改进的截断核范数及在视频前背景分离中的应用

Improved Truncated Nuclear Norm and Its Application in Video Foreground-background Separation

视频前背景分离的主要目的是从视频中提取感兴趣目标,但是由于噪声、光照变化等的影响使其仍是计算机视觉等领域最具有挑战性的任务之一。截断核范数(truncated nuclear norm,TNN)算法是一种经典的鲁棒主成分分析(robust principal component analysis,RPCA)算法,被广泛地应用于视频前背景分离。但是,该算法中的截断核范数对传统鲁棒主成分分析中的秩函数逼近度不高,导致其稳定性不强,对一些复杂场景下的视频前背景分离精度不高。针对该问题,本文提出了一种改进的截断核范数(improved truncated nuclear norm,ITNN)算法。该算法首先采用非凸γ范数替代TNN模型中的核范数,并分析了相对于核范数而言,非凸γ范数对秩函数具有更高的逼近度,同时提出了该算法所对应的模型;其次,为了求解提出的模型,本文引入了广义交替方向乘子法(generalized alternating direction method of multipliers,GADMM)对该模型进行求解;最后,将提出的ITNN算法应用于多个公共视频的前背景分离实验中,并通过展示提取不同视频的前景效果,从视觉角度验证了ITNN算法的有效性。同时,计算提出算法和对比算法提取的视频前景的F-measure值,从量化的角度进一步验证了ITNN算法的有效性。另外,实验还记录了各算法的视频前背景分离的运行时间,验证了ITNN算法的效率。总之,本文通过实验验证了提出的ITNN算法在视频前背景分离中的有效性和优越性。

The main purpose of video foreground-background separation is to extract interesting objects from video,but it is still one of the most challenging tasks in the field of computer vision due to the influence of noise and illumination changes.Truncated nuclear norm(TNN)algorithm is a classical robust principal component analysis(RPCA)algorithm,which is widely used in video foreground-background separation.However,the TNN in this algorithm does not approach the rank function of the traditional robust principal component analysis better,resulting in weak stability and low accuracy of video foreground-background separation in some complex scenes.To solve this problem,an improved ITNN method is proposed.Firstly,the method adopts the nonconvexγnorm to replace the nuclear norm of TNN method.The problem that the nonconvexγnorm approaches the rank function more closely than the nuclear norm is analyzed,and the corresponding model of ITNN is proposed.Secondly,in or-der to solve the proposed ITNN model,the generalized alternating direction method of multipliers(GADMM)is introduced.Finally,the proposed ITNN is applied to the experiments of video foreground-background separation for different public videos.The foreground which is extracted from different videos by different methods verifies the effect of our proposed ITNN methods.Meanwhile,the F-measure values and running time are also recorded for extracting foreground from different videos by different methods.These all verify the effect of the proposed ITNN method.In summary,experiments show that the proposed ITNN algorithm is effective and superior in video foreground and background separation.