

1cos

,,2

221

sincos,,1

yzxz

y

z

x

z

yxLyxI

yzxz

y

z

x

z

yxLyxI

yzxz

x

z

yxLyxI



Its resolution gives:

And then the image of the relief is given through double integral of z according to these equations. C. Experimental Apparatus Experiments are performed on a special device which authorizes the use of the proposed measurement technique. At this stage, we have chosen to validate and to compare the measurements the following shape: a corrugated plastic (wave length = 70 mm, amplitude = 20 mm, fig. 2). A blue random white dot pattern has been fixed on each shape. The pattern is generated by means of a synthetic image generator. The size is 280×200 mm2 yielding an optical resolution of 100 µm/pixel.

Fig. 2: Corrugated plastic and two-axis translation and one-axis rotation stages

A tri-CCD Sony camera with a 768576 pixel2 resolution is placed along the Z-axis and recorded the observed images for the different locations of the shape. Three light sources fixed at 15° with regard to the z-axis are placed at 120° each other. For each location, three expositions are recorded. The camera and the light sources are placed far enough to have parallel lines and homogenous illumination.

Fig. 3: Experimental setup: acquisition and light sources position

Combined movements of translation and rotation have been recorded by the camera. The range of displacement is included between 0.1 mm to 15 mm in translation and between 1° to

sin321

cos323

sin321

cos3212

III

II

y

z

III

III

x

z

Three light Sources

CCD

Camera



40° in rotation. The precision of the traversing system is about 5 m and about 0.5° for the rotation stage. III. RESULTS First results have been obtained on the case of the corrugated plastic. The method display with accuracy the 3D shape of the plastic (Fig. 4). The amplitude and the wave length of the shape are determined with a good agreement if we compare to the real profile (fig. 5). Evaluation of the displacements gives the same accuracy. The photometric model seems well adapted to measure 3-D shapes and the small differences found for the different positions of the plastic make this technique able to measure the 3D displacement

Fig. 4: 3D shape extraction by photometric stereovision.

Fig. 5: Estimated displacement of a profile section of the 3D surface

IV. FUTURE WORK In conclusion, the first results have shown the feasibility of this technique to measure shape location in space and to follow displacement of this kind of surface. So, we have now to adapt this approach to the case of real dynamic free surface. For doing that, we are going on one hand to exploit the spectral properties of coloured image of the surface, and on the other hand



to develop other photometric model in order to take into account surface with specular behaviour [9]. So, we expect that the use of the RVB images will allow us to extract shape information through one image acquisition. We hope that at the date of the conference, we’ll be able to present good results concerning this last step. REFERENCES [1] Calluaud D., David L.: Stereoscopic Particle Image Velocimetry measurements of the flow around a surface mounted block. Experiments in Fluids, Vol 36 n°1, 53-61, 2004. [2] Dana K., van Ginnken B., Nayar S.K., Koenderink J.J., Reflectance and texture of real world surfaces ACM Transactions on Graphics, 18(1), p.1-35, 1999. [3] Khoudeir M., Brochard, J., Benslimane A, Do M.T.,: Estimation to the luminance map for a Lambertian photometric model: application to the study of road surface roughness. Journal of Electronic Imaging, Vol 13(3), 515-522, 2004. [4] McGunnigle G. and. Chantler M.J, Rough surface classification using point statistics from photometric stereo, Pattern Recognition Letters, n°21, p. 593-604, 2000. [5] McGunnigle G. and Chantler M.J., Rough surface description using photometric stereo, Measurement Science and Technology, n°14, p.699-709, 2003. [6] Oren M. and Nayar S., Generalization of the Lambertian Model and implications for machine vision International Journal of Computer Vision, n°14, p. 227-251, 1995 [7] Pirodda L.,: Shadow and Projection moiré technique for absolute or relative mapping of surface shapes. Opt. Eng. 21, 640-9, 1982 [8]WienekeB.,:Stereo-PIV using self-calibration on particle images. Experiments in Fluids (Online) s00348-005-0962-z, 2005. [9]Bringier B., Bony A., and Khoudeir M.,Specularity and shadow detection for the multisource photometric reconstruction of a textured surface.J. Opt Soc Am Sci Vis29(1):11-21 (2012).

localization of free 3 d surfaces by the mean of photometric

Technology

d free surface

d solid surface

surface normal

d textured surface

kind of surface

opaque surface

surface orientation

considered surface