On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
SIAM Journal on Matrix Analysis and Applications
Summed-area tables for texture mapping
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
D-eigenvalues of diffusion kurtosis tensors
Journal of Computational and Applied Mathematics
Eigenvalues of a real supersymmetric tensor
Journal of Symbolic Computation
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In this paper, we propose the definition of D-eigenvalue for an arbitrary order tensor related with a second-order tensor D, and introduce the gradient skewness tensor which involves a three-order tensor derived from the skewness statistic of gradient images. As we happen to find out that the skewness of oriented gradients can measure the directional characteristic of illumination in an image, the local illumination detection problem for an image can be abstracted as solving the largest D-eigenvalue of gradient skewness tensors. We discuss the properties of D-eigenvalues, and especially for gradient skewness tensors we provide the calculation method of its D-eigenvalues and D-characteristic polynomial. Some numerical experiments show its effective application in illumination detection. Our method also presents excellent results in a class of image authenticity verification problems, which is to distinguish artificial ''flat'' objects in a photograph.