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Image field categorization and edge/corner detection from gradient covariance

机译:图像字段分类和基于梯度协方差的边缘/角检测

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Edges, corners, and vertices in an image correspond to 1D (one-dimensional) and 2D discontinuities in the intensity surface of the underlying scene. Ridges and peaks correspond to 1D and 2D extrema in it. All of them can be characterized by the distribution of gradients, particularly by the dimensionality of it. The approach to image field categorization here is to construct a covariance matrix of the gradient vector in each small window and apply the canonical correlation analysis to it. Schwarz's inequality on the matrix determinant and the related differential equation is the key to this analysis. We obtain two operators P/sub EG/ and Q/sub EG/ to categorize the image field into a unidirectionally varying region (UNIVAR), an omidirectionally varying region (OMNIVAR), and a nonvarying region. We investigate the conditions under which their absolute maximum response, i.e. P/sub EG/=1 and Q/sub EG/=1, occurs in the small window and show that they are, respectively, the desired 1D and 2D discontinuities/extrema and OMNIVAR, is in many cases, a 1D pattern in polar coordinates. This leads to an algorithm to obtain further classification and accurate localization of them into edges, ridges, peaks, corners, and vertices through detailed analysis in the informative (varying) axis of them. We examined and compared the performance of the operators and the localization algorithm on various types of images and various noise levels. The results indicate that the proposed method is superior with respect to stability, localization, and resolution.
机译:图像中的边缘,角和顶点对应于基础场景的强度表面中的1D(一维)和2D不连续。脊和峰对应于其中的一维和二维极值。所有这些特征都可以通过梯度分布来表征,尤其是可以通过其维数来表征。此处的图像场分类方法是在每个小窗口中构造梯度矢量的协方差矩阵,然后对其进行规范相关分析。 Schwarz关于矩阵行列式和相关微分方程的不等式是此分析的关键。我们获得两个算子P / sub EG /和Q / sub EG /,将图像场分为单向变化区域(UNIVAR),全向变化区域(OMNIVAR)和不变区域。我们调查在小窗口中发生其绝对最大响应(即P / sub EG / = 1和Q / sub EG / = 1)的条件,并表明它们分别是所需的1D和2D不连续/极值和OMNIVAR在许多情况下是极坐标中的一维图案。这导致了一种算法,可以通过在它们的信息(变化)轴上进行详细分析来获取它们的进一步分类并将其精确定位为边缘,山脊,峰,角和顶点。我们在各种类型的图像和各种噪声水平上检查并比较了算子的性能和定位算法。结果表明,所提出的方法在稳定性,局域性和分辨率方面均具有优势。

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