Ronald W. Ferguson

Statement of Research Interests

I am interested in understanding the nature of visual thinking. My research investigates the role of spatial relations in symmetry detection and in other visual reasoning tasks.  This research has both cognitive and applied aspects.  In my cognitive research, I have designed, implemented, and explored the psychological implications of a new computer-based model of symmetry detection, called MAGI. In my more applied research, I have used both MAGI and a spatial reasoning engine called GeoRep to build more flexible and effective computer reasoners for diagrams and sketches.

A Computer Model of Symmetry Detection

The MAGI model is based on a new framework that I have proposed for symmetry and repetition detection.  This framework utilizes some simple but powerful ideas. In this framework, the visual system detects symmetry and repetition by aligning sets of perceptual relations. This alignment uses a structure mapping process, similar to that proposed by Dedre Gentner for analogy and similarity comparisons.  This means that symmetry is detected not by mentally folding or rotating a figure about an axis, but by aligning maximally interconnected systems of similar spatial relations within the figure.  For example, the symmetry of a star-shaped figure is detected by aligning the corners and other visual elements based on common concavity, placement, connectivity or other qualitative characteristics.

The MAGI computer model implements this framework.  The MAGI program can take a line-drawn figure, detect a set of qualitative spatial relations (using the GeoRep system described below), and then determine the qualitative symmetry of the figure by aligning systems of those relations.  This model has significant implications: it provides a more robust method for detecting inexact symmetry, and it more effectively explains how humans detect complex structural symmetry.  More pragmatically, because MAGI can also align conceptual structure (MAGI can detect symmetry in non-visual input, such as equations and story narratives), it can explain the relationship between perceptual and conceptual symmetry, which is a key ability in reasoning from diagrams.

I have collaborated with psychologists to test the cognitive implications of the MAGI model.  Research conducted with Gentner and Alex Aminoff provides evidence that, as MAGI predicts, human subjects are sensitive to qualitative visual structure in symmetry judgments of polygons, even for extremely short display times (50 ms).  MAGI has also been used to simulate the results of classic symmetry experiments by Palmer & Hemenway (1978).  These experiments demonstrated an interaction between symmetry orientation and ease of symmetry judgment.  Our simulation showed that MAGI could explain a key result of these experiments – why bilateral symmetries at some orientations (such as vertically) are perceived more easily than at other orientations. 

I plan to continue my interdisciplinary collaboration with psychologists to test other aspects of symmetry detection using the MAGI model. MAGI’s strength in this research is its ability to use the same line-drawn stimuli frequently given to human subjects, so that their results can be compared with MAGI’s directly.  Symmetry detection occurs early both developmentally and in the visual process, yet is still only partially understood.  I believe that resolving open problems in this area – most centrally the role of spatial relations – could provide key insights into perception and cognition. I also plan to use MAGI in future diagrammatic reasoners.

A Diagrammatic Reasoning Toolkit

I have also built a system called GeoRep.  GeoRep is a spatial representation system that takes vector graphics files (i.e., line drawings) as input, and produces a predicate calculus spatial representation.  It builds higher-level diagrammatic vocabularies (e.g., gates and wires in a logic circuit diagram) in terms of lower-level spatial relations (e.g., corners, closed shapes and boundary characteristics, and intersections).  GeoRep is not a model of drawing or sketch recognition, but a diagrammatic reasoner that models how particular visual relations support particular spatial inferences.  Although its object-recognition ability is limited, once it has identified an object it can reason extensively about its spatial characteristics and how those characteristics support higher-level spatial inferences.

GeoRep’s two-level architecture makes it easy to use and extend.  An initial stage builds a low-level representation using a library of visual operations.  A second stage builds a domain-specific diagrammatic representation using a rule-based domain theory.  Extending GeoRep to cover a new kind of diagram often requires only the writing of a new domain theory.  We have used GeoRep to handle diagrams for logic circuits, military planning, and for simple physics diagrams.

More recently, we've explored the possibility of using GeoRep with multimodal sketching systems.  In a prototype system called nuSketch (built in collaboration with Ken Forbus and Jeff Usher), military planners combine speech and sketching gestures to input information on a planning diagram.  For each drawn element, boundary and category information is passed on to GeoRep, which then uses this information to answer qualitative geographic queries (such as “What enemy obstacles are along this path?”). 

In future research I hope to use GeoRep in new diagrammatic domains, such as architecture or teaching diagrams, as well as extend its basic capabilities. We are also investigating how GeoRep might be used for reasoning with single-use diagrammatic conventions, such as conventions invented in the course of drawing.  Current research issues include how to provide more flexible bottom-up recognition of shapes (which may involve probabilistic or multi-scale approaches to recognition), as well as how to better incorporate top-down influences on recognition, such as domain knowledge or information from an interactive dialogue with the user.