基于双向稀疏表示的鲁棒目标跟踪算法∗

摘要

At present the visual tracking model based on sparse representation is mainly divided into two types: one is to use the template set to reconstruct candidate samples, which is called forward model; the other is to project the template set into a candidate space, which is called reverse model. What the two models have in common is to compute the sparse correlation coefficient matrix of candidate sample and template set. Based on this, the paper establishes a bidirectional cooperative sparse representation tracking model. Using L2-norm constraint item, the forward and reverse sparse correlation matrix coefficients could be uniformly convergent. In comparison to conventional unidirectional sparse tracking model, bidirectional sparse tracking model could fully excavate the sparse mapping relation of the whole candidate sample and template set. And the candidate that scores highest in the sparse mapping table for the positive and negative templates is the tracking result. Based on the accelerated proximal gradient fast method, the paper derives the optimum solution (in matrix form) of bidirectional sparse tracking model. As a result, it allows the candidates and templates to be calculated in parallel, which can improve the calculation efficiency to some extent. Numerical examples show that the proposed tracking algorithm has certain priority over against the conventional unidirectional sparse tracking methods.%目前，基于稀疏表示的目标跟踪通常为在目标模板集上重构候选样本的正向模型或者在候选样本集上描述目标模板的反向模型。两个模型的共同点是均需计算候选样本与模板集合之间的稀疏相关系数矩阵。基于此，建立了一个双向联合稀疏表示的跟踪模型，该模型通过L2范数约束正反向稀疏相关系数矩阵达到一致收敛。与之前的单向稀疏表示模型相比，双向稀疏表示跟踪模型在正反向联合求解框架下可以更加充分地挖掘所有候选样本与模板集之间的稀疏映射关系，并将稀疏映射表上对正负模板区分度最好的候选样本作为目标。基于加速逼近梯度(accelerated proximal gradient)快速算法，以矩阵形式推导了双向稀疏表示模型的求解框架，使得候选样本集和目标模板集均以矩阵方式并行求解，在一定程度上提高了计算效率。实验数据表明所提出的算法优于传统的单向稀疏表示目标跟踪算法。