Dept. de Engenharia Electrotecnica e de Comput., Inst. Superior Tecnico, Lisbon.
IEEE Trans Image Process. 1997;6(8):1089-102. doi: 10.1109/83.605407.
Discontinuity-preserving Bayesian image restoration typically involves two Markov random fields: one representing the image intensities/gray levels to be recovered and another one signaling discontinuities/edges to be preserved. The usual strategy is to perform joint maximum a posterori (MAP) estimation of the image and its edges, which requires the specification of priors for both fields. Instead of taking an edge prior, we interpret discontinuities (in fact their locations) as deterministic unknown parameters of the compound Gauss-Markov random field (CGMRF), which is assumed to model the intensities. This strategy should allow inferring the discontinuity locations directly from the image with no further assumptions. However, an additional problem emerges: the number of parameters (edges) is unknown. To deal with it, we invoke the minimum description length (MDL) principle; according to MDL, the best edge configuration is the one that allows the shortest description of the image and its edges. Taking the other model parameters (noise and CGMRF variances) also as unknown, we propose a new unsupervised discontinuity-preserving image restoration criterion. Implementation is carried out by a continuation-type iterative algorithm which provides estimates of the number of discontinuities, their locations, the noise variance, the original image variance, and the original image itself (restored image). Experimental results with real and synthetic images are reported.
一个表示要恢复的图像强度/灰度级，另一个表示要保留的不连续/边缘。通常的策略是对图像及其边缘进行联合最大后验（MAP）估计，这需要为两个场指定先验。我们不是采用边缘先验，而是将不连续性（实际上是它们的位置）解释为复合高斯-马尔可夫随机场（CGMRF）的确定性未知参数，该随机场被假设为模型的强度。这种策略应该允许直接从图像中推断出不连续性的位置，而无需进一步的假设。然而，出现了一个额外的问题：参数的数量（边缘）是未知的。为了解决这个问题，我们调用了最小描述长度（MDL）原则；根据 MDL，最佳的边缘配置是允许对图像及其边缘进行最短描述的配置。将其他模型参数（噪声和 CGMRF 方差）也视为未知，我们提出了一种新的无监督保持不连续的图像恢复准则。通过一个连续型迭代算法来实现，该算法提供了不连续的数量、位置、噪声方差、原始图像方差和原始图像本身（恢复后的图像）的估计值。报告了使用真实和合成图像的实验结果。
