Books and Book Chapters

Permanent URI for this collectionhttps://hdl.handle.net/10294/16747

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Browsing Books and Book Chapters by Author "Hepting, Daryl H."

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    Discernibility in the Analysis of Binary Card Sort Data
    (Springer, 2013-10-11) Hepting, Daryl H.
    In an open card sorting study of 356 facial photographs, each of 25 participants created an unconstrained number of piles. We consider all 63,190 possible pairs of photos: if both photos are in the same pile for a participant, we consider them as rated similar; otherwise we consider them as rated dissimilar. Each pair of photos is an attribute in an information system where the participants are the objects. We consider whether the attribute values permit accurate classification of the objects according to binary decision classes, without loss of generality. We propose a discernibility coefficient to measure the support of an attribute for classification according to a given decision class pair. We hypothesize that decision class pairs with the support of many attributes are more representative of the data than those with the support of few attributes. We present some computational experiments and discuss opportunities for future work.
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    A Linear Model for Three-Way Analysis of Facial Similarity
    (Springer, Cham, 2018-05-18) Hepting, Daryl H.; Bin Amer, Hadeel Hatim; Yao, Yiyu
    Card sorting was used to gather information about facial similarity judgments. A group of raters put a set of facial photos into an unrestricted number of different piles according to each rater’s judgment of similarity. This paper proposes a linear model for 3-way analysis of similarity. An overall rating function is a weighted linear combination of ratings from individual raters. A pair of photos is considered to be similar, dissimilar, or divided, respectively, if the overall rating function is greater than or equal to a certain threshold, is less than or equal to another threshold, or is between the two thresholds. The proposed framework for 3-way analysis of similarity is complementary to studies of similarity based on features of photos.
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    Rendering Methods for Iterated Function Systems
    (North-Holland, 1991-12) Hepting, Daryl H.; Prusinkiewicz, Przemyslaw; Saupe, Dietmar
    This paper describes rendering methods for iterated function systems (IFS’s). The rendering process consists of the generation of a field of data using an IFS and its visualization by means of computer graphics. Two groups of methods are presented: 1. Rendering of the attractor A of an IFS. These attracting methods may visualize the geometry and additionally the invariant measure supported by the attractor. 2. Rendering the complement of the attractor. There are three approaches, namely methods representing Euclidean distance from A; repelling methods, computing the escape time of a point from A, and methods using (electrostatic) potential functions of the attractor. The last of these methods calculates integrals with respect to the invariant measure of the attractor. An algorithm which generates an approximation of such integrals with prescribed tolerance is presented. This provides an alternative to the usual approach based on Elton's ergodic theorem and time average of trajectories generated by the “chaos game", where no error bound is available. Algorithms specifying the details of all methods are presented, some of them in the form of pseudocode. Examples of images obtained using these algorithms are given. The relationship to previously developed methods for visualizing Mandelbrot and Julia sets is also discussed.