Daisuke Miyazaki, Masataka Kagesawa, Katsushi Ikeuchi, - - PDF document

Daisuke Miyazaki, Masataka Kagesawa, Katsushi Ikeuchi, "Polarization-based Transparent Surface Modeling from Two Views," in Proceedings of International Conference on Computer Vision, pp.1381-1386, Nice, France, 2003.10 http://www.cvl.iis.u-tokyo.ac.jp/~miyazaki/

Polarization Polarization-

• based Transparent Surface Modeling from Two Views

based Transparent Surface Modeling from Two Views

Daisuke Miyazaki, Masataka Kagesawa, Katsushi Ikeuchi http://www.cvl.iis.u-tokyo.ac.jp/

Abstract We developed a method to obtain 3D shape of object surface from the polarization state of reflected light on transparent objects observed from two views. Method

• 1. Measure the polarization state of the light reflected on the surface.
• 2. Rotate the object in a small angle, and again measure the polarization data.
• 3. Apply a region segmentation method to both two DOP(degree of polarization) data.
• 4. Detect a point which represent the same surface point in each region in each DOP data.
• 5. Determine the surface normal by comparing two DOPs taken before/after rotation at corresponding points.
• 6. Obtain the surface shape of transparent objects from the distribution of surface normal.

Real Image Obtained Surface Shape

1 polarization image each 2 viewpoint Shape from polarization Our method [Miyazaki et al. 2003] Only visible camera ⇔ Need infrared camera 2 polarization images 1 viewpoint Shape from polarization Previous method [Miyazaki et al. 2002] Solved the problem ⇔ Ambiguity problem 3 or more images for 1 polarization image 1 polarization image 1 viewpoint Shape from polarization Previous method [Saito et al. 1999] Many types of

• bjects

⇔ Only parameterized

• bject

1 image each Multiple viewpoint Shape from motion Ben-Ezra & Nayar 2003 Smooth objects ⇔ Only edged object Multiple images with different focus 1 viewpoint Shape from focus Ohara et al. 2003 No calibration needed ⇔ Need calibration between camera and projector Multiple images with different projected pattern light 1 viewpoint Pattern light projecting Hata et al. 1996 Solid objects ⇔ Only water wave Multiple images with different time 1 viewpoint Optical flow Murase 1990 Advantage in our method vs Disadvantage Number of input images for each viewpoints Number of viewpoints Approach

Transparent Surface Modeling Methods

ICCV proceeding pp.1381-1386

Gaussian Mapping and Regions Outline

Daisuke Miyazaki, Masataka Kagesawa, Katsushi Ikeuchi, “Polarization-based Transparent Surface Modeling from Two Views”

Reflection and Polarization DOP (Degree Of Polarization) Rotating the Object

Rotate the object Target

• bject

DOP (Degree Of Polarization) images Region segmentation Search corresponding points 3D model Object Surface normal Camera Linear Polarizer Light source Incident angle Reflection angle Unpolarized light Partially polarized light

θ θ ρ θ ρ θ θ ρ ∆ ′ = − ∆ + ) ( ) ( ) (

DOP before rotation DOP after rotation Rotation angle Derivative

• f DOP

Rotate Camera Object

• r

N E B B: Brewster curve N: North pole E: Equator F: Folding curve N F B E N B E N B E F N B-E region B-B region B-N region Regions DOP image Gaussian spheres Observation

θ θ θ θ θ θ ρ

4 2 2 2 2 2 2 2 min max min max

sin 2 sin sin sin cos sin 2 + − − − = + − = n n n I I I I

2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2

) sin 2 sin sin ( sin ) sin sin 2 )( sin sin ( sin 2 θ θ θ θ θ θ θ θ θ ρ + − − − − − − − = ′ n n n n n n n

Derivative

• f

DOP + ñ 1 Brewster angle 90° Reflection angle Degree Of Polarization DOP ρ ρí

Corresponding Point Folding Curve

Improvement of the precision

by dealing with inter-reflections by using multiple data taken under different illuminations by using multiple data taken from different views

Estimation of

the shape of backward surface the refractive index the extinction coefficient (=color of translucent objects)

Real-time system Applications to

entertainments and VR modeling cultural assets industrial robots for productions such as transparent cellular phones, PCs, toys, etc. classifying glass bottles for recycling

Experimental Setup Result for Bell-shaped Transparent Object Result for Another Object Future Work

Folding curve Brewster curve Equator North pole Gaussian sphere Object Camera Polarizer Light Light Light Spherical diffuser Real Image Obtained Surface Shape Rendered Image Solid Line: Ground Truth Dotted Line: Obtained Shape

Theorem: Folding curve is parabolic curve

Parabolic curve = a curve where Gaussian curvature is 0 ⇒ Folding curve = geometrical invariant

• r

Corresponding point Rotate the

• bject

North side Gaussian sphere Gaussian sphere North pole North pole B-B region B-B region Rotation circle Rotation circle Rotation direction Rotation direction F F B B E E B-B region Corresponding point Rotate the

• bject

South side North pole North pole B-B region B-B region Rotation circle Rotation circle Rotation direction Rotation direction Gaussian sphere Gaussian sphere F F B B E E Real Image Obtained Surface Shape Diameter(width): 24mm Height error: 0.4mm Computer Vision Laboratory, Institute of Industrial Science, The University of Tokyo, Japan