terabytes of diff erent mul tispatial, mul tispectr al, multiradiom etric, and mul titemp oral
resoluti on digital data, the necess ity for autom ated an alytical methods is paramo unt
(Hay et al., 2005 ).
Critical to these resear ch acti vities is the need to unders tand the concept of scale in
its many guises, wor k wi thin its limitati ons, and bene fit from its po tential. Though
scale is consi dered one of the centr al concept s in many disciplines which study
human –environmen t syst ems, a wide diver sity o f scale de fi nitions across numerous
disciplines (Gibson et al., 20 00) can confus ingl y resul t in inappropri ate samp ling
designs, incor rect resul ts, and misleadi ng conclusions (O ’ Neill and Kin g, 1998 ;
Wheat ley and Johnso n, 2009; Wu and Li, 2009). As an examp le, Wikipedia
1 provides
60 different meanings of scale, most of which are related to meas urement units.
Regardl ess of which de finition is used, scale concept ually represents the wi ndow of
perception (Hay e t al., 2002a), a continuum throu gh which enti ties, pa tterns, and
proces ses can be perceived and link ed toget her (Mar ceau, 1999). Change the spatial/
temporal charact eristics of the windo w (e.g., size, shape, viewing time), and the
correspond ing view is alte red. Thu s, knowing how this view is altered and the effects
upon the scene such alterati ons produce are critical to the validity a nd utility of
decisions based on this view. Scale affect s everyt hing. Thus its mast ery holds the
promise of powe rful insigh t and un derstandin g. But what scale(s) should we choose
for our analys is and how shoul d we asses s infor mation within and between scales?
Where is wi thin and betw een?
From an ecolog ical perspe ctive, it is well recogni zed that the same ecolog ical
proces ses may reveal different p atterns if observ ed at different scales (Peter son, 20 00;
Wheat ley and Johnso n, 2009). Thus, if we study a syst em at an “inappropri ate ” scale,
we may mis s the actual system dynam ics and may instead ident ify patterns that are
artifacts of scale (Wiens, 1989), like looking at the world through the wro ng pair of
glasses. Furthe rmore, patterns observ ed across scale s will form the bases of hypotheses explor ing underl ying proces ses (Swih art et al., 2002). Ideally what we need are
adaptive meth ods that are able to autom atically query the v arying sized , shaped, and
spatially distrib uted compo nents of a lands cape and “tell us ” the correct scale (s) and
locations over which to conduct analys is (Hay et al., 2001; Hay a nd Marce au, 20 04;
Hay et al., 2005; Dra ̌ gut ̧ et al., 2010).
In an effort to addres s these challenges, we pose the multip art question “What does
a scale domai n look like; where is it locat ed, and how can we visua lize it? ” In
respon se, we introduce and describe a novel geo-obje ct-based fram ework that
integrates high-resolution remote sensing imagery, hierarchy theory, and scale space
(SS) for automatically visualizing and modeling dominant (i.e., most salient) landscape structures through multiple scales and within uniquely defined scale domains.
We also report on three main goals:
(i) We describe a three-tier hierarchical methodology for automatically delineating and assessing the dominant structural components within 200 different
multiscale representations of a complex agro-forested landscape.
1 http://en.wikipedia.org/wiki/Scale, last accessed May 24, 2012.
142
VISUALIZING SCALE-DOMAIN MANIFOLDS
resoluti on digital data, the necess ity for autom ated an alytical methods is paramo unt
(Hay et al., 2005 ).
Critical to these resear ch acti vities is the need to unders tand the concept of scale in
its many guises, wor k wi thin its limitati ons, and bene fit from its po tential. Though
scale is consi dered one of the centr al concept s in many disciplines which study
human –environmen t syst ems, a wide diver sity o f scale de fi nitions across numerous
disciplines (Gibson et al., 20 00) can confus ingl y resul t in inappropri ate samp ling
designs, incor rect resul ts, and misleadi ng conclusions (O ’ Neill and Kin g, 1998 ;
Wheat ley and Johnso n, 2009; Wu and Li, 2009). As an examp le, Wikipedia
1 provides
60 different meanings of scale, most of which are related to meas urement units.
Regardl ess of which de finition is used, scale concept ually represents the wi ndow of
perception (Hay e t al., 2002a), a continuum throu gh which enti ties, pa tterns, and
proces ses can be perceived and link ed toget her (Mar ceau, 1999). Change the spatial/
temporal charact eristics of the windo w (e.g., size, shape, viewing time), and the
correspond ing view is alte red. Thu s, knowing how this view is altered and the effects
upon the scene such alterati ons produce are critical to the validity a nd utility of
decisions based on this view. Scale affect s everyt hing. Thus its mast ery holds the
promise of powe rful insigh t and un derstandin g. But what scale(s) should we choose
for our analys is and how shoul d we asses s infor mation within and between scales?
Where is wi thin and betw een?
From an ecolog ical perspe ctive, it is well recogni zed that the same ecolog ical
proces ses may reveal different p atterns if observ ed at different scales (Peter son, 20 00;
Wheat ley and Johnso n, 2009). Thus, if we study a syst em at an “inappropri ate ” scale,
we may mis s the actual system dynam ics and may instead ident ify patterns that are
artifacts of scale (Wiens, 1989), like looking at the world through the wro ng pair of
glasses. Furthe rmore, patterns observ ed across scale s will form the bases of hypotheses explor ing underl ying proces ses (Swih art et al., 2002). Ideally what we need are
adaptive meth ods that are able to autom atically query the v arying sized , shaped, and
spatially distrib uted compo nents of a lands cape and “tell us ” the correct scale (s) and
locations over which to conduct analys is (Hay et al., 2001; Hay a nd Marce au, 20 04;
Hay et al., 2005; Dra ̌ gut ̧ et al., 2010).
In an effort to addres s these challenges, we pose the multip art question “What does
a scale domai n look like; where is it locat ed, and how can we visua lize it? ” In
respon se, we introduce and describe a novel geo-obje ct-based fram ework that
integrates high-resolution remote sensing imagery, hierarchy theory, and scale space
(SS) for automatically visualizing and modeling dominant (i.e., most salient) landscape structures through multiple scales and within uniquely defined scale domains.
We also report on three main goals:
(i) We describe a three-tier hierarchical methodology for automatically delineating and assessing the dominant structural components within 200 different
multiscale representations of a complex agro-forested landscape.
1 http://en.wikipedia.org/wiki/Scale, last accessed May 24, 2012.
142
VISUALIZING SCALE-DOMAIN MANIFOLDS