Revolutionizing Two-Dimensional Pattern Arrangement: Innovative Image Processing Approaches

The efficient arrangement of patterns on a substrate surface is of paramount importance across diverse domains, including manufacturing, design, nanotechnology, and printed electronics. This paper introduces three distinct strategies for pattern arrangement within the realm of two-dimensional cutting and packing challenges. Firstly, for irregular patterns, we have developed a modified genetic algorithm that effectively determines the spatial relationships between patterns, facilitating subsequent packing processes. Secondly, we present the "MaxiRectPack" method designed for rectangular patterns. This method utilizes partitioning techniques and a variety of orientation schemes to maximize pattern packing efficiency. Lastly, we propose a technique based on normalized 2-D cross-correlation for patterns of diverse shapes, allowing precise placement while accounting for variations in substrate and pattern energy. These methodologies are adaptable, catering to irregular, rectangular, and diverse pattern shapes, offering versatile solutions for pattern placement in the context of two-dimensional cutting and packing. With a strong emphasis on resource conservation and spatial efficiency, this research equips practitioners and researchers with practical tools for optimizing material utilization and pattern arrangement on substrates.