**Abstract:**
Minimal path techniques can efficiently extract geometrically curve-like structures by finding the path with minimal accumulated cost between two given endpoints. The conventional minimal path techniques suffer from some notable problems such as endpoint problem, shortcut problem and accumulation problem. Here a Minimal path techniques that can efficiently extract geometrically curve-like structures is find out as a solution called Minimal Path Propagation with Backtracking (MPP-BT). The MPP-BT method first applies a minimal path propagation from one single starting point and then, at each reached point, traces certain steps back to the starting point. The backtracking in the proposed approach goes beyond the basic tracking backward operation by fully exploiting the information on visiting preference and cost increments during this backtracking process to give an overall effective structure extraction. A robust stopping strategy is built by evaluating the evolution of cost increments in backtracking during the propagation. It only requires a coarsely user-defined starting point for the whole structure extraction and is robust to parameter setting. The three problems can be well solved by the discriminative revisiting and the cost resetting scheme along the backtracking paths in the proposed MPP-BT method. This MPP-BT algorithm was tested on 2D crack images and 2D vessel images.

**Keywords:**
Curve-like structure, centerline, minimal path tracking, backtracking, endpoint problem, shortcut problem, accumulation problem.