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| 利用小波变换由明暗度恢复表面形状 |
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钟声1,2,3, 石青云1,2,3, 程民德1,2,3
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1.北京大学数学系,北京,1000871;2.北京大学信息科学中心,北京,100871;3.北京大学视觉听觉信息处理国家重点实验室,北京,100871
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| 摘要: |
| 本文提出利用小波变换多分辨率逼近锥来解决ＳｈａｐｅＦｒｏｍＳｈａｄｉｎｇ问题（即利用景物表面明暗度来恢复景物三维信息）的一个有效方法，多分辨率方法应用于ＳＦＳ问题主要是想使求解ＳＦＳ问题的选代算法得益于多分辨率方法带来的计算速度的提高及一个较精确的解的尽快收敛，直接作用于原始图像上的ＳＦＳ方法很多时候很难收敛．那么构造一个较好的多分辨率锥成为一个关键的问题；另外，用多分辨率方法解决ＳＦＳ问题引出了一个非线性问题，即由缩小分辨率的表面产生的反射光强度图像并不等于原来未缩小表面的反射光强度图像缩小分辨率所得的 |
| 关键词: shapefromshading，紧支正交小波变换，多分辨率锥，非线性问题 |
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| SHAPE FROM SHADING USING WAVELET TRANSFORM |
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Zhong Sheng,Shi Qingyun,Cheng Minde
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| Abstract: |
| In shape from shading, iterative algorithms are often used to compute the surface derivatives. These algoritghms are, however, very time-consuming when the iterations are performed on the original image. In this paper the authors propose a multiresolution method which makes use of the orthonormal wavelet transform to construct a multiresolution pyramid and let most iterations be performed on the low resolution images to give good predictions of the initial values of the surface derivatives of higher resolution images and thus save many computations. On the other hand, the nonlinearity of imaging makes the direct reduction of the image resolution not an optimal way of utilizing the multiresolution method. Instead, they construct the pyramid of the norm of the surface direction. They prove that this strategy gives out excellent results when the surface is smooth and the support length of the wavelet is small. Factors that may affect the selection of the wavelet in the multiresolution shape form shading are also studied. Experiments show the superiority of this strategy to other methods. |
| Key words: Shape from shading compactly supported orthogonal wavelet basis multiresolution pyramid nonlinearity. |
