  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 towards 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 constitutes 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.
