Abstract Natural images are usually composed of multiple objects at different scales in flat and slanted regions. Traditional labeling/segmentation approaches based on total variation minimization may produce staircase results with discontinuities and rough boundaries. In this paper, we propose a novel weighted variational model for image labeling/segmentation in the space of functions of bounded Hessian, the weights of which are automatically estimated based on edge information of the observed images. Especially, by minimizing the combined first and second-order regularizer, our model can overcome the shortage of total variation and provide more meaningful results. The efficient alternating direction method of multipliers based algorithm is established, all subproblems of which can be solved by either the fast Fourier transform or closed-form solution. We further introduce the weighted bounded Hessian regularizer into the two-stage segmentation framework for dealing with noisy and blurry image segmentation problems. Numerous experiments are conducted on both two-phase and multi-phase labeling/segmentation problems. By comparing with several state-of-the-art methods both qualitatively and quantitatively, it demonstrates that the proposed models can prominently improve the accuracy of image labeling and segmentation.

中文翻译：

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用于图像标记和分割的加权有界 Hessian 变分模型

摘要 自然图像通常由平坦和倾斜区域中不同尺度的多个对象组成。基于总变异最小化的传统标记/分割方法可能会产生具有不连续性和粗糙边界的阶梯结果。在本文中，我们提出了一种新的加权变分模型，用于有界 Hessian 函数空间中的图像标记/分割，其权重根据观察图像的边缘信息自动估计。特别是，通过最小化组合的一阶和二阶正则化器，我们的模型可以克服总变异的不足并提供更有意义的结果。建立了基于乘法器算法的高效交替方向法，其所有子问题都可以通过快速傅立叶变换或闭式解来解决。我们进一步将加权有界 Hessian 正则化器引入两阶段分割框架，以处理嘈杂和模糊的图像分割问题。对两阶段和多阶段标记/分割问题进行了大量实验。通过与几种最先进的方法进行定性和定量的比较，表明所提出的模型可以显着提高图像标记和分割的准确性。