Accurate image rotation using hermite expansions.
Accurate image rotation using hermite expansions.
复制标题
使用 Hermite 扩展进行精确的图像旋转。
DOI：
10.1109/tip.2009.2024582
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Chirikjian,GregoryS
中科院分区：
文献类型：
--
作者：
Park,Wooram;Leibon,Gregory;Rockmore,DanielN;Chirikjian,GregoryS
在本文中，我们提出了一种方法，用于精确旋转的数字图像使用厄米展开。这利用了这样一个事实，即如果旋转2-D连续带限Hermite展开，则所得函数可以表示为具有相同带限的Hermite展开。此外，初始二维展开和旋转展开的Hermite系数通过可逆线性关系映射。提出了两种有效的方法来计算旋转过程中Hermite系数之间的映射。我们还提出了一种方法连接的Hermite展开和离散图像。使用这种方法，我们可以从离散图像获得Hermite展开，反之亦然。结合这些技术，我们提出了新的方法旋转的离散图像。我们评估我们的方法的准确性，并将其与现有的基于FFT的方法实现三剪。我们发现，这里提出的方法始终具有更好的精度比基于FFT的方法。
In this paper, we propose an approach for the accurate rotation of a digital image using Hermite expansions. This exploits the fact that if a 2-D continuous bandlimited Hermite expansion is rotated, the resulting function can be expressed as a Hermite expansion with the same bandlimit. Furthermore, the Hermite coefficients of the initial 2-D expansion and the rotated expansion are mapped through an invertible linear relationship. Two efficient methods to compute the mapping between Hermite coefficients during rotation are proposed. We also propose a method for connecting the Hermite expansion and a discrete image. Using this method, we can obtain the Hermite expansion from a discrete image and vice versa. Combining these techniques, we propose new methods for the rotation of discrete images. We assess the accuracy of our methods and compare them with an existing FFT-based method implementing three shears. We find that the method proposed here consistently has better accuracy than the FFT-based method.