Fast online high-order time lacunarity for characterizing active sonar echographs of harbor environment

High-order time lacunarity (HOT-Lac) is an effective feature for characterizing active sonar echographs of harbor environments. However, it involves high computational complexity of loop summations. Motivated by the idea of integral image, this Letter extends an echo-intensity integral sequence, a representation of filtering with time domain recursion, permitting fast and online updates of HOT-Lac in a constant number of operations. Evaluated by a set of real-world harbor data, the proposed method is capable of computing HOT-Lac extremely rapidly while maintaining equivalent area under curve performances to its off-line counterpart, demonstrating its potential for real-time surveillance of the harbor.