Po Duncan D Y, Do Minh N
Department of Electrical and Computer, Engineering, University of Illinois at Urbana-Champaign, 61801, USA.
IEEE Trans Image Process. 2006 Jun;15(6):1610-20. doi: 10.1109/tip.2006.873450.
The contourlet transform is a new two-dimensional extension of the wavelet transform using multiscale and directional filter banks. The contourlet expansion is composed of basis images oriented at various directions in multiple scales, with flexible aspect ratios. Given this rich set of basis images, the contourlet transform effectively captures smooth contours that are the dominant feature in natural images. We begin with a detailed study on the statistics of the contourlet coefficients of natural images: using histograms to estimate the marginal and joint distributions and mutual information to measure the dependencies between coefficients. This study reveals the highly non-Gaussian marginal statistics and strong interlocation, interscale, and interdirection dependencies of contourlet coefficients. We also find that conditioned on the magnitudes of their generalized neighborhood coefficients, contourlet coefficients can be approximately modeled as Gaussian random variables. Based on these findings, we model contourlet coefficients using a hidden Markov tree (HMT) model with Gaussian mixtures that can capture all interscale, interdirection, and interlocation dependencies. We present experimental results using this model in image denoising and texture retrieval applications. In denoising, the contourlet HMT outperforms other wavelet methods in terms of visual quality, especially around edges. In texture retrieval, it shows improvements in performance for various oriented textures.
轮廓波变换是一种使用多尺度和方向滤波器组的新型二维小波变换扩展。轮廓波展开由多尺度下不同方向的基图像组成，具有灵活的宽高比。鉴于这组丰富的基图像，轮廓波变换有效地捕捉了自然图像中的主要特征——平滑轮廓。我们首先详细研究自然图像轮廓波系数的统计特性：使用直方图估计边缘分布和联合分布，并使用互信息来衡量系数之间的相关性。这项研究揭示了轮廓波系数高度非高斯的边缘统计特性以及强的位置间、尺度间和方向间相关性。我们还发现，在其广义邻域系数的幅度条件下，轮廓波系数可以近似建模为高斯随机变量。基于这些发现，我们使用具有高斯混合的隐马尔可夫树（HMT）模型对轮廓波系数进行建模，该模型可以捕捉所有的尺度间、方向间和位置间相关性。我们展示了在图像去噪和纹理检索应用中使用该模型的实验结果。在去噪方面，轮廓波HMT在视觉质量上优于其他小波方法，尤其是在边缘附近。在纹理检索中，它在各种方向纹理的性能上有提升。
