We use a new contour-based map analysis technique to measure the mass and size of molecular cloud fragments continuously over a wide range of spatial scales \\((0.05 \≤ r/pc \≤ 10)\\), i.e., from the scale of dense cores to those of entire clouds. The present paper presents the method via a detailed exploration of the Perseus molecular cloud. Dust extinction and emission data are combined to yield reliable scale-dependent measurements of mass. This scale-independent analysis approach is useful for several reasons. First, it provides a more comprehensive characterization of a map (i.e., not biased toward a particular spatial scale). Such a lack of bias is extremely useful for the joint analysis of many data sets taken with different spatial resolution. This includes comparisons between different cloud complexes. Second, the multi-scale mass-size data constitute a unique resource to derive slopes of mass-size laws (via power-law fits). Such slopes provide singular constraints on large-scale density gradients in clouds.
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Kauffmann et al. (2010) studied this question.