One-scan algorithm for arbitrarily oriented 1-D morphological opening and slope pattern spectrum

This paper presents a fast, one-scan algorithm for 1-D morphological opening on 2-D support. The algorithm is further extended to compute the pattern spectrum during a single image scan. The structuring element (SE) can be oriented under arbitrary angle that makes it possible to perform different orientation-involved image analysis, such as the local angle extraction, directional granulometry, etc. The algorithm processes an image in constant time regardless the SE orientation and size in one scan, with minimal latency and very low memory requirements. For pattern spectra, the C-implementation yields an experimental speed-up of 27× compared to other suitable solutions. Aforementioned properties allow for efficient implementation on hardware platforms such as GPU or FPGA that opens a new opportunity of parallel computation, and consequently, further speed-up.