Background subtraction via truncated nuclear norm minimization

The background subtraction is one of the main topics in video analysis. Among the various conventional approaches related to this topic, low-rank and sparse decomposition based method has shown a great ability to decompose foreground and background. This method approximates the matrix rank by robust principal component analysis via the nuclear norm minimization. However, since the nuclear norm based method minimizes sum of all singular values, it has limitation that the low-rank may not be well approximated. Especially when the number of input image sequences is limited, nuclear norm minimization cannot clearly separate background and objects. In this paper, to solve this problem, a truncated nuclear norm based method is proposed. This method minimizes the sum of the truncated singular values except the largest few values corresponding to low-rank of background image sequence matrix. Since the rank of background sequence is known to be 1, by minimizing sum of singular values except the largest value only, the more accurate results could be obtained even when the number of frame is limited. The experimental results confirm this efficiency of the proposed method.