Polarization Multiplexing for Bidirectional Imaging CVPR2005 Oana G. Cula, Kristin J. Dana, Dinesh K. Pai, Dongsheng Wang (Rutgers University) Surveyed by Daisuke Miyazaki

関連研究 Y.Y. Schechner, S.K. Nayar, P.N. Belhumeur, "A theory of multiplexed illumination", ICCV2003 複数の光源下での画像から個々の光源下での画像を復元 単一光源下の画像は暗いので複数の光源で明るくすべき

目的 複数光源で物体を照らして，個々の光源下での画像を復元する 偏光を使って分離する

偏光 Light = wave  oscillates Oscillates in certain direction  polarization DOP = degree of polarization Partially polarized (DOP 0~1) Incident Reflected Air Object Transmitted Unpolarized (DOP 0) Light Perfectly polarized (DOP 1) Polarizer

２色性反射モデル Specular reflection component Specular Surface Diffuse normal Incident light Interface Medium Pigment this slide introduces the dichromatic reflection model. this model states that the observed light over the object surface is consisted of two components. specular reflection component and diffuse reflection component. specular reflection component is a highlight of the object. diffuse reflection component represents the color of the object surface. in this figure, this line represents the interface between the air and the object. when the light hits the object surface, some part of the light directly reflects, and this reflection is called specular reflection. the color of the specular reflection is the same as the illumination color. another part of the light strikes into the object, multiply reflects inside the object, then go back to the air. this reflection is called diffuse reflection. during the multiple reflection inside the object, the light is affected by the pigments, and becomes the same color as the pigments. the observed light of the object surface is the composition of the specular refleciton component and the diffuse reflection component. the explanation i have done in this slide for the dichromatic reflection model is not physically true, but it is a good explanation to easily understand about the dichromatic reflection model. Diffuse reflection component

２色性反射モデルと偏光 Light source Specular reflection Linear polarizer Diffuse Air this slide shows how to separate each components. the light source such as incandescent lamps is almost unpolarized. when such light goes through the linear polarizer, it will be perfectly linear polarized light. the reflection of the specular reflection is done immediately, so the specuarly reflected light is still polarized. but for the diffuse reflection, the light randomly reflects many times inside the object, and the light is depolarized during such diffusion. so the diffusely reflected light is almost unpolarized. by rotating the linear polarizer set in front of the camera, we can separate the specular reflection and the diffuse reflection. Object

分離の原理 Surface normal qP Reflection angle Camera Surface normal qQ Polarizer qP Incident angle Light source qQ Incident angle If we assume the surface of a transparent object as a pure specular surface, then light will hit the object in perfect mirror direction. (click) By knowing the reflection angle and the phase angle, we can determine the surface normal of the object. (click) Also, if we illuminate the object from all directions, then the entire surface shape of the object can be computed. It’s possible to observe the DOP (Degree Of Polarization) by the polarizer-mounted CCD camera located at the top of the object. The DOP depends on the reflection angle, in turn, if we obtain the DOP, we can estimate the reflection angle. Surface normal can be represented by zenith angle and azimuth angle. Reflection angle is equivalent to zenith angle, and phase angle is equivalent to azimuth angle. Thus, if we determine both reflection angle and phase angle, then the surface normal can be determined. Object Light source P Q P Phase angle Q Phase angle

基本原理

実験装置 カメラの前にも偏光板 ６×４のLED光源

観測値 θ φ θ：偏光板の透過方向 φ：光の振動方向

行列のランクは３ 光源が３つの場合，逆行列で解が求まる 光源が４つ以上のときはあとで示す

光源が３つの場合の結果 光の偏光方向はヒストグラムから検出

N個の光源の場合 最初の３個の計測はいままでどおり 各N-3個の計測に対し これで行列はランクNになり逆行列が求まる 光源を一つだけ非偏光にする ３枚画像を撮影 これで行列はランクNになり逆行列が求まる

１～３枚目の画像 （全て偏光） ４～６枚目の画像 （４が非偏光） ７～９枚目の画像 （２が非偏光） ランク５

ヒストグラム上である部分だけを取り出せば，その部分の光だけの画像が作れる LED49個

光源数も分かる

Daisuke Miyazaki 2005 Creative Commons Attribution 4 Daisuke Miyazaki 2005 Creative Commons Attribution 4.0 International License. http://www.cvl.iis.u-tokyo.ac.jp/