Tensor scale: An analytic approach with efficient computation and applications.
Tensor scale: An analytic approach with efficient computation and applications.
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DOI：
10.1016/j.cviu.2012.05.006
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发表时间：
2012-10-01
期刊：
影响因子：
--
通讯作者：
Dasgupta S
中科院分区：
文献类型：
--
作者：
Xu Z;Saha PK;Dasgupta S
尺度是计算机视觉和图像理解中广泛使用的概念，它以尺度空间理论的形式发展而来，其关键思想是在各种分辨率下表示和分析图像。最近，我们引入了一种局部形态计量尺度的概念，称为“张量尺度”，使用椭球模型产生结构尺寸，方向和各向异性的统一表示。在以前的工作中，张量尺度是用二维算法来描述的，缺少精确的解析定义。此外，使用先前的框架在三维中应用张量尺度由于计算复杂度高而不实用。本文对n维（n-D）图像给出了张量尺度的解析定义，以捕获局部结构尺寸、方向和各向异性。同时，利用几种新颖的微分几何方法，给出了二维和三维的有效计算解，并通过实验验证了计算结果的准确性。此外，导出了张量尺度的矩阵表示，方便了包括张量场平滑在内的一些操作，以获取更大的上下文知识。最后，介绍了张量尺度在图像滤波和n线性插值中的应用，并将其结果与各自的最新方法进行了比较。具体来说，将基于张量尺度的图像滤波与梯度滤波和基于Weickert结构张量的扩散滤波算法进行了比较。此外，将基于张量尺度的n-线性插值方法与标准n-线性插值方法和加窗插值方法进行了比较。
Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods.