Summary: Based on the basic idea of the homotopy perturbation method (HPM) which was proposed by J. He
[Comput. Methods Appl. Mech. Eng. 178, No. 3–4, 257–262 (1999; Zbl 0956.70017
)], a target controllable image segmentation model and the corresponding multiscale wavelet numerical method are constructed. Using the novel model, we can get the only right object from the multiobject images, which is helpful to avoid the oversegmentation and insufficient segmentation. The solution of the variational model is the nonlinear partial differential equation deduced by the variational approach. So, the bottleneck of the variational model on image segmentation is the lower efficiency of the algorithm. Combining the multiscale wavelet interpolation operator and HPM, a semianalytical numerical method can be obtained, which can improve the computational efficiency and accuracy greatly. The numerical results on some images segmentation show that the novel model and the numerical method are effective and practical.