Open bisimilarity is an equivalence relation for the π-calculus that is also congruence, making it suitable to use in compositional reasoning for mobile processes and communication protocols. The original definition of open bisimilarity, due to Sangiorgi, does not account for the mismatch operator, that is crucial in modelling real-world protocols. When mismatch is present, the congruence property no longer holds for open bisimilarity. In a LICS 2018 paper, Horne et al. proposed an extension of open bisimilarity, using a history-indexed class of relations, to address this problem. That definition, however, turns out to be non-compositional as we shall demonstrate in this paper. This paper presents a new definition of open bisimilarity in the π-calculus that incorporates mismatch. This is achieved by augmenting the transition semantics of the π-calculus with an explicit assumption about name distinctions, and by requiring that open bisimulation to be closed under an arbitary extension of the name distinctions assumption. We then prove that the resulting open bisimilarity is both an equivalence relation and a congruence.

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods—AutoStep MCMC—that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is $\pi$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

The lines in topographic maps are difficult to be separated from each other because of their confusing colors. To solve this problem, we propose a novel line separation method using their regional color and spatial information. Firstly, we divide the lines into lots of circular regions with a certain diameter, and consider these regions as the basic processing units. Then based on a new concept of regional color confusion, we classify all the divided circular regions into two kinds of regions by whether the color is pure or mixed. Further, for pure color regions, a fuzzy clustering algorithm with Gaussian kernel can be used to cluster them into different lines based on their color information. Meanwhile, we determine the memberships of the mixed color regions according to their spatial relations with the clustered pure color regions. The concept of regional color confusion is proposed to reduce the influences of the confusing colors to line separation, and the spatial relations are utilized to solve the problems of the membership determination of the mixed color regions. The experimental results demonstrate that our method can achieve higher accuracy compare with other two state-of-the-art methods, which provides a novel idea for line element segmentation from scanned topographic maps.

Superpixels have been widely used in lots of computer vision and image processing tasks but rarely used in topographic map processing due to the complex distribution of geographic elements in this kind of images. We propose a novel superpixel-generating method based on guided watershed transform (GWT). Before GWT, the cues of geographic element distribution and boundaries between different elements need to be obtained. A linear feature extraction method based on a compound opposite Gaussian filter and a shear transform is presented to acquire the distribution information. Meanwhile, a boundary detection method, which based on the color-opponent mechanisms of the visual system, is employed to get the boundary information. Then, both linear features and boundaries are input to the final partition procedure to obtain superpixels. The experiments show that our method has the best performance in shape control, size control, and boundary adherence, among all the comparison methods, which are classic and state of the art. Furthermore, we verify the low complexity and low cost of memory in our method through experiments, which makes it possible to deal with large-scale topographic maps.

Linear features are difficult to be separated from complicated background in color scanned topographic maps, especially when the color of linear features approximate to that of background in some particular images. This paper presents a method, which is based on energy density and the shear transform, for the separation of lines from background. First, the shear transform, which could add the directional characteristics of the lines, is introduced to overcome the disadvantage that linear information loss would happen if the separation method is used in an image, which is in only one direction. Then templates in the horizontal and vertical directions are built to separate lines from background on account of the fact that the energy concentration of the lines usually reaches a higher level than that of the background in the negtive image. Furthermore, the remaining grid background can be wiped off by grid templates matching. The isolated patches, which include only one pixel or less than ten pixels, are removed according to the connected region area measurement. Finally, using the union operation, the linear features obtained in different sheared images could supplement each other, thus the lines of the final result are more complete. The basic property of this method is introducing the energy density instead of color information commonly used in traditional methods. The experiment results indicate that the proposed method could distinguish the linear features from the background more effectively, and obtain good results for its ability in changing the directions of the lines with the shear transform.