Comments on "optimal approximation of uniformly rotated images: relationship between Karhumen-Loeve expansion and discrete cosine transform"
Comments on "optimal approximation of uniformly rotated images: relationship between Karhumen-Loeve expansion and discrete cosine transform"
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对“均匀旋转图像的最优近似：Karhumen-Loeve展开与离散余弦变换之间的关系”的评论
DOI：
10.1109/83.988965
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Rae
中科院分区：
文献类型：
--
作者：
Rae
本文指出了上野原和Kanade的错误表述（见同上，vol.7，p.116-19，1998），在基于离散余弦变换（DCT）的特征向量表示的上下文中。利用重复的特征值，利用奇异值分解（SVD）可以构造出P × P真实的对称循环矩阵的特征向量矩阵，其中P表示均匀旋转图像的数目。或者等效地，它可以用离散哈特莱变换（DHT）来公式化。最后给出了一个P=4的算例，证明了分析的正确性.
This paper points out the incorrect expressions of Uenohara and Kanade (see ibid., vol.7, p.116-19, 1998), in the context of the representation of the eigenvectors based on the discrete cosine transform (DCT). With the repeated eigenvalues, the eigenvector matrix of the P x P real symmetric circulant matrix can be constructed using the singular value decomposition (SVD), where P denotes the number of uniformly rotated images. Or equivalently it can be formulated in terms of the discrete Hartley transform (DHT). An example with P=4 is presented to show the correctness of our analysis.