Natural scenes consist of a wide variety of stochastic patterns. While many patterns are represented well by statistical models in two dimensional regions as most image segmentation work assume, some other patterns are fundamentally one dimensional and thus cause major problems in segmentation. We call the former region processes and the latter curve processes. In this paper, we propose a stochastic algorithm for parsing an image into a number of region and curve processes. The paper makes the following contributions to the literature. Firstly, it presents a generative rope model for curve processes in the formm of Hidden Markov Model (HMM). The hidden layer is a Markov chain with each element being an image base selected from an over-complete basis, such as Difference of Gaussians (DOG) or Difference of Offset Gaussians (DOOG) at various scales and orientations. The rope model accounts for the geometric smoothness and phototmetric coherence of the curve processes. Secondly, it integrates both 2D region models, such as textures, splines etc. with 1D curve models under the Bayes framework. Because both region and curve models are generative, they compete to explain input images in a layered representation. Thirdly, it achieves global optimization by effective Markov chain Monte Carlo methods in the sense of maximizing a posterior probability. The Markov chain consists of reversible jumps and diffusions driven by bottom up information. The algorithm is applied to real images with satisfactory results. We verify the results through random synthesis and compare them against segmentations with region processes only.