Motion estimation is a common ingredient in many state-of- the-art video processing algorithms, serving as an effective way to capture the spatial-temporal correlation in video signals. However, the robustness of motion estimation often suffers from problems such as ambiguities of motion trajectory (i.e. the aperture problem) and illumination variances. In this paper, we explore a new framework for video processing based on the recently proposed surfacelet transform. Instead of containing an explicit motion estimation step, the surfacelet transform provides a motion-selective subband decomposition for video signals. We demonstrate the potential of this new technique in a video denoising application.
Recently, the classical two-dimensional directional filter banks have been extended to higher dimensions. In this paper, we study one of the key components in this new construction, namely the multidimensional nonsubsampled hourglass filter banks. Starting with a rigorous analysis on the geometry of multidimensional hourglass-shaped passband supports, we propose a novel design for these filter banks in arbitrary dimensions, featuring perfect reconstruction and finite impulse response (FIR) filters. We analyze necessary and sufficient conditions for the resulting filters to achieve good frequency responses, and provide an optimal solution that satisfies these conditions using simplest filters. The proposed filter design technique is verified by a design example in 3-D.
The contourlet transform was proposed as a directional multiresolution image representation that can efficiently capture and represent singularities along smooth object boundaries in natural images. Its efficient filter bank construction as well as low redundancy make it an attractive computational framework for various image processing applications. However, a major drawback of the original contourlet construction is that its basis images are not localized in the frequency domain. In this paper, we analyze the cause of this problem, and propose a new contourlet construction as a solution. Instead of using the Laplacian pyramid, we employ a new multiscale decomposition defined in the frequency domain. The resulting basis images are sharply localized in the frequency domain and exhibit smoothness along their main ridges in the spatial domain. Numerical experiments on image denoising show that the proposed new contourlet transform can significantly outperform the original transform both in terms of PSNR (by several dB’s) and in visual quality, while with similar computational complexity.