Emergence of Border & Surface Completion (both Spatial and Temporal) in a Flowcentric Model of Narrow Slit Viewing David Pierre Leibovitz (dpleibovitz@ieee.org) & Robert L. West (robert_west@carleton.ca) Institute of Cognitive Science, 2201 DT, Carleton University 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6 Canada Abstract In this paper, we describe a model of narrow slit viewing that deals with both spatial and temporal completion for borders and surfaces. The model is based on functionality derived from the dynamic interactions of a neural model. We contrast this model with FACADE, which models vision using neural models of modules corresponding to functionality. Keywords: Border completion; Emergence; Emergic Cognitive Model; FACADE; Flowcentric; Slit Viewing; Spatial; Surface completion; Temporal; Unified Modeling. Introduction With regard to border and surface completion, the complexity of FACADE (e.g., Grossberg & Rudd, 1992) will be contrasted to the simplicity of ECM (Leibovitz, 2013a). However, it must be stressed that this paper is less about comparing these models and more about opening up epistemic options for analysis and decomposition as well as in explicating unrecognized modeling tradeoffs. To ground the discussion, we will mostly focus on demonstrating and explaining the emergence of border and surface completion effects within a flowcentric model of narrow slit viewing (Leibovitz, 2013b). FACADE exemplifies a class of connectionist models with large-grained systems engineered to directly and isomorphically realize large-grained functions such as border and surface completion under motion. Although, the model is still being refined (Grossberg, Léveillé, & Versace, 2011; Grossberg, 2010), it represents a style of modeling and analysis prevalent throughout cognitive science and neurobiology. In contrast, ECM uses the interactions between finer-grained, but more complex units to create emergent functions capable of producing the same phenomena. As such, ECM can be thought of representing a dynamic systems approached based on a lower level of analysis. The goal of the ECM approach is to generate high level functional complexity as an emergent property of relatively simple, lower level interactions FACADE FACADE class models are quite complex in terms of the number of unique neural units, subsystems and parameters. For example, FACADE includes a static boundary contour system (BCS), a feature contour system (FCS), as well as a separate motion BCS. An example application of FACADE required 6 high-level kinds of neural units or subsystems involving 10 different interactions with parameters governed under 36 equations (Hu, Zhou, & Wang, 2011). However, in general, these solutions are not robust and highly sensitive to parameter changes. A more detailed model lists 62 parameters under the control of 43 equations (Berzhanskaya, Grossberg, & Mingolla, 2007). These models use low-level neural circuitry to produce distinct higher-level functions that can be thought of as distinct modules that interact. ECM ECM is also a connectionist model but decomposes behaviour into finer functional grains that correspond to recurrent interactions of bottom-up, top-down and lateral flows of information. ECM has a single Receptive Field (RF) unit that is the locus of two functions and determines their interaction (see Figure 1). The RFs are arranged in a spatiotemporal hierarchy as indicated in Figure 2 (and Figure 7), but the behaviour of ECM can be fully understood by focusing solely on the RFs as we do in this paper. On the visual stimuli processing side within each RF (the right hand side), the bottom-up, top-down and lateral flows of information interact according to the handling missing data function. This will be responsible for spatial completion according to the following algorithm: if a bottom-up visual value is missing (due to an eye blink or blind spot) then use a corresponding lateral value, and if that value is also missing, use a corresponding top-down value. Then send the value back out. The single output port directs the value up, down and laterally with additional local fan-out to allow for visual content to “shift”. While the content of these three flows is similar, their usage differs. For example, lateral flows have the same spatial resolution as their RFs and produce memory- like effects. Spatiotemporal summation occurs naturally at all input ports, and so the RF has no further computation to perform. Receptive Field (Emergic Unit) Out D Shift Shift L U Figure 1: Functional Interactions in an Emergic RF Shift Shift Shift Distribution Processing Visual Flow Processing