Revisioning the unification of syntax, semantics and statistics in shape analysis

摘要

Hidden patterns, rendered visible by hindsight, often stand revealed as strong influences. Rama Chellap-pa's lab in the mid to late '80s molded our character and scholarship in more ways than one. Rama ably handled the transition from image processing to computer vision and established an applied math and computing infrastructure from which we continue to benefit. In particular, the themes important to King-Sun Fu-syntax, semantics and statistics-were all debated in Rama's lab at that time. We argue that this triad remains important. With syntactic representations losing mindshare to statistics, we remain in the hunt for unification. And with the syntax versus semantics debate unresolved, it deserves a hearing as well. We offer two themes-uncertainty and interaction-to aid in the process of unification. First, we show that complex wave functions carry probabilistic location information in their magnitude and syntactic (curve) information in their phase while representing uncertainty at a fundamental level. Next, after reviewing work in analytic philosophy, we connect semantics to intentional, mental content. Analytic philosophy reminds us to take human experience seriously but remaining physicalist if possible. To this end, we introduce a nondualist interactionist model of experience, wherein compositional (physical) subjects are constantly shaping and being shaped by a physical world. We then demonstrate that wave functions can accommodate interaction, closely tracking previous work in physics on the measurement problem. The linearity and superposition properties of wave functions allow for literal addition of waves created by human interaction with shapes. Finally, we briefly survey the current situation in the human-computer interaction (HCI) field and argue that mathematical models of interaction akin to those in pattern recognition can aid HCI. We close by arguing that we can follow in Fu's footsteps and incorporate the mathematical modeling of human interaction into pattern recognition.