A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Pseudo-Polar Based Estimation of Large Translations Rotations and Scalings in Images
WACV-MOTION '05 Proceedings of the IEEE Workshop on Motion and Video Computing (WACV/MOTION'05) - Volume 2 - Volume 02
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In this paper, we study the result of applying a lowpass variant filtering using scaling-rotating kernels to both the spatial and spatial-frequency representations of a two-dimensional (2-D) signal (image). It is shown that if we apply this transformation to a Fourier pair, the two resulting signals can also form a Fourier pair when the filters used in each domain maintain a dual relationship. For a large class of “self-dual” filters, a perfect symmetry exists, so that the lowpass scaling-rotating variant filtering (SRVF) is the same in both domains, thus commuting with the Fourier transform operator. The lowpass SRVF of an image is often referred to as a “foveated” image, whereas its Fourier pair (the lowpass SRVF of its spectrum) can be realized as a local spectrum estimation around the point of attention. This lowpass SRVF is equivalent to a log-polar warping of the image representation followed by a lowpass invariant filtering and the corresponding inverse warping. The use of the log-polar warped representation allows us to extend the one-dimensional (1-D) scale transform to higher dimensions, in particular to images, for which we have defined a scale-rotation invariant representation. We also present an efficient implementation using steerable filters to compute both the foveated image and the local spectrum