Algorithm 1 The proposed method:

Input: Model point set $\mathbf{X}$ and scene point set $\mathbf{Y}$.

Output: Transformed model point set.

Initialize: Parameters $T$, $\tau$, $\varsigma$, $\rho$, ${\lambda }_1^{init}$, ${\lambda }_2^{init}$, and $K$, and probabilities $p_{mn}=1/(MN)$.

Begin: Construct kernel matrix, and perform the QR decomposition of model point set.

Repeat: Compute the AD and AD-correspondences using Equations (3) and (4), respectively; Compute the RD and RD-correspondences using Equation (5) and Hungarian method, and assign confidence for RD-correspondences using Equations (6)–(8); Compute the collaborative correspondences and corresponding matrix using Equations (9) and (10), respectively; Compute the transformation parameters of affine and nonaffine parts using Equations (22) and (23), respectively; Update $T=\tau T$, ${\lambda }_1={\lambda }_1^{init}T$, and ${\lambda }_2={\lambda }_2^{init}T$.

Until: Achieve the maximum number of iterations;

Output the transformed points using Equation (14).