Comparison of different height measures

determine deviations, distances orthogonally to double-bounce lines are measured to corresponding edges w. Double-bounce line positions vary between minus and plus two pixels, σ_db,proj is set to σ_db,proj = 2×σ_Opt= 0.74 m.

Gable roof heights are computed in slant range geometry. Double-bounce line and edges of the bright single-bounce line are observed. It is shown in [Wegner et al., 2010] that double-bounce lines can be automatically segmented with an accuracy of about one pixel in slant range. This value is chosen as standard deviation for, both, double-bounce lines and edges of single-bounce lines in slant rangeσ_db,slant = 0.39 m, which corresponds to the resolution in range direction.

Standard deviation σ_lay is needed for the near range end of layover in a SAR magnitude image in ground range geometry, as used for height computation in equation 3.10. An investigation of a straight building roof edge, which should also map exactly straight in the SAR magnitude image, shows deviations of plus an minus two pixels leading. This frayed signature of a roof edge in layover can be seen in figure 2.7(a), for example. Thus, two times the SAR range resolution is considered as standard deviation σ_lay = 0.78m.

The accuracy of maximum robust InSAR heights within layover ramps of flat roof buildings is assessed by direct comparison to LiDAR ground truth. Heights vary about ± 0.5 meters around reference heights, a standard deviationσInSAR= 0.5mis set. It corresponds to Aes-1 InSAR height accuracy values reported by Schwäbisch & Moreira [1999].

Incidence angle observations of sun and viewing angle observations of the SAR sensor are made, too. Sun incidence angle ρ is computed with software NREL SOLPOS with a standard deviation σρ = 0.01^◦ [Rymes, 2000]. SAR sensor viewing angle θ at the location of a particular gable roof building in the image is assumed to have a standard deviation ofσ_θ = 0.02^◦.

(a) (b)

Figure 4.14.: Flat roof buildings (a) in the orthophoto used for measurements and (b) oblique view from Microsoft Bing Maps^TM ( c 2011 Microsoft Corporation, c 2010 Blom).

the orthophoto. Visualization with footprints automatically detected with CRF classification would hamper interpretability due to irregular footprint shapes. A refinement of building detection results, either through an improved classification or via post-processing, would allow using automatically detected footprints. It is left for future work.

All cut-outs of a SAR magnitude image (entire image given in Fig. 4.2) of the InSAR image pair are shown in ground range geometry in order to ease interpretability and comparisons with corresponding orthophoto cut-outs. The latter are part of the original orthophoto provided in figure 4.14. Indices of buildings are overlaid to oblique optical images taken as screenshots from Microsoft Bing Maps^TM. Their perspective was chosen to correspond as much as possible to the three-dimensional visualizations in order to facilitate understanding.

Flat roof buildings

All height measurements of flat roof buildings are based on observations in the orthophoto, a SAR magnitude image, or InSAR heights. Several primitives are segmented manually in order to prepare for observations: Roof edges e, nadir point ν, shadow edge s, and the location w where building walls meet ground in the orthophoto⁴.

SAR double-bounce linesdbare automatically segmented and projected to orthophoto geometry.

Robust maximum InSAR heights h_l in layover ramps are extracted automatically in slant range geometry, too, within parallelograms as explained in section 3.2.1. The widths of parallelograms is set as a function of the maximum unambiguous building height in InSAR data of approximately 30 meters. In the Dorsten scene no buildings higher than 30 meters occur. In case of a lower

4Automatic segmentation of all primitives is possible, too, but calls for adapted processing decreasing artefacts as much as possible. It is left for future work. The goal here is to assess the best achievable building height accuracy and thus manual measurements are well justified.

(a) (b)

(c) (d)

Figure 4.15.: Results of flat roof building height measurements determined via (a)sun shadow (h_s), (b) perspective distortion in the optical image (h_pd), (c) double-bounce line and roof edge overlap (hdb), (d) SAR layover (hl).

Figure 4.16.: Results of flat roof building height measurements determined via robust maximum InSAR height in layover phase ramp (h_InSAR).

maximum phase to height ambiguity or higher buildings phase unwrapping has to be conducted before computing h_l. It is unnecessary here.

Observations are conducted automatically between manually or automatically segmented prim-itives, which are all lines (except the nadir point ν in the orthophoto). Multiple measurements along line primitives are done, paying attention to uncorrelated values. Two observations at a line primitive have to be separated by a minimum distance corresponding to the resolution of the data (cf. Tab. 4.7).

An oblique optical image (screenshot from Microsoft Bing Maps^TM) in figure 4.14(b) gives an impression of the three-dimensional extent of flat roof buildings used for testing. Indices are assigned to each building being part of tests concerning the proposed height measures and adjustment. The corresponding part in the orthophoto is shown in figure 4.14(a), magnitude SAR image and InSAR heights can be viewed in figure 3.10. All single height measurements per flat roof building are given in table B.1 in Annex B, a diagram providing an overview is given in figure 4.21.

Figure 4.15 illustrates three-dimensionally single measured heights without an explicit height value as input to the equation. All measures are purely based on inherent height information caused by characteristic effects. In figure 4.16 robust maximum InSAR heights h_InSAR measured in layover phase ramps are visualized.

Gable roof buildings

Multiple gable roof buildings are investigated in terms of height measurements. Often, not all proposed height measurements can be conducted due to missing observations in data. All single height values per gable roof building are given in table B.2 in Annex B.

No robust maximum InSAR heights in layover phase ramps (hInSAR) are measured for gable roof buildings. Similar to the intensity values, all phase contributions of the tilted roof plane, from eave up to ridge, are collected in the near range bright line. The phase value of the dominant scatterer on the roof plane, anywhere between eave and ridge, is recorded. Layover between double-bounce and single-bounce line originates from the building facade, the highest point in this layover phase ramp does not correspond to the roof ridge (i.e., the building height), but to the eave. Moreover, gable roof buildings are usually smaller than flat roof buildings and thus signal from elevated objects in front of them like trees interferes. As a consquence, h_InSAR is not a good measure for gable roof building heights, it is not conducted. Height measurements of gable roof buildings are based on observations in the orthophoto, one SAR magnitude image, and double-bounce lines. As in case of flat roof buildings, some primitives are segmented manually: Building width c, roof edges e, nadir point ν, shadow edge s, the locationw where building walls meet ground in the orthophoto, near and far range edges of bright SAR lines caused by single-bounce reflection at the tilted roof plane.

SAR double-bounce lines db are automatically segmented and projected to orthophoto geome-try. Observations (e.g., distance measurements) are conducted automatically between manually or

(a) (b)

(c) (d)

(e) (f)

Figure 4.17.: Height measurements for gable roof buildings 1 to 12: (a) via parallel bright lines in SAR data (hr), Eq. 3.11 & 3.12), (b) corresponding cut-outs of one SAR magnitude image of the InSAR image pair (ground range geometry, range direction right to left), (c) optical perspective distortion heights (h_pd), Eq. 3.8 with w instead of db), (d) corresponding cut-out of the orthophoto, (e) heights via sun shadow of roof ridge (hs), Eq. 3.7), (f) oblique view from Microsoft Bing Maps^TM ( c 2011 Microsoft Corporation, c2010 Blom).

automatically segmented line primitives. Like in case of flat roof buildings, attention is payed to achieve uncorrelated values. Distances between single observations either correspond to orthophoto or InSAR resolution, 0.37 meters or 0.385 meters, respectively. The mean of each observation is introduced into the height measurement equation. Single building height measurements of gable roof buildings one to twelve are shown in figure 4.19. Corresponding cut-outs of SAR magnitude image (Fig. 4.19)(b), orthophoto (Fig. 4.19(d)), and oblique optical image from Microsoft Bing

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

Figure 4.18.: Results of building height measurements for gable roof buildings viaparallel bright lines in SAR data (h_r, Eq. 3.11 & 3.12), corresponding cut-outs of one SAR magnitude image of the InSAR image pair (ground range geometry, range direction right to left), of the orthophoto, and oblique view from Microsoft Bing Maps^TM ( c 2011 Microsoft Corporation, c 2010 Blom): (a)-(d) buildings 20 to 23, (e)-(h) buildings 24 to 31, (i)-(l) buildings 33 to 35.

(a) (b) (c)

Figure 4.19.: Results of building height measurements for gable roof buildings via sun shadow of roof ridge (hs, Eq. 3.7) and optical distortion (hpd): (a) sun shadow heights 24 to 32, (b)optical distortion heights 24 to 32, (c)sun shadow heights 33 to 35; no heights can be determined at buildings depicted in white; no heights can be measured at buildings 20 to 23 (cf. Fig. 4.18(a)-(c)).

Maps^TM (Fig. 4.19(f)) are provided, too. Three different height measurements could be conducted for most buildings: hr via parallel bright lines in SAR data, h_pd via optical perspective distortion heights at northern short building sides (cf. Fig. 4.19(d)), and hs via sun shadow of the roof ridge.

At buildings 20 to 23 no heights based on the extent of sun shadow can be determined because,

dealing with hip roofs, the ridge is invisible in the shadow (cf. Fig. 4.18(c)). Moreover, optical distortion cannot be used for height measurements neither due to buildings being positioned very close to nadir. Only very few heights depending on sun shadow (Eq. 3.7) and optical distortion (Eq. 3.8 withwinstead ofdb) can be obtained in building groups 24 to 35. Most buildings in figure 4.19 appear white, no additional heights besides the ones depending on parallel bright SAR lines (cf.

Fig. 4.18) can be determined. In total, merely two gabel roof buildings facilitate computation of three different heights (cf. Fig. 4.18(d) & Fig. 4.19(a,b)), one building with two heights is present (cf. Fig. 4.18(g) & Fig. 4.19(c)).