Arboriculture & Urban Forestry 37(4): July 2011 wrapped tightly against the crown’s surface undulations by automated computer processing (Lee et al. 2003) (Figure 2). Once manual inputs were completed, computer analysis of the image was executed and estimates of crown dimen- sions were automatically calculated. UrbanCrowns calcu- lates crown density by analyzing the relative color of each pixel within the unobstructed crown region previously digi- tized for this purpose. Each pixel is classified as either back- ground (e.g., sky or building façade) or tree structure (leaves, branches, stems, and trunks). Density is then calculated as the percentage of pixels within the delineated crown region that are classified as tree structure. UrbanCrowns calculates crown volume based on the scaled width and height of each row of pixels in the delineated crown image. An imaginary cylinder is generated for each row of pixels that has a height equal to the calculated height of one pixel and a diameter equal to the calculated width of the row (i.e. crown diameter at that particular height in the crown). Calculated volumes for each row of pixels are then summed to obtain the volume estimate for the digitally delineated crown. This estimate of crown volume includes both tree structure and voids, so the program multiplies total crown volume by the crown densi- ty percentage to estimate the volume of tree structure only. In addition to software computations, crown volume was also calculated using equations for four geometric solids, similar visu- ally to the observed crown shapes of the sampled sugar maples: 1) sphere, (2) vertical ellipsoid, 3) circular paraboloid, and 4) conical frustum with top radius to bottom radius ratio equaling two-thirds. The equations used for these geometric solids were: [1] Volume = 4/3 • π • r3 [2] Volume = 4/3 • π • r2 [3] Volume = 1/2 • π • r2 [4] Volume = 1/3 • π • h • [r2 • h • h + (2/3 • r)2 + (r • (2/3 • r))] where r equals maximum field-measured crown radius perpendicular to the photograph- ic position, and h equals field-measured crown height. All statistical analyses were performed using JMP 8.0 (SAS Institute Inc., Cary, North Carolina, U.S.). Values of response variables (crown volume and crown density) were tested for normality and equal variance prior to Analysis of Variance (ANOVA). Crown volume was transformed with the cubic root and crown density with the cubic power to meet ANOVA as- sumptions. The effects of trunk diameter class and photographic distance on the response variables were analyzed using a 5 × 4 ANOVA model. Where main effects were significant, multiple comparisons of means were conducted using Tukey’s HSD test at α = 0.05 significance level. One-sample t-tests were also used to test the absolute percentage differences in computed crown metrics between photographic distance intervals against hypoth- esized values of 0%, 1%, 5%, and 10%. Polynomial regression was used to model the relationship between trunk diameter and computed crown volume. Simple linear regression was used to assess the precision and accuracy of software-computed crown volume relative to crown volume calculated using geometric sol- ids. Precision was assessed using the coefficient of determina- tion (R2 ), and accuracy was assessed using the slope coefficient (Β1 by geometric calculation, and Β1 ), where Β1 175 < 1 indicated overestimation of crown volume > 1 indicated underestimation. RESULTS Average crown volume and density across the five trunk diam- eter classes ranged 22 – 2,743 m3 and 83%–92%, respectively (Table 1). Crown volume was significantly greater with each incremental increase in trunk diameter class regardless of pho- tographic distance. Crown density showed a similar pattern, but the larger diameter classes had a tendency to not significantly differ from one another. Regardless of trunk diameter class, a significant effect of photographic distance on neither crown volume nor crown density could be detected with ANOVA. Testing absolute percentage differences in computed crown metrics between photographic distance intervals revealed that computations were highly repeatable across distances (Table 2). For crown volume, about two-thirds of the repeated com- putations had absolute differences of less than 5%, and about one-third ranged 5%–10% difference. These errors had a ten- dency to occur in the larger trunk diameter classes and when moving over long distance intervals from the tree. The highest average error (15.7%) occurred for the 31–45 cm class when moving from 1.5× to 3× tree height. Crown density showed even greater repeatability across photographic distances. Two- thirds of the repeated computations had absolute differences of less than 1%, and all others did not exceed 5%. Crown density was most sensitive to photographic distance for smaller trees. Crown volume showed a very strong relationship to trunk di- ameter for the sampled sugar maples (Figure 3). A cubic equation was found to be the best candidate polynomial model with an adjusted R2 geometric solids provided precise estimates of crown volume relative to the UrbanCrowns computations (Table 3) with ad- justed R2 Relative to the UrbanCrowns computation, the vertical ellip- soid substantially overestimated crown volume (Β1 whereas the circular paraboloid substantially underestimated values ranging from 0.9460 to 0.9783 (all P < 0.0001). = 0.5335), value of 0.8901 (P < 0.0001). All of the evaluated Figure 3. Polynomial regression of crown volume computed us- ing UrbanCrowns image analysis software and trunk diameter (TD) measured at 1.37 m above ground line. Regression model (P < 0.0001) is based on measurements of 50 open-grown sugar maples (Acer saccharum). ©2011 International Society of Arboriculture
July 2011
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