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U. Glaeser

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FIGURE 28.18 The resolution of a time/frequency representation and a wavelet representation in the timefrequency<br />

plane.<br />

be used (leading to a different “optimal” set of functions, the prolate spheroidal functions). The appropriateness<br />

of the various measures again depends on the application. Their biological (psychophysical) relevance<br />

remains to be determined.<br />

All the previously mentioned points are relevant for both spatial/spatial-frequency and spatial/scale<br />

representations (wavelets). Wavelets, however, present some special considerations. Suppose one wishes<br />

to compare the resolutions of time/frequency and wavelet decompositions? Specifically, what is the<br />

resolution of a multiresolution method? This question can be illustrated by considering the 1-D case,<br />

and examining the behavior of the two methods in the time-frequency plane (Fig. 28.18).<br />

In the time/frequency representation, the dimensions ∆t and ∆ξ t remain the same throughout the<br />

time-frequency plane. In wavelet representations the dimensions vary, but their product remains constant.<br />

The resolution characteristics of wavelets may lead one to believe that the uncertainty of a wavelet<br />

decomposition may fall below the bound in Eq. (28.42). This is not the case. The tradeoff between ∆t<br />

and ∆ξ t simply varies. The fundamental limit remains.<br />

A final point relates more specifically to the representation of image sequences. The HVS has a specific<br />

(bandlimited) spatiotemporal frequency response. Beyond indicating the maximum perceivable frequencies<br />

(setting an upper bound on resolution) it seems feasible to exploit this point further, to achieve a<br />

more efficient representation. Recalling the relationship between motion and temporal frequency, a<br />

surface with high spatial frequency components, moving quickly, has high temporal frequency components.<br />

When it is static, it does not. The characteristics of the spatiotemporal CSF may lead us to the<br />

conclusions that static regions of an image require little temporal resolution, but high spatial resolution,<br />

and that regions in an image undergoing significant motion require less spatial resolution (due to the<br />

lowered sensitivity of the CSF), but require high temporal resolution (for smooth motion rendition).<br />

The first conclusion is essentially correct (although not trivial to exploit). The second conclusion,<br />

however, neglects eye tracking. If the eye is tracking a moving object, the spatiotemporal frequency<br />

characteristics experienced by the viewer are very similar to those in the static case, i.e., visual sensitivity<br />

to spatial structure is not reduced significantly.<br />

28.5 The Computation of Motion<br />

Many approaches are used for the computation of motion (or, more precisely, the estimation of motion<br />

based on image data). Before examining some of these approaches in more detail, it is worthwhile to<br />

review the relationship between the motion in a scene and the changes observed in an image of the scene.<br />

The Motion Field<br />

The motion field [20] is determined by establishing a correspondence between the motion of points in<br />

the scene (the real world) and the motion of points in the image plane. This correspondence is found<br />

geometrically, and is independent of the brightness patterns in the scene (e.g., the presence or absence<br />

of surface textures, changes in luminance, etc.).<br />

© 2002 by CRC Press LLC

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