An algorithm is described for optimal following of the lines in digitized TV pictures. Initially, the picture is subjected to an edge detection operation resulting in short edge-line pieces (strokes). The bifurcation points of the lines in the picture are detected on the basis of variances in stroke angles. A mathematical model using graph theoretical concepts is set up on the arrays of strokes (streaks) to be found among the bifurcation points. The model assumes that the streaks will follow the lines of the picture in an optimal way. An algorithm is given which finds the streaks. The correctness of the algorithm is proved in a pure mathematical way. Experiments with on-line TV pictures show the performance of the algorithm.