Many of the computer vision problems at the low to intermediate levels can be considered to be labeling problems. Defined over the image plane, the labels form a function mapping that uniquely maps a set of pixels onto an attribute label. The quality of the labeling is signified with an energy function – a functional of the label function. Depending on the applications, energy functions have various different forms in their terms and relationships but have some common categories in their forms and solution methods. Finding correct representations for energy function and energy minimization methods (Heyden 2013; Szeliski *et al*. 2008) are key issues in vision problems.

Energy functions are found in many different domains, including optimization, Bayesian estimation, network flow (Ahuja *et al*. 1993; Cormen *et al*. 2001), and thermodynamics domains. In optimization domains, energy functions are known by various names, such as objective functions, loss functions, cost functions, and utility functions. The energy function used in thermodynamics is called (Helmholtz or Gibbs) free energy (Wikipedia 2013h) and equilibrium is the state in which the energy is at a minimum. In Bayesian estimation, the energy function is the likelihood of the ensemble probability, and the goal is often to determine the maximum a posteriori (MAP) estimate, the area where the energy is at a minimum. In a flow network, the energy is the maximum flow from the source to the sink and the purpose ...

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