Mathematical Morphology Operations for 1D Signals: Erosion, Dilation, Opening, and Closing

MATLAB-implemented mathematical morphology operations for 1D signals—including erosion, dilation, opening, and closing—can effectively filter sharp impulse signals from data streams, making them particularly suitable for vibration signal preprocessing. These operations perform morphological transformations that enhance signal quality by altering signal shapes. The erosion operation, implemented using minimum value filtering with a structuring element, reduces signal peaks and valleys to eliminate noise and sharp impulses. Conversely, the dilation operation employs maximum value filtering to expand signal peaks and valleys, thereby emphasizing signal characteristics. The opening operation, which sequentially applies erosion followed by dilation, effectively removes minor noise and smoothes signal contours. The closing operation, performing dilation first then erosion, fills gaps in signals and connects discontinuous contours through neighborhood analysis. These morphological processing techniques serve as valuable preprocessing tools that significantly improve signal quality and analytical accuracy through pixel-level geometric transformations.