Analogical Mapping Through Visual Abstraction

Analogical Mapping Through Visual Abstraction Jim Davies (jim@jimdavies.org) Science of Imagination Laboratory Institute of Cognitive Science; Carleton University; 1125 Colonel By Drive Ottawa, Ontario, K1S 5B6 Canada Patrick W. Yaner (patrick.yaner@gmail.com) Artificial Intelligence Laboratory College of Computing; Georgia Institute of Technology; 801 Atlantic Drive Atlanta, GA 30332-0280 USA Abstract want to align x and y to f and g, if indeed f is-above g in the other analog—regardless of what shape x, y, f and g are. Structure Mapping Theory (Gen- tner, 1983) uses identicality of the symbols describ- ing structure to find mappings between analogs. Analogical mapping theories tend to focus on matching identical symbols (either for objects or the relations between them). In the domain of visual representations we implemented a mapping system that uses separate domain knowledge (a shape-type superclass hierarchy) to re-represent analogs such that identicality can be found at different levels of abstraction. Such a scheme is useful where shape, and not the spatial layout of the analog images, is important to aligning visual objects. Grouping Introduction Mapping, a core part of analogy, is finding the align- ments between the elements of two analogs. For ex- ample, in an analogy between a face and the front of a car, a mapping might include an alignment be- tween the eyes and the windshield. Such an align- ment might be based on the fact that the “percep- tual” input to the car happens at the windshield for a car as do the eyes for a face. Mapping is combinatorially complex, and this complexity is reduced by finding similarity between the elements to be mapped. In the example above, the alignment is justified by the functional similar- ity between the eyes and the windshield. In the dis- cussion section we will describe different similarity measures for implemented mapping systems. Our work focuses on mapping for purely visual analogs. That is, we are exploring different sim- ilarity measures that are appropriate for mapping the visual components of images. To return to the car/face example, rather than functionally aligning the eyes and the windshield, an agent that focused on visual similarity might align the eyes to the head- lights because they both consist of two elements, are both round, and are horizontally oriented. One way to find similarity between visual elements is by identification of identical symbols relating the elements. Most simply, if two elements are described in the representation as square, then the mapping agent can favor their alignment. Another way is to identify identical symbols that relate elements of the same image. For example, if in one image element-x is related to element-y with a symbol is-above, then a mapper interested in the structure of images might The Gestalt psychologists found that people percep- tually grouped visual elements according to, among other aspects, shared orientation, color, and prox- imity. This provides psychological evidence for an explicit representation of visual element grouping. Broadly speaking there are two kinds of groups in our work: aggregations and sets. Aggregations are multiple visual elements that form one coherent shape (e.g. a square is an aggregate of four lines). Sets are groups of elements that are unconnected but similar in some way (e.g. nuts in a bowl). Sets and aggregates appear at a certain level of ab- straction, at which they can be aligned to each other as visual elements. An agent with a flexible rep- resentation can, however, zoom into these groups. There are two reasons an agent might want to do this: First, If the agent must decide which group to align to which other group, the conflict resolu- tion might require an examination of the contents of that group. Second, it might be important to align group members. For example, imagine align- ing two armies—at this level of abstraction armies can be moved and split apart, and it makes sense to have the armies’ generals simply be members of the army sets. But if the agent needs to reason about the generals in particular, it could be important to know that the general in one set aligns to the gen- eral in the other. In analogical problem solving, for example, certain operations need to be applied to elements of analogs. Different levels of representation are needed for different transformations applied to the analog (Davies, Goel, & Nersessian, 2003). Likewise with aggregates, mapping one box to another is the right level of abstraction for motion of the entire set, but opening one side of the box by moving one of its con- stituent lines requires a mapping at the component level. For these reasons it is helpful for an agent to be