Flow and transport phenomena in porous media are the governing processes in many natural and industrial systems. Not only do these flow and transport phenomena occur on different space and time scales, but it is also the porous medium itself which is heterogeneous where the heterogeneities are present on all spatial scales. We consider a large domain with randomly distributed heterogeneities wh...

We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables in the second layer. Numerical experiments demonstrate that this two layer convolution network, which involves no learning and no max pooling, performs effici...

Xiaohui Xue Dept. of Computer Science, Harbin Institute of Technology, Harbin, Heilongjiang, P.R.China [email protected] The mainstream of image compression research has been based on the Shannon Information Theory for years. In image data, there exist statistical redundancy, knowledge redundancy and psychophysiological redundancy, and the latter two cannot be handled by Shannon theory. Th...

In this paper, two new geodesic distance transforms for gray-scale images are presented. The first transform, the Distance Transform on Curved Space (DTOCS), performs the calculation with integer numbers. The second transform, the Weighted Distance Transform on Curved Space (WDTOCS), gives a weighted distance map with real numbers for an arbitrary gray-value image. Both transforms give a distan...

This paper describes a novel image transform called Multi-Scale Autoconvolution which is invariant with respect to affine transformations of the spatial image coordinates. The transform can be applied directly to image patches without segmentation. Algebraically, the transform is simple requiring only rescaling of the image and computation of two-dimensional convolutions that can be performed e...

in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with...