Critical point detection (CPD) of planar curves can be well applied in approaching of curves using poly-lines

which has very important applications in image recognition

measurement and analysis.As digital lines are commonly composed by several continuous short lines

which are horizontal (k is 0)

vertical (k is 1) and ±45°(k is ±1) lines.We call these four lines basic lines and define the maximum length of every basic line as corresponded directional pixel length (DPL)

which are further denoted as Lx

Ly

L+ and L-.Furthermore

four theorems on DPL are proposed

based on which

an automatic algorithm for CPD is also presented.The comparisons of algorithms from Ansari-Huang

Zhu-Chirlian and ours was showed.The satisfactory experimental results have demonstrated that our algorithm has apparent advantages in reducing critical point number and spatial-temporal spending.