偏光解析と幾何学的解析に基づく透明物体の表面形状計測 - 池内研究室

Measurement of Surface Shape of Transparent ObjectsBased on Polarization and Geometrical AnalysisDaisuke Miyazaki and Katsushi IkeuchiComputer Science, Graduate School ofInformation Science and Technology, The University ofTokyoAbstract In the eld of computer vision, no useful methods of measuring the surface shape oftransparent objects such as glasses have been proposed. In this paper, we propose a convenient andbenecial method for measuring the surface shape of transparent objects. The degree of polarizationof the light reected at the object surface depends on the reecting angle. The reecting angledepends on the surface normal of the object, thus, by measuring the degree of polarization, weare able to calculate the surface normal of the object. But unfortunately, the relation between thedegree of polarization and the surface normal is not 1 to 1, thus, to obtain the correct surface normal,we have to resolve this ambiguity problem. In this paper, we explain the method of resolving theambiguityby using the dierential-geometrical property of object surface.1 shapefrom-(shading/texture/contour)Bhat [1]Oren [2] Ikeuchi[3]Nayar [4]Sato [5] Koshikawa[6] Wol [7] 1

Saito [8] Miyazaki [9] Saito Rahmann [10] Wol Boult Rahmann Rahmann MiyazakiSaito Wol Miyazaki Rahmann 2 3 1: 4 5 2 [7,8,9] 1 1.0 n 0 1 0 1 1 [8, 9] = 2 sin2 pn 2 ; sin 2 ; n 2 sin 2 +sin 4 n 2 ; sin 2 ; n 2 sin 2 +2sin 4 : (1) n 2 (1) B 2

5: 3.2 5 B-B 6 B-B =0 =90 B-B B-B 7 P P 0 6: B-B 7: P P 0 8 B-B B-B 9 4

10: 8: 9: 3.3 () ( +) ( +) ; () ' 0 () : (2) 0 10 10(b) 10(a) 0 0

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