Correction to: International Journal of Computer Vision

https://doi.org/10.1007/s11263-025-02468-6

The original publication of this article inadvertently omitted the text “we do the force analysis on an infinitesimal segment ΔS in [x, x + Δx] of contour curve. In principle, the movement of small segment would incur by two endpoint tension forces along the tangential direction of contour curve, while the adjacent segments pull the two endpoints. Formally, we denote the left/right tensions with T1, T2, respectively. Since the curve vibration is transverse, i.e., the only change of u(x), there is no movement in the x direction. Moreover, in the condition of micro movement, the horizontal angles have ϑ1, ϑ2 → 0, and the force magnitude has T1 = T2 = T, where Ti = ∥Ti∥. Therefore, the force on contour segment ΔS could be represented as:” at the end of Contour curve analysis in Sect. 3.

The correct and complete Contour curve analysis should read as follows:

Contour curve analysis: As those conventional snake based models, we reconsider the boundary curve (or shape) of object contour. Contrastively, we inspect the motion evolution of contour curve from the view of string vibration. Relevant to physical motion, as shown in Fig. 1(b), we do the force analysis on an infinitesimal segment ΔS in [x, x + Δx] of contour curve. In principle, the movement of small segment would incur by two endpoint tension forces along the tangential direction of contour curve, while the adjacent segments pull the two endpoints. Formally, we denote the left/right tensions with T1, T2, respectively. Since the curve vibration is transverse, i.e., the only change of u(x), there is no movement in the x direction. Moreover, in the condition of micro movement, the horizontal angles have ϑ1, ϑ2 → 0, and the force magnitude has T1 = T2 = T, where Ti = ∥Ti∥. Therefore, the force on contour segment ΔS could be represented as:

The Original article has been corrected.