Threshold Decomposition of Gray-Scale Morphology into Binary Morphology

Mathematical morphology operations are becoming increasingly important in industrial vision applications for object recognition and defect inspection. Binary morphological operations of dilation and erosion have been successfully extended to gray-scale image processing. But gray-scale morphological operations are difficult to implement in real time. Recently, a superposition property called threshold decomposition and another property called stacking were introduced and have been found to apply successfully to gray-scale morphological operations. This property allows gray-scale signals to be decomposed into multiple binary signals. These signals are processed in parallel, and the results are combined to produce the desired gray-scale result. In this paper, we present the threshold decomposition architecture and the stacking property which allows the implementation of this architecture. Gray-scale operations are decomposed into binary operations with the same dimensionality as the original operations. This decomposition allows gray-scale morphological operations to be implemented using only logic gates in new VLSI architectures, which may significantly improve speed as well as give new theoretical insight into the operations.