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The Morphing Space

: Alexa, M.; Müller, W.
: TU Darmstadt, Fachgebiet Graphisch-Interaktive Systeme

Darmstadt, 1998
Reportnr.: GRIS-98-2
Research Report
Fraunhofer IGD ()
morphing; warping; vector space; synthesis; analysis

Morphing is a well known technique to generate smooth transitions between two objects. We propose a more general understanding of morphing: First, we use morphing to describe objects as a composite of other objects. Second, we allow this description to incorporate more than two base objects. Given this concept a set of objects produced by morphing among multiple objects forms a mathematical space, which we call morphing space.
In this paper, we present a mathematical framework to discuss the properties of such spaces and their relation to the applied morphing algorithms for synthesizing the elements. Moreover, we show that not only synthesis of objects but also analysis of objects is possible in a morphing space. In our context, analysis means finding the (best) representation of a given object in the morphing space. Algorithms are proposed for both the synthesis and the analysis process. As a fact, these algorithms are independentof the object's representation and the utilized morphing technique and, thus, generally applicable.
Applications of the proposed techniques reach from synthesis of objects as combination of principal objects to the analysis of objects, which results in possible compression or feature recognition. A sample application presents the combination of an analysis and synthesis process in morphing spaces.