We propose the definition of D-eigenvalue for an arbitrary order tensor related with a second-order tensor D, and introduce the 2-dimensional 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 image 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. Numerical experiments show its effective application in illumination detection. The method also presents excellent results in a class of image authenticity verification problems, which is to distinguish artificial flat objects in a photograph.
Moreover, a series of algorithms are proposed to describe and analyze the natures of dynamic textures also. Experiments show that the methods are very effective in many applications, such as dynamic background subtraction, modeling, coding and classification of dynamic textures, and crowd density estimation.