The bas-relief ambiguity
The bas-relief ambiguity
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DOI：
10.1023/a:1008154927611
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发表时间：
1999-11-01
影响因子：
19.5
通讯作者：
Yuille, AL
中科院分区：
文献类型：
--
作者：
Belhumeur, PN;Kriegman, DJ;Yuille, AL
当一个具有朗伯反射率的未知物体被正视观察时，在确定其三维结构时存在隐性歧义：我们表明，物体的可见表面f（x, y）与物体几何形状的“广义浅浮雕”变换难以区分，(f)除以bar(x, y) = lambda f(x, y) + mu x + nu y，以及物体反照率的相应变换。对于被任意数量的远处光源照射的物体的每一个图像，存在一个被类似的变换光源照射的变换后的物体的相同图像。这个结果既适用于物体的照明区域，也适用于投射和附加阴影的区域。此外，无论是物体的小运动，还是观察者的小运动，都不能解决确定物体表面的平坦（或缩放）lambda的模糊性。讨论了这种模糊性对结构恢复和形状表示的影响。
When an unknown object with Lambertian reflectance is viewed orthographically, there is an implicit ambiguity in determining its 3-d structure: we show that the object's visible surface f(x, y) is indistinguishable from a "generalized bas-relief" transformation of the object's geometry, (f) over bar(x, y) = lambda f(x, y) + mu x + nu y, and a corresponding transformation on the object's albedo. For each image of the object illuminated by an arbitrary number of distant light sources, there exists an identical image of the transformed object illuminated by similarly transformed light sources. This result holds both for the illuminated regions of the object as well as those in cast and attached shadows. Furthermore, neither small motion of the object, nor of the viewer will resolve the ambiguity in determining the flattening (or scaling) lambda of the object's surface. Implications of this ambiguity on structure recovery and shape representation are discussed.