On Visual Semantic Algebra (VSA): A Denotational Mathematical Structure for Modeling and Manipulating Visual Objects and Patterns

A new form of denotational mathematics known as Visual Semantic Algebra (VSA) is presented for abstract visual object and architecture manipulations. A set of cognitive theories for pattern recognition is explored such as cognitive principles of visual perception and basic mechanisms of object and pattern recognition. The cognitive process of pattern recognition is rigorously modeled using VSA and RealTime Process Algebra (RTPA), which reveals the fundamental mechanisms of natural pattern recognition by the brain. Case studies on VSA in pattern recognition are presented to demonstrate VAS’ expressive power for algebraic manipulations of visual objects. VSA can be applied not only in machinable visual and spatial reasoning, but also in computational intelligence as a powerful man-machine language for representing and manipulating visual objects and patterns. On the basis of VSA, computational intelligent systems such as robots and cognitive computers may process and inference visual and image objects rigorously and efficiently. DOI: 10.4018/978-1-4666-0261-8.ch005