<![CDATA[This study presents an optimized implementation of the gaussian filter in the Canny edge detection algorithm, focusing on reducing computational complexity while balancing power, timing, and resource utilization. Traditional implementations rely on the common subexpression elimination (CSE) algorithm for multiplierless constant multiplication, which results in high logic operations and resource consumption. To address this, we explore the constant array vector multiplication (CAVM) technique with two graph-based algorithms (exact GB and approximate GB). These algorithms offer a novel graph-structured approach to constant multiplication, differing from existing methods by modeling multiple paths to achieve optimal adder reuse. The architectures were implemented using Xilinx system generator (XSG) and evaluated in Vivado 2018.1. Experimental results reveal that both exact GB and approximate GB reduce logic operations and improve timing performance compared to CSE_csd. Among them, approximate GB achieves the fastest computation and lowest LUT utilization, making it the most hardware-efficient design. However, it exhibits the highest power consumption, whereas exact GB offers the best trade-off between speed and power efficiency. This optimization framework shows potential not only in image processing but also in embedded vision systems and low-power digital signal processing (DSP) applications. These findings demonstrate that GB Algorithms can effectively optimize gaussian filter design for real-time image processing applications.]]>
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