In order to handle device matching for analog circuits, some pairs of modules need to be placed symmetrically with respect to a common axis. In this paper, we deal with the module placement with symmetry constraints for analog design using the Transitive Closure Graph-Sequence (TCG-S) representation. Since the geometric relationships of modules are transparent to TCG-S and its induced operations, TCG-S has better flexibility than previous works in dealing with symmetry constraints. We first propose the necessary and sufficient conditions of TCG-S for symmetry modules. Then, we propose a polynomialtime packing algorithm for a TCG-S with symmetry constraints. Experimental results show that the TCG-S based algorithm results in the best area utilization.

Abstract-This paper is concerned with efficient derivation of the medial axis transform of a two-dimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform. The potential valleys are found by following force field, thus, avoiding twodimensional search. The potential field is computed in closed form using the equations of the border segments. The simple Newtonian potential is shown to be inadequate for this purpose. A higher order potential is defined which decays faster with distance than as inverse of distance. It is shown that as the potential order becomes arbitrarily large, the axes approach those computed using the shortest distance to the border. Algorithms are given for the computation of axes, which can run in linear parallel time for part of the axes having initial guesses. Experimental results are presented for a number of examples.

Camera calibration and radial distortion correction are the crucial prerequisites for many applications in image big data and computer vision. Many existing works rely on the Manhattan world assumption to estimate the camera parameters automatically; however, they may perform poorly when there was lack of man-made structure in the scene. As walking humans are the common objects in video surveillance, they have also been used for camera self-calibration, but the main challenges include the noise reduction for the estimation of vanishing points, the relaxation of assumptions on unknown camera parameters, and the radial distortion correction. In this paper, we present a novel framework for camera self-calibration and automatic radial distortion correction. Our approach starts with the reliable human body segmentation that is facilitated by robust object tracking. Mean shift clustering and Laplace linear regression are, respectively, introduced in the estimation of the vertical vanishing point and the horizon line. The estimation of distribution algorithm, an evolutionary optimization scheme, is then utilized to optimize the camera parameters and the distortion coefficients, in which all the unknowns in camera projection can be fine-tuned simultaneously. Experiments on the three public benchmarks and our own captured dataset demonstrate the robustness of the proposed method. The superiority of this algorithm is also verified by the capability of reliably converting 2D object tracking into 3D space.

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