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Single image matting refers to the problem of accurately estimating the foreground object given only one input image. It is a fundamental technique in many image editing applications and has been extensively studied in the literature. Various matting techniques and systems have been proposed and impressive advances have been achieved in efficiently extracting high quality mattes. However, existing matting methods usually perform well for relatively uniform and smooth images only but generate noisy alpha mattes for complex images. The main motivation of this thesis is to develop a new matting approach that can handle complex images. We examine the color sampling and alpha propagation techniques in detail, which are two popular techniques employed by many state-of-the-art matting methods, to understand the reasons why the performance of these methods degrade significantly for complex images. The main contribution of this thesis is the development of two novel matting algorithms that can handle images with complex texture patterns. The first proposed matting method is aimed at complex images with homogeneous texture pattern background. A novel texture synthesis scheme is developed to utilize the known texture information to infer the texture information in the unknown region and thus alleviate the problems introduced by textured background. The second proposed matting algorithm is for complex images with heterogeneous texture patterns. A new foreground and background pixels identification algorithm is used to identify the pure foreground and background pixels in the unknown region and thus effectively handle the challenges of large color variation introduced by complex images. Our experimental results, both qualitative and quantitative, show that the proposed matting methods can effectively handle images with complex background and generate cleaner alpha mattes than existing matting methods.