Measuring the Physical Composition of Urban Morphology Using Multiple Endmember Spectral Mixture Models

The application of multiple en dm eiub er spec tral mixture ana lysis (MJ::SA1A) to map the ph ysical com pos ition of urban morphology using Landsat Thematic Mapp er (TM) data is evaluated and tested. MESMA models mixed pixels as lin ear com binations of pure spec tra, called en dm em bers, while allowing the types and number of endmembers to V(]l}' on a per-pixe l basis. A total of 63 two-, three -, and [our-endm ember models were applied to a Landsat Tlvl image for Los Angeles County. an d a sm aller subset of these models was chosen based on f raction and root-m ean-squared error (R,VlSE) crite­ ria. From this subset, an optimal model was selected for each pixel based on optim iza tion for m ax im um area coverage. The resultant endm ember frac tions were then ma pped into four main com ponents of urban land cover: vegetation, Imp ervious surfaces, Soil, and \1\fateriShade. The mapped frac tions were validated using aerial pho tos. The results sho wed that a ma­ jority of the image could be modeled successfull y with twoor three-etidtnember m odels. The validation results indicated the robustness of MESMlI for deriving spatially con tin uous vari­ ables qu antif ied at the sub-p ixel level. These para meters can be readily integrated into a wide range ofapplications and m odels concerned with physical, econom ic, and/or socio­ dem ographi c phenom ena that influence the m orphological pa tterns of the city. Introduction i\ recur re n t th eme in urban remote se nsing studies has been how to der ive sum mary indicators of physical components of urban morph olo gy from remotely sen se d dat a (Green . 1955; Forster. 1985; Ridd . 1995; Jen sen and Cowen . '\999). Th is typ e of analys is has tradition ally be en limited due to the spectra l heterogeneit y of urban features in re lation to th e spatial reso­ lution of th e remote sens ing sen sors (Weber. 1994 ). This is es pec ia lly tru e in th e contex t of mult isp ectral images with medium sp atia l resolut ion suc h as th ose provided by Landsat , SPOT , and the Indian sat ell ites. Becaus e of th e presence of spectral mixing in th e p ixe ls of these images. th e identi fica­ tion of urb an land cov er using perpixel an alyti cal techn iqu es becom es very diffi cult because the con tin uum of land cover cannot be readi ly di vided in to d iscr ete cla sses. T. Rashed , J.R. Weeks . and J. Rogan are with the Dep artment of Geography, San Diego State Univers ity, San Diego , CA 92182 (TRash [email protected]; john.we [email protected] ; roga n@ro han .sdsu .ed u). D. Roberts and R. Pow ell are with the Dep artment of Geography . Un ive rsity o f Californ ia Santa Barbara , San ta Barb ara, CA 93106 ([email protected] : [email protected] sb.edu). PHOTOGRA MM ETRIC ENG INE ERING & REMOTE SENSING Strah ler et al. (1986) d ivid e scene mo dels into two types, I-lan d L-resolu tion mod els, de pen d ing on the relat ion ship bet ween th e s ize of e leme nts (e.g.. vegela tion) in the scene and th e resolut ion ce ll of th e sensor. In the H-resol ut ion model. scene elements ar e larger than res olu tion ce lls and, th erefore. th e spa tia l arr angement of scen e elements can di rectly be detected . Th e L-reso lut ion mode l is th e opposite . w her e sce ne e lements ar e not indi viduall y delect abl e becau se th ey ar e smaller than th e reso lution ce lls. Detect in g the spa tial arran gement of objects may require a resolution ce ll s ize sev­ era l times sm all er than th ei r s ize. Accordingly. for multispec­ tral images w ith medium spatia l res olut ion . th e sc ene mod el o f urba n lan dscap es can be regarde d as an L-resolu lion mod el. Further, as th e si ze of objects in th e urban scene beco mes in ­ cr easingly sm all re lative to th e resolution cell si ze , it may no longer be possibl e to con sider objec ts in dividuall y (Strah ler et al.. 198 6). Instead , the ur ban sc ene model can be rega rde d as a contin uous mo de l, in wh ich the measurem ent of eac h pi xel can be treated as a sum of sp ect ral interacti on s between vari ou s scene eleme nts weight ed by th ei r concentra tio n or relat ive aeria l p roportions with in th e reso lution cell (i.e. , a mi xture model) . The re fore . it can be asser ted th at , in the con­ text of medium reso lution multi sp ect ral images, H-resolution mod els in urb an areas sh ould operate in a subservient role to L-resolution models (Graet z, 1990; Rash ed et al .. 200 1; Phinn et 01.• 2002 ). Over th e past ten yea rs , there has been a trend toward de­ scribin g the spatially var ying char acte r of land cov er in terms of co ntinuous surfaces (Mather, 1999) . Thro ugh thi s trend. th e pro porti ons of different co mpone n ts of land cov er are esti­ mated for eac h p ixe l of th e image. Fuzzy classifi cati on and sp ectra l mi xt ure ana lysi s (S MA) are two grou ps of techniques that have been pro pose d to provide soft analysi s of mixed pixels. The work we pr esent in thi s pa per is based on th e SMA approach . The SMA approach assumes that a lan dscape is formed from continuously va rying proportions of id ealized types of land covel' with pure sp ect ra . called en c! members (Adams et al.. 1986; Ad am s et al.. 1993). Endmemb ers are abstrac tions of land-cover materials with uniform properti es pr esent in th e sc ene. In an urban enviro nme nt. these may include im pervio us sur faces , vege ta tion typ es . wat er bodi es , and bar e soi ls (Ridd, 1995). Linea r SMA is th e proces s of so lv­ in g for endmember fracti on s, assuming that th e s pectru m measured for ea ch pixel represen ts a linear combination of Photogra rnme tric Engin eering & Remote Sen s ing Vol. 69, No. 9. Septem ber 200 3, pp . 10111020 . 0099-11 12/03/ 6909-1011 $3.00/0 © 200 3 Ame ric an So cie ty for Ph otogrammetry and Remote Sen s ing