A QUANTITATIVE, THREE-DIMENSIONAL METHOD FOR ANALYZING ROTATIONAL MOVEMENT FROM SINGLE-VIEW MOVIES
The study of animal movement is an important aspect of functional morphological research. The three-dimensional movements of (parts of) animals are usually recorded on two-dimensional film frames. For a quantitative analysis, the real movements should be reconstructed from their projections. If movements occur in one plane, their projection is distorted only if this plane is not parallel to the film plane. Provided that the parallel orientation of the movement with respect to the film plane is checked accurately, a two-dimensional method of analysis (ignoring projection errors) can be justified for quantitative analysis of planar movements. Films of movements of skeletal elements of the fish head have generally been analyzed with the two-dimensional method (e.g. Sibbing, 1982; Hoogenboezem et al. 1990; Westneat, 1990; Claes and de Vree, 1991), which is justifiable for planar movements. Unfortunately, the movements of the head bones of fish are often strongly non-planar, e.g. the movement of the pharyngeal jaws and the gill arches. The two-dimensional method is inappropriate for studying such complex movements (Sibbing, 1982; Hoogenboezem et al. 1990). For a qualitative description of movement patterns, the conditions for the use of the two-dimensional method may be somewhat relaxed. When two (or more) views of a movement are recorded simultaneously, the three-dimensional movements can readily be reconstructed using two two-dimensional images (e.g. Zarnack, 1972; Nachtigall, 1983; van Leeuwen, 1984; Drost and van den Boogaart, 1986). However, because of technical (and budget) limitations, simultaneous views of a movement cannot always be shot. In this paper, a method is presented for reconstructing the three-dimensional orientation and rotational movement of structures using single-view films and for calculating rotation in an object-bound frame. Ellington (1984) presented a similar method for determining three-dimensional wing movements from single-view films of flying insects. Ellington's method is based upon the bilateral symmetry of the wing movements. The present method does not depend on symmetry and can be applied to a variety of kinematic investigations. It eliminates a systematic error: the projection error. The measuring error is not discussed; it is the same in the two-dimensional and three-dimensional method of analysis.
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