Development of Phase Congruency to Estimate the Direction of Maximum Information (tDMI) in Images with Straight Line Segments

This paper aims to better understand a new property of Phase Congruency (PC) based image processing technique. It is illustrated that by optimizing the PC orientation, the direction that contains maximum information can be detected in images with straight line segments. We formulate the Direction of Maximum Information (tDMI) and develop the PC orientation optimization paradigm to compute it in such images. We also develop the Holmholtz Principle and Hough Transform based Line Segment Detection (HP-LSD and HT-LSD) methods to compute tDMI. We apply these methods to identify tDMI in 32 test images corrupted with gaussian and speckle noises with different variances. All methods show fairly good robustness to the noise variance. However, the results show that the PC orientation optimization method detects tDMI with estimation errors significantly lower than those of HP-LSD and HT-LSD methods. Furthermore, PC estimates tDMI directly, whereas, HT-LSD and HP-LSD require to measure lines' widths and lengths. The worst estimation error is obtained by using HT-LSD method, with an average error 102.81% for images with straight line segments of the same thickness. The average error of HP-LSD method over all 32 test images and noise conditions is 47.58%. The average estimation error of PC method over all scenarios is 15.80%, which shows more than 30% and 70% improvement compared to HP-LSD and HT-LSD methods, respectively. The results also show that it is better to consider both maximum and minimum momentums into the PC orientation optimization.