(ii ) By consid ering scale -space events as critical domain threshold s , we d escribe
and apply a new scale-dom ain topology that facil itates improved queryi ng
and analys is of this compl ex mul tiscale scene.
(iii) We spatiall y model and visua lize the hierarchic al structure of dominant geoobjects withi n a scene as scale -domain manifol ds — which we sugges t
represents a multiscale extens ion to the hiera rchic al scalin g ladder as de fined
in the hiera rchical patch dynam ics paradi gm.
To bett er evalua te these results, we p rovide a brief backgro und on hiera rchical
theories, geo-obj ect-ba sed hierarchie s, mul tiscale analys is, and ima ge object s. This is
followed by a brief descri ption of the metho ds underlying linear SS and blob feature
detection, whi ch is accom panied by a discu ssion of the visua lization resul ts.
8.1.1 Hierarchic al Theo ries
Ecologists have long recogni zed that many “natur al” proces ses produce clusters of
entities that emer ge (and interact) at a speci fi c range of spatial, spect ral, and tempo ral
scales. These clusters resul t in visually distinct spati al patt erns [typi cally referr ed to as
patches — a relatively homo geneous area that differs from its surro unding
2 (Form an,
1995)] which are typi cally generat ed by a small set of self-organ izing princ iples
(Allen and Starr 1982; Waldrop, 1992). The refore, one way to und erstand, explain,
and forecas t the e ffects of natur al proces ses is to e xamine these natur al patterns at
their corres pondin g na tural scale s of emerg ence (Wess man, 1992; Rosin, 1998;
Levin, 1999; Hay et al., 2001). To assist in this task, the conc eptual fram ework of
hierarchy theory has been adopte d in this chapte r, as it builds upon this idea of natural
scales. Here the term scale refers to the spatial dimensi ons (i.e., grain and extent ) at
which entities , patterns, and proces ses can be observ ed and meas ured. Grain refers to
the smalles t distingu ishab le compo nent (i.e., spatial resolution), while extent refers to
the enti re area or scene under analys is. For related de fin itions of scale see Quat trochi
and Good child (1996) , Marce au (1999), Marce au and Hay (1999) , Wu and Li (2005) ,
Manson (2006) , and Wu and Li (2009) .
Hi erarchy theor y was develo ped in the framewo rk of general system ’ s theor y,
mathematics , and philosophy in the 1960s and 19 70s (Wu and Loucks, 1995) and is
generally regard ed as being introduced into ecolog y by Allen and Starr (1982) .
However , it should be noted that early work by Watt (1947) , Whit taker (1953), and
others embr aces ideas that are implic itly hiera rchical (Ur ban et al., 1987). Hierarch y
theory attempts to analyze the effect of scale on the organization of complex systems
(Simon, 1973). It does not assume that a system is hierarchically structured but rather
partitions “the world” into hierarchical levels to simplify the analysis of cross-scale
interactions (Allen and Starr, 1982; Ahl and Allen, 1996; Peterson, 2000). Here,
“complex systems” are characterized by a large number of components that interact in
a nonlinear way and exhibit adaptive properties through time (Kay, 1991).
2 This is also noted as such in Wikipedia ( http://en.wikipedia.org/wiki/Landscape_ecology), last accessed
April 21, 2013.
INTRODUCTION
143
and apply a new scale-dom ain topology that facil itates improved queryi ng
and analys is of this compl ex mul tiscale scene.
(iii) We spatiall y model and visua lize the hierarchic al structure of dominant geoobjects withi n a scene as scale -domain manifol ds — which we sugges t
represents a multiscale extens ion to the hiera rchic al scalin g ladder as de fined
in the hiera rchical patch dynam ics paradi gm.
To bett er evalua te these results, we p rovide a brief backgro und on hiera rchical
theories, geo-obj ect-ba sed hierarchie s, mul tiscale analys is, and ima ge object s. This is
followed by a brief descri ption of the metho ds underlying linear SS and blob feature
detection, whi ch is accom panied by a discu ssion of the visua lization resul ts.
8.1.1 Hierarchic al Theo ries
Ecologists have long recogni zed that many “natur al” proces ses produce clusters of
entities that emer ge (and interact) at a speci fi c range of spatial, spect ral, and tempo ral
scales. These clusters resul t in visually distinct spati al patt erns [typi cally referr ed to as
patches — a relatively homo geneous area that differs from its surro unding
2 (Form an,
1995)] which are typi cally generat ed by a small set of self-organ izing princ iples
(Allen and Starr 1982; Waldrop, 1992). The refore, one way to und erstand, explain,
and forecas t the e ffects of natur al proces ses is to e xamine these natur al patterns at
their corres pondin g na tural scale s of emerg ence (Wess man, 1992; Rosin, 1998;
Levin, 1999; Hay et al., 2001). To assist in this task, the conc eptual fram ework of
hierarchy theory has been adopte d in this chapte r, as it builds upon this idea of natural
scales. Here the term scale refers to the spatial dimensi ons (i.e., grain and extent ) at
which entities , patterns, and proces ses can be observ ed and meas ured. Grain refers to
the smalles t distingu ishab le compo nent (i.e., spatial resolution), while extent refers to
the enti re area or scene under analys is. For related de fin itions of scale see Quat trochi
and Good child (1996) , Marce au (1999), Marce au and Hay (1999) , Wu and Li (2005) ,
Manson (2006) , and Wu and Li (2009) .
Hi erarchy theor y was develo ped in the framewo rk of general system ’ s theor y,
mathematics , and philosophy in the 1960s and 19 70s (Wu and Loucks, 1995) and is
generally regard ed as being introduced into ecolog y by Allen and Starr (1982) .
However , it should be noted that early work by Watt (1947) , Whit taker (1953), and
others embr aces ideas that are implic itly hiera rchical (Ur ban et al., 1987). Hierarch y
theory attempts to analyze the effect of scale on the organization of complex systems
(Simon, 1973). It does not assume that a system is hierarchically structured but rather
partitions “the world” into hierarchical levels to simplify the analysis of cross-scale
interactions (Allen and Starr, 1982; Ahl and Allen, 1996; Peterson, 2000). Here,
“complex systems” are characterized by a large number of components that interact in
a nonlinear way and exhibit adaptive properties through time (Kay, 1991).
2 This is also noted as such in Wikipedia ( http://en.wikipedia.org/wiki/Landscape_ecology), last accessed
April 21, 2013.
INTRODUCTION
143