条件随机域(场)(conditional random fields,简称 CRF,或CRFs),是一种判别式概率模型,是随机场的一种,常用于标注或分析序列资料,如自然语言文字或是生物序列。 如同马尔可夫随机场,条件随机场为具有无向的图模型,图中的顶点代表随机变量,顶点间的连线代表随机变量间的相依关系,在条件随机场中,随机变量 Y 的分布为条件机率,给定的观察值则为随机变量 X。原则上,条件随机场的图模型布局是可以任意给定的,一般常用的布局是链结式的架构,链结式架构不论在训练(training)、推论(inference)、或是解码(decoding)上,都存在效率较高的算法可供演算。

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Weakly supervised segmentation requires assigning a label to every pixel based on training instances with partial annotations such as image-level tags, object bounding boxes, labeled points and scribbles. This task is challenging, as coarse annotations (tags, boxes) lack precise pixel localization whereas sparse annotations (points, scribbles) lack broad region coverage. Existing methods tackle these two types of weak supervision differently: Class activation maps are used to localize coarse labels and iteratively refine the segmentation model, whereas conditional random fields are used to propagate sparse labels to the entire image. We formulate weakly supervised segmentation as a semi-supervised metric learning problem, where pixels of the same (different) semantics need to be mapped to the same (distinctive) features. We propose 4 types of contrastive relationships between pixels and segments in the feature space, capturing low-level image similarity, semantic annotation, co-occurrence, and feature affinity They act as priors; the pixel-wise feature can be learned from training images with any partial annotations in a data-driven fashion. In particular, unlabeled pixels in training images participate not only in data-driven grouping within each image, but also in discriminative feature learning within and across images. We deliver a universal weakly supervised segmenter with significant gains on Pascal VOC and DensePose. Our code is publicly available at https://github.com/twke18/SPML.

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