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As a requisite of content-based multimedia technologies, video-object (VO) extraction is a very important yet challenging task. In recent years, classification-based approaches have been proposed to handle VO extraction as a classification problem, for which some promising results have been reported using adaptive neural networks and support vector machines (SVMs). We observe that some training samples in video sequences exhibit partial or ambiguous class memberships, which does not comply with standard membership setups. This problem is addressed in the context of SVM in this paper. By reformulating SVM for the noncrisp classification scenario, we propose a machine which is capable of dealing with binary (or hard) as well as real-valued (or soft) class memberships. The new machine, which is named Soft SVM, is integrated into a VO extraction method, and its effectiveness is demonstrated by the experimental results.