• Login
    View Item 
    •   SMARTech Home
    • Georgia Tech Theses and Dissertations
    • Georgia Tech Theses and Dissertations
    • View Item
    •   SMARTech Home
    • Georgia Tech Theses and Dissertations
    • Georgia Tech Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Fractal reasoning

    Thumbnail
    View/Open
    MCGREGGOR-DISSERTATION-2013.pdf (16.74Mb)
    Date
    2013-11-18
    Author
    McGreggor, Brian Keith
    Metadata
    Show full item record
    Abstract
    Humans are experts at understanding what they see. Similarity and analogy play a significant role in making sense of the visual world by forming analogies to similar images encountered previously. Yet, while these acts of visual reasoning may be commonplace, the processes of visual analogy are not yet well understood. In this dissertation, I investigate the utility of representing visual information in a fractal manner for computing visual similarity and analogy. In particular, I develop a computational technique of fractal reasoning for addressing problems of visual similarity and novelty. I illustrate the effectiveness of fractal reasoning on problems of visual similarity and analogy on the Raven’s Progressive Matrices and Miller’s Analogies tests of intelligence, problems of visual novelty and oddity on the Odd One Out test of intelligence, and problems of visual similarity and oddity on the Dehaene test of core geometric reasoning. I show that the performance of my computational model on these various tests is comparable to human performance. Fractal reasoning provides a new method for computing answers to such problems. Specifically, I show that the choice of the level of abstraction of problem representation determines the degree to which an answer may be regarded as confident, and that that choice of abstraction may be controlled automatically by the algorithm as a means of seeking that confident answer. This emergence of ambiguity and its remedy via problem re-representation is afforded by the fractal representation. I also show how reasoning over sparse data (at coarse levels of abstraction) or homogeneous data (at finest levels of abstraction) could both drive the automatic exclusion of certain levels of abstraction, as well as provide a signal to shift the analogical reasoning from consideration of simple analogies (such as analogies between pairs of objects) to more complex analogies (such as analogies among triplets, or larger groups of objects). My dissertation also explores fractal reasoning in perception, including both biologically-inspired imprinting and bistable perception. In particular, it provides a computational explanation of bistable perception in the famous Necker cube problem that is directly tied to the process of determining a confident interpretation via re-representation. Thus, my research makes two primary contributions to AI theories of visual similarity and analogy. The first contribution is the Extended Analogy By Recall (ABR*) algorithm, the computational technique for visual reasoning that automatically adjusts fractal representations to an appropriate level of abstraction. The second contribution is the fractal representation itself, a knowledge representation that add the notion of self-similarity and re-representation to analogy making.
    URI
    http://hdl.handle.net/1853/50337
    Collections
    • College of Computing Theses and Dissertations [1191]
    • Georgia Tech Theses and Dissertations [23877]
    • School of Interactive Computing Theses and Dissertations [144]

    Browse

    All of SMARTechCommunities & CollectionsDatesAuthorsTitlesSubjectsTypesThis CollectionDatesAuthorsTitlesSubjectsTypes

    My SMARTech

    Login

    Statistics

    View Usage StatisticsView Google Analytics Statistics
    facebook instagram twitter youtube
    • My Account
    • Contact us
    • Directory
    • Campus Map
    • Support/Give
    • Library Accessibility
      • About SMARTech
      • SMARTech Terms of Use
    Georgia Tech Library266 4th Street NW, Atlanta, GA 30332
    404.894.4500
    • Emergency Information
    • Legal and Privacy Information
    • Human Trafficking Notice
    • Accessibility
    • Accountability
    • Accreditation
    • Employment
    © 2020 Georgia Institute of Technology