clifford algebra’s geometric product properties in image-processing and its efficient implementation

Clifford algebra (ca) is an effective substitute for classic algebra as the modern generation of mathematics. however, massive computational loads of ca-based algorithms have hindered its practical usage in the past decades. nowadays, due to magnificent developments in computational architectures and systems, ca framework plays a vital role in the intuitive description of many scientific issues. geometric product is the most important ca operator, which created a novel perspective on image processing problems. in this work, geometric product and its properties are discussed precisely, and it is used for image partitioning as a straightforward instance. efficient implementation of ca operators needs a specialized structure, therefore a hardware architecture is proposed that achieves 25x speed-up in comparison to the software approach.