Scale-invariant measurability in Wiener space

Scale-invariant growth processes in expanding space.

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behavior depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in un...

Time-Limited Time-Invariant Wiener Filtering

Invariant image descriptors and affine morphological scale-space

In this research report we propose a novel approach to build interest points and descriptors which are invariant to a subclass of affine transformations. Scale and rotation invariant interest points are usually obtained via the linear scale-space representation, and it has been shown that affine invariance can be achieved by warping the smoothing kernel to match the local image structure. Our a...

Generalized Wiener Reconstruction of Images from Colour Sensor Data Using a Scale Invariant Prior

An algorithm is described for reconstructing images from colour sensor samples, which need not be aligned nor conform to a rectangular sampling geometry. The algorithm has applications in demosaicing digital camera CFA data, and processing other imaging modalities such as scanned images and captured video. A unique scale invariant WSS prior model is described for the uncorrupted surface spectra...

Cumulants on the Wiener Space

We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual “graph/diagram computations” adopted in most of the ...