(Figure 8.14). Conceptually, events are dimensionless points, but computationally
they represent at a minimum a single pixel in SS (x, y, t). More commonly, they are
blob areas composed of many pixels. In an ideal computational system, a C&A would
never exist, because there would be (infinitely) many scales between the two shared
events that would allow for each individual event to be isolated at a different t.
However, for practical reasons, the resolution of our system has been defined as a
whole-number increment of STD + 1. Since each C&A only exists at a single scale,
these events have a correspondingly short lifetime; consequently their persistence is
low, as is the probability of them being ecologically meaningful and/or spatially
dominant in the landscape. Thus, it is more likely that C&A events are the result of
image noise even though great effort was taken to normalize the data (see Section
8.2.3.3). This supposition corresponds with our findings that 84.5% (802/949) of all
C&A events are defined within the first 11 of 200 scales, after which their numbers
dramatically diminish at higher t. Image noise—typically small random variations in
the tone of the data—is integrated into the stronger background signal of the matrix
through scale, which is the same pattern we see manifest in these data.
8.3.2 SS Events and Domain Thresholds: What Does a Scale Domain Look
Like and Where Do We Go from Here?
What does a scale domain look like? To the best of our knowledge, no one has
spatially modeled a scale domain based on remote sensing data for a single instant in
time. Wu (1999) has proposed the hierarchical scaling ladder in relation to the HPDP,
but this is a conceptual model. Similarly, time–space scales have been created
illustrating zooplankton biomass variability as in the Stommel diagram (Haury
et al., 1978), and boreal forest structures in relation to disturbance and atmospheric
possesses, as described by Holling (1992), but none of these explicitly illustrate a
single instance, and none of them actually define in detail what a scale domain may
look like or the area over which they “exist.” In the process of conceptualizing scaledomain manifolds and methods to visualize them, it became apparent that while the
domain-level concept works for topologically discriminating ranked blobs (Section
8.3.1.2), the assumption that a single scale domain exists between the first and last
FIGURE 8.14 Four new dual-instant blob events. The ? represents no blobs found at these
scales.
160
VISUALIZING SCALE-DOMAIN MANIFOLDS
they represent at a minimum a single pixel in SS (x, y, t). More commonly, they are
blob areas composed of many pixels. In an ideal computational system, a C&A would
never exist, because there would be (infinitely) many scales between the two shared
events that would allow for each individual event to be isolated at a different t.
However, for practical reasons, the resolution of our system has been defined as a
whole-number increment of STD + 1. Since each C&A only exists at a single scale,
these events have a correspondingly short lifetime; consequently their persistence is
low, as is the probability of them being ecologically meaningful and/or spatially
dominant in the landscape. Thus, it is more likely that C&A events are the result of
image noise even though great effort was taken to normalize the data (see Section
8.2.3.3). This supposition corresponds with our findings that 84.5% (802/949) of all
C&A events are defined within the first 11 of 200 scales, after which their numbers
dramatically diminish at higher t. Image noise—typically small random variations in
the tone of the data—is integrated into the stronger background signal of the matrix
through scale, which is the same pattern we see manifest in these data.
8.3.2 SS Events and Domain Thresholds: What Does a Scale Domain Look
Like and Where Do We Go from Here?
What does a scale domain look like? To the best of our knowledge, no one has
spatially modeled a scale domain based on remote sensing data for a single instant in
time. Wu (1999) has proposed the hierarchical scaling ladder in relation to the HPDP,
but this is a conceptual model. Similarly, time–space scales have been created
illustrating zooplankton biomass variability as in the Stommel diagram (Haury
et al., 1978), and boreal forest structures in relation to disturbance and atmospheric
possesses, as described by Holling (1992), but none of these explicitly illustrate a
single instance, and none of them actually define in detail what a scale domain may
look like or the area over which they “exist.” In the process of conceptualizing scaledomain manifolds and methods to visualize them, it became apparent that while the
domain-level concept works for topologically discriminating ranked blobs (Section
8.3.1.2), the assumption that a single scale domain exists between the first and last
FIGURE 8.14 Four new dual-instant blob events. The ? represents no blobs found at these
scales.
160
VISUALIZING SCALE-DOMAIN MANIFOLDS