In this paper, we present an algorithm for parsing natural images into middle level vision representations–regions, curves, and curve groups (parallel curves and trees). This algorithm is targeted for an integrated solution to image segmentation and curve grouping through Bayesian inference. The paper makes the following contributions. (1) It adopts a layered (or 2.1D-sketch) representation integrating both region and curve models which compete to explain an input image. The curve layer occludes the region layer and curves observe a partial order occlusion relation. (2) A Markov chain search scheme Metropolized Gibbs Samplers (MGS) is studied. It consists of several pairs of reversible jumps to traverse the complex solution space. An MGS proposes the next state within the jump scope of the current state according to a conditional probability like a Gibbs sampler and then accepts the proposal with a Metropolis-Hastings step. This paper discusses systematic design strategies of devising reversible jumps for a complex inference task. (3) The proposal probability ratios in jumps are factorized into ratios of discriminative probabilities. The latter are computed in a bottom-up process, and they drive the Markov chain dynamics in a data-driven Markov chain Monte Carlo framework. We demonstrate the performance of the algorithm in experiments with a number of natural images.