Traditional Mean Shift (MS) algorithm can only follow objects with translation and scale change

and fails to handle objects with similarity transformation or complex affine transformation. To address this problem

the paper presents two improved algorithms. The first one focuses on the affine motion. According to the theory of Singular Value Decomposition

the affine matrix can be factored into product of two rotation matrixes and one diagonal matrix

based on which a new candidate model is proposed. With Bhattacharyya coefficient as a similarity function

the object tracking is formulated as an optimization problem

and the corresponding MS algorithm can be derived by calculating the first derivative of the similarity function with respect to affine parameters and setting them to be zero. Furthermore

a new candidate model is proposed that handles similarity transformation

and the corresponding MS algorithm can be obtained that estimates the translation vector and rotation angle. Experimental results show that

the proposed algorithms can track objects with similarity or affine tranformations

and have better tracking performance than the traditional one.