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

1 Image Processing

• 12. Photometric Stereo

Aleix M. Martinez aleix@ece.osu.edu

Illumination

^ n ^ s a

I(u,v) A 3D object illuminated with a light source. Intensity at image point (u,v)T.

2 Photometric Stereo

( )

i i i

y x y x y x k y x kB y x I V g S N × = × = = ) , ( ) , ( ) , ( ) , ( ) , ( r

Dealing with shadows

I1

2(x,y)

I2

2(x,y)

.. In

2(x,y)

æ è ç ç ç ç ö ø ÷ ÷ ÷ ÷ = I1(x,y) .. I2(x,y) .. .. .. .. .. .. In(x,y) æ è ç ç ç ç ö ø ÷ ÷ ÷ ÷ V

1 T

V2

T

.. Vn

T

æ è ç ç ç ç ö ø ÷ ÷ ÷ ÷ g(x,y)

Known Known Known Unknown

3 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

4 Recovered normal field

Surface recovered by integration

5