Image Processing 12. Photometric Stereo Aleix M. Martinez - PDF document

Image Processing 12. Photometric Stereo Aleix M. Martinez aleix@ece.osu.edu Illumination A 3D object illuminated with a light source. ^ n ^ s a Intensity at image point I(u,v) (u,v) T . 1

Photometric Stereo = I ( x , y ) kB ( x , y ) i ( ) = r × k ( x , y ) N ( x , y ) S i = × g ( x , y ) V i Dealing with shadows æ ö æ ö æ ö T 2 ( x , y ) I 1 ( x , y ) 0 .. 0 I 1 V 1 ç ÷ ç ÷ ç ÷ T 2 ( x , y ) I 2 0 I 2 ( x , y ) .. .. ç V 2 ÷ ç ÷ ç ÷ = g ( x , y ) ç ÷ ç ÷ ç ÷ .. .. .. .. 0 .. ç ÷ ç ÷ ç ÷ è ø è 2 ( x , y ) ø T 0 .. 0 I n ( x , y ) è ø I n V n Known Known Known Unknown 2

Recovering normal and reflectance • Given sufficient sources, we can solve the previous equation (most likely need a least squares solution) for g (x, y) • Recall that N (x, y) is the unit normal. This means that r ( x,y) is the magnitude of g (x, y). • • This yields a check – If the magnitude of g (x, y) is greater than 1, there’s a problem And N (x, y) = g (x, y) / r ( x,y) • Example Recovered reflectance 3

Recovered normal field Surface recovered by integration 4

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