Polygonal approximation using integer particle swarm optimization

Polygonal approximation is an effective yet challenging digital curve representation for image analysis, pattern recognition and computer vision. This paper proposes a novel approach, integer particle swarm optimization (iPSO), for polygonal approximation. When compared to the traditional binary version of particle swarm optimization (bPSO), the new iPSO directly uses an integer vector to represent the candidate solution and provides a more efficient and convenient means for solution processing. The velocity and position updating mechanisms in iPSO not only have clear physical meaning, but also guarantee the optimality of the solutions. The method is suitable for polygonal approximation which could otherwise be an intractable optimization problem. The proposed method has been tested on commonly used synthesized shapes and lake contours extracted from the maps of four famous lakes in the world. The experimental results show that the proposed iPSO has better solution quality and computational efficiency than the bPSO-based methods and better solution quality than the other state-of-the-art methods. Digital curve representation is an important topic in image analysis, pattern recognition and computer vision. After a contour is extracted from an object in the scene, a sequence of coordinate points can be obtained by traversing along the contour. This sequence of points can be viewed as a digital curve. It contains a large amount of shape information of the object [1], especially around the corners. Effective representation of a digital curve facilitates the subsequent image analysis tasks, such as shape matching, object recognition and image retrieval. Polygonal approximation is an effective digital curve representation method, providing a piecewise-linear representation of a curve by dividing the curve into a number of connected straight line segments. It removes a large number of redundant points from the digital curve while preserving major characteristics. As an example, take a square-shaped digital curve with 1000 points. Its optimal polygonal approximation consists of just the four corner points, which represents the same 1000-point curve without loss of shape information. Seeking the optimal approximation of a general digital curve is a challenging and unsolved problem however, because it is a combinatorial optimization problem without an