Optimal ridge orientation estimator using integrated second directional derivative

In this paper, we discuss a unified theory for and performance evaluation of the ridge direction estimation through the minimization of the integral of the second directional derivative of the gray-level intensity function. The primary emphasis of this paper is on the ridge orientation estimation. The subsequent ridge detection can be performed using the traditional methods of using the zero crossing of the first directional derivative. The performance evaluation of the ridge orientation estimation is performed in terms of the mean orientation bias and orientation standard deviation given the true orientation and the same two measures given the noise standard deviation. We discuss two forms of our new ridge detector— first (ISDDRO-CN) using the noise covariance matrix estimation procedure under colored noise assumption, and the second (ISDDROWN) using the white noise assumption. ISDDRO-CN performs better than the ISDDRO-WN in the presence of strong correlated noise. When the noise levels are moderate it performs as well as ISDDRO-WN. ISDDRO-CN has superior noise sensitivity characteristics. We also compare both forms of our algorithm with the algorithm, Maximum Level Set Extrinsic Curvature (MLSEC) designed by A. López [IEEE Trans. Patter Anal. Mach. Intell. 21, 327–335 (1999)]. © 2005 SPIE and IS&T. [DOI: 10.1117/1.1901683]