Fast anisotropic Gauss filtering
Fast anisotropic Gauss filtering
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DOI：
10.1109/tip.2003.812429
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发表时间：
2003-08-01
影响因子：
10.6
通讯作者：
van de Weijer, J
中科院分区：
文献类型：
--
作者：
Geusebroek, JM;Smeulders, AWM;van de Weijer, J
我们推导出各向异性高斯分解在一个一维（I-D）高斯滤波器在x方向，然后在一个非正交方向的1-D滤波器。因此，各向异性高斯也可以通过维度分解。从计算的角度来看，这似乎非常有效。提出了一种正态卷积和递归滤波的实现方案。对于递归实现，在当前最先进的PC上在40 msec内对512 x 512图像进行滤波，对于典型滤波器，性能提高了3倍以上，与滤波器的标准偏差和方向无关。与截断误差或递归逼近误差相比，滤波器的精度仍然是合理的。各向异性高斯滤波方法允许快速计算边缘和脊图，具有高的空间和角度精度。对于跟踪应用，正常的各向异性卷积方案是更有利的，在工程图中的虚线检测中的应用。递归实现在特征检测应用中更有吸引力，例如在计算机视觉中的仿射不变边缘和脊检测中。所提出的计算滤波方法使方向尺度空间分析的实用性。
We derive the decomposition of the anisotropic Gaussian in a one-dimensional (I-D) Gauss filter in the x-direction followed by a 1-D filter in a nonorthogonal direction phi. So also the anisotropic Gaussian can be decomposed by dimension. This appears to be extremely efficient from a computing perspective. An implementation scheme for normal convolution and for recursive filtering is proposed. Also directed derivative filters are demonstrated.For the recursive implementation, filtering an 512 x 512 image is performed within 40 msec on a current state of the art PC, gaining over 3 times in performance for a typical filter, independent of the standard deviations and orientation of the filter. Accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error.The anisotropic Gaussian filtering method allows fast calculation of edge and ridge maps, with high spatial and angular accuracy. For tracking applications, the normal anisotropic convolution scheme is more advantageous, with applications in the detection of dashed lines in engineering drawings. The recursive implementation is more attractive in feature detection applications, for instance in affine invariant edge and ridge detection in computer vision. The proposed computational filtering method enables the practical applicability of orientation scale-space analysis.