Most existing methods for object segmentation in computer vision are formulated as a labeling task. This, in general, could be transferred to a pixel-wise label assignment task, which is quite similar to the structure of hidden Markov random field. In terms of Markov random field, each pixel can be regarded as a state and has a transition probability to its neighbor pixel, the label behind each pixel is a latent variable and has an emission probability from its corresponding state. In this paper, we reviewed several modern image labeling methods based on Markov random field and conditional random Field. And we compare the result of these methods with some classical image labeling methods. The experiment demonstrates that the introduction of Markov random field and conditional random field make a big difference in the segmentation result.
The first time that Markov random field is introduced for segmentation is in @cite_23 , where it's only for the application of medical image. Then the attempt of modeling segmentation task with Markov random field is largely growing due to the similarity of their representation. But learning and inference for Markov random field is quite computationally expensive so that lots of approximation and learning scheme is invented for obtaining the robust segmentation result. In addition to Markov random field, one point worth to highlight is conditional random field, which in @cite_4 @cite_17 @cite_12 is heavily used for segmentation in the recent decades. The benefit of conditional random field is that, for image labeling task, we actually don't care about the joint distribution of image pixel. So modeling only the label conditioned on image observation is enough and will decrease huge mount of parameters to estimate. Most recently, with the revolution of deep learning, conditional random field is usually used as a post-precessing step in @cite_21 to refine the segmentation result produced by deep convolutional neural network. More attempt @cite_7 etries to incorporate conditional random field into network architecture instead of post processing and achieve better result.
@cite_4 @cite_7 @cite_21 @cite_23 @cite_12 @cite_17
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In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation as a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The algorithm constructs the parsing graph and re-configures it dynamically using a set of moves, which are mostly reversible Markov chain jumps. This computational framework integrates two popular inference approaches--generative (top-down) methods and discriminative (bottom-up) methods. The former formulates the posterior probability in terms of generative models for images defined by likelihood functions and priors. The latter computes discriminative probabilities based on a sequence (cascade) of bottom-up tests filters. In our Markov chain algorithm design, the posterior probability, defined by the generative models, is the invariant (target) probability for the Markov chain, and the discriminative probabilities are used to construct proposal probabilities to drive the Markov chain. Intuitively, the bottom-up discriminative probabilities activate top-down generative models. In this paper, we focus on two types of visual patterns--generic visual patterns, such as texture and shading, and object patterns including human faces and text. These types of patterns compete and cooperate to explain the image and so image parsing unifies image segmentation, object detection, and recognition (if we use generic visual patterns only then image parsing will correspond to image segmentation (Tu and Zhu, 2002. IEEE Trans. PAMI, 24(5):657--673). We illustrate our algorithm on natural images of complex city scenes and show examples where image segmentation can be improved by allowing object specific knowledge to disambiguate low-level segmentation cues, and conversely where object detection can be improved by using generic visual patterns to explain away shadows and occlusions. Markov and Conditional random fields (CRFs) used in computer vision typically model only local interactions between variables, as this is computationally tractable. In this paper we consider a class of global potentials defined over all variables in the CRF. We show how they can be readily optimised using standard graph cut algorithms at little extra expense compared to a standard pairwise field. This result can be directly used for the problem of class based image segmentation which has seen increasing recent interest within computer vision. Here the aim is to assign a label to each pixel of a given image from a set of possible object classes. Typically these methods use random fields to model local interactions between pixels or super-pixels. One of the cues that helps recognition is global object co-occurrence statistics, a measure of which classes (such as chair or motorbike) are likely to occur in the same image together. There have been several approaches proposed to exploit this property, but all of them suffer from different limitations and typically carry a high computational cost, preventing their application on large images. We find that the new model we propose produces an improvement in the labelling compared to just using a pairwise model. Are we using the right potential functions in the Conditional Random Field models that are popular in the Vision community? Semantic segmentation and other pixel-level labelling tasks have made significant progress recently due to the deep learning paradigm. However, most state-of-the-art structured prediction methods also include a random field model with a hand-crafted Gaussian potential to model spatial priors, label consistencies and feature-based image conditioning. In this paper, we challenge this view by developing a new inference and learning framework which can learn pairwise CRF potentials restricted only by their dependence on the image pixel values and the size of the support. Both standard spatial and high-dimensional bilateral kernels are considered. Our framework is based on the observation that CRF inference can be achieved via projected gradient descent and consequently, can easily be integrated in deep neural networks to allow for end-to-end training. It is empirically demonstrated that such learned potentials can improve segmentation accuracy and that certain label class interactions are indeed better modelled by a non-Gaussian potential. In addition, we compare our inference method to the commonly used mean-field algorithm. Our framework is evaluated on several public benchmarks for semantic segmentation with improved performance compared to previous state-of-the-art CNN+CRF models. Infinite Hidden Markov Random Fields have been proposed for image segmentation as a solution to the problem of automatically determining the number of regions in an image; however, the model does not maintain identity of segmented regions among multiple images. In order to identify segmented regions in images, we developed Hierarchical Dirichlet Process Markov Random Fields. Our model maintains global identification of segmented regions in multiple images by incorporating the idea of hierarchical modeling and automatically determines the number of segmented regions in each image. We show an experimental comparison between the previous model and our proposed model by changing the observation features from RGB value to color histogram features.