A Computational Model of the Visual Oddity Task

A Computational Model of the Visual Oddity Task Andrew Lovett (andrew-lovett@northwestern.edu) Kate Lockwood (kate@cs.northwestern.edu) Kenneth Forbus (forbus@northwestern.edu) Qualitative Reasoning Group, Northwestern University 2133 Sheridan Rd, Evanston, IL 60208-3118 USA of each image in the array. We model this in our simulation by automatically generating representations with our sketch understanding system, CogSketch 1 (Forbus et al., 2008). (2) Qualitative spatial representations are compared via structure-mapping (Gentner, 1983). In structure-mapping, relational representations are compared by aligning their common structure, which highlights common features and makes it easier to spot the image that lacks those features (cf. Markman & Gentner, 1996). The visual oddity task is difficult because common features must be identified across multiple stimuli. We use analogical generalization to achieve a similar highlighting effect, as explained below. The combination of automatically generated qualitative visual representations and structure-mapping has been used to model several spatial tasks, including answering geometric Miller Analogy Test questions (Tomai et al., 2005), solving a subset of the Raven’s Progressive Matrices, a visual intelligence test (Lovett, Forbus, & Usher, 2007); and making same-different judgments (Lovett, Gentner, & Forbus, 2006). However, none of these tasks offer as much discriminatory power in terms of testing for the presence or absence of particular visual properties. We begin by briefly reviewing the Structure-Mapping Engine (SME), since it plays a key role in multiple stages of the model. Next we outline our qualitative spatial representations, including how we represent properties of both edges and shapes. Then we describe how comparisons and analogical generalization are used to perform the task. Initial simulation results are discussed, including some predictions from the model. We close with future work. Abstract Understanding how high-level visual properties are computed is a central problem in perception. Oddity tasks, where participants must identify a stimulus that is distinct in some way from others in an array, provide a method for determining what features are being computed. We describe a computational model of oddity detection that models data by Dehaene et al. (2006) on perception of simple geometric shapes. It starts with virtually the same input stimuli as given to human subjects and automatically constructs representations. Oddity detection is accomplished by analogical processing, using SME and SEQL. The simulation is able to perform the task, and moreover, provides some insight as to what makes one problem harder than another for humans. Keywords: Analogy; comparison; qualitative representations; spatial reasoning; sketch perception. Introduction Understanding how high-level visual properties, such as geometric relationships, are computed is a central problem in perception. One method of exploring what properties are computed is the oddity task. That is, participants are given an array of stimuli, and told to pick the one that is “different” or “odd”. If people can do it easily, then they must be computing the property that distinguishes one stimulus from the others, assuming no confounds of course. Dehaene et al. (2006) used the visual oddity task to investigate perception of simple geometric shapes across different cultures. Participants were shown a series of arrays containing six similar images (Figure 1). They were asked to pick out the image that did not fit with the other five. The participant pool included both Americans and Munduruku, a South American indigenous group, and both children and adults. One finding was that certain problems were much harder than others, for all participant groups. By looking at what makes some problems harder than others, we can gain insight into both what visual properties people tend to compute, and also how they detect oddities. For this paper, we focus entirely on their results for American children, aged 8 to 13. Figure 1 shows their accuracy on a subset of the problems. There are 45 problems in all. This paper describes a computational model of the visual oddity task. The two key ideas are: (1) Qualitative spatial relations play an important role in much of visual processing (Forbus, Ferguson, & Usher, 2001). Thus, when participants are given a visual array such as the ones used in this study, we propose that they construct a qualitative representation The Structure-Mapping Engine SME (Falkenhainer et al. 1986) is a computational model of comparison. Structured, relational descriptions are assumed, including higher-order relations that connect and constrain lower-order relations. Given two descriptions, a base and a target, SME computes one or more mappings. A mapping consists of (1) a set of correspondences, which indicate what goes with what between the two descriptions, (2) a set of candidate inferences that represent conjectures about the target, using the correspondences and unmapped structure in the base, and (3) a structural evaluation score, a numerical estimate of overall similarity. SME prefers mappings with high systematicity, where connected relational structure, especially with higher-order relations, is mapped. http://spatialintelligence.org/projects/cogsketch_index. html