A raster approach to population estimation using high-altitude aerial and space photographs

REMOTE SENS. ENVIRON. 27:59-71 (1989)

A Raster Approach to Population Estimation Using High-Altitude Aerial and Space Photographs C.P. Lo Department of Geography, University o f Georgia

t h a n effort to automate the time-consuming procedure of the dwelling unit count method of population estimation using aerial photographs, a raster approach was adopted to extract residential building density data on a grid cell by grid cell basis from high-altitude aerial and space photographs. The maximum possible occurrence of dwelling units in each grid cell was determined with reference to the dwelling unit sizes and existing housing data from the census. The actual percentage of occurrence of residential buildings in each grid cell was then estimated from the photographs and translated into a population estimate. This approach was applied to the Providence area, Rhode Island, using both black-and-white National High Altitude Photography (NHAP) at 1:80,000 scale and Large Format Camera (LFC) photography enlarged to 1 : 50,000 scale. It was found that the number of dwelling units so obtained from NHAP had to be corrected with the application of a double logarithmic model and that tone was the sole element used in dwelling unit estimation in the case of LFC photography. At census tract level, population estimates exhibited mean relative errors between

Address correspondence to Dr. C. P. Lo, Dept. of Geography, Univ. of Georgia, Athens, GA 30602. Received 11 May 1988; revised 11 November 1988. 0034-4257/89/$3.50 ©Elsevier Science Publishing Co. Inc., 1989 655 Avenue o f the Americas, New York, NY 10010

+ 2.50 and + 6.94 % in NHAP and between - 8.24 and - 13.64 % in LFC photography, depending on whether regional or overall household size values respectively were employed in computing the population size fiom the number of dwelling units. The raster approach permitted the application of a microcomputer-based GIS package to model and update the population estimation fiom high altitude aerial and space photographs.

INTRODUCTION The use of large-scale aerial photographs for population estimation employing the dwelling unit count method has been capable of producing population estimates at the census tract level with an accuracy (in terms of relative error) of about + 0.90% (Lo, 1986). According to Watldns (1984) and Watkins and Morrow-Jones (1985), the accuracy of population estimation primarily depends on the occurrence of multiunit structures, which make the counting of dwelling units difficult. In addition, the accuracy of the household size and vacancy rate figures, which have to be employed to compute the population size from the number of dwelling units counted, could also affect the ultimate accuracy of the population estimates. De-

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spite these difficulties, it is generally agreed that the photographically derived dwelling unit count method of population estimation using large-scale (say, 1:10,000) aerial photographs can produce fairly accurate results at the census tract level. One major handicap of this method of population estimation is the time-consuming process of counting dwelling units, which normally is conducted with the aid of a mirror stereoscope and magnifying binoculars. Another problem is the large number of aerial photographs that have to be used to cover one whole city. In moving from one photograph to another, care must be taken to avoid omission or commission in identifying and counting the dwelling units. Thus, the main objective of this research is to find a new approach which could ease the tedious nature of the dwelling unit count method of population estimation while maintaining the high level of accuracy specifed above. Another objective is to evaluate such an approach on the basis of both high altitude aerial photographs and space photographs, which provide a better synoptic view of the city area. Finally, the incorporation of population estimation into a Geographic Information System (GIS) is also explored to demonstrate the ease with which other types of socioeconomic data can be employed to improve the accuracy of the population estimates.

THE RASTER APPROACH TO DWELLING UNIT DETERMINATION

One possible approach to simplifying the procedure of dwelling unit count is to determine the residential building density in different parts of the photograph. This is equivalent to determining the tonal density of the photograph, which should be directly correlated with building density. An accurate way of doing this is to divide the aerial photograph into a number of small regular-sized grid cells, the size of which is determined by the spatial resolution and scale of the aerial photograph being used. Such a procedure, therefore, converts the photographic data into a raster format which can be easily accommodated by the computer. This was originally proposed by Hsu (1973) and more recently was tested by Iisaka and Hegedus (1982) using digital Landsat MSS data,

which were in raster format. No one has yet applied this approach to aerial photographs. The procedure for determining building density on a grid cell by grid cell basis varies according to whether high-altitude aerial photographs or space photographs are used. In the case of highaltitude aerial photographs, such as the National High Altitude Photographs (NHAP), the spatial resolution is sufficiently high to permit individual buildings to be detected. The stereoscopic coverage of the high-altitude aerial photographs further enhances visual discrimination of individual buildings and their heights with the aid of a mirror stereoscope at 6×magnification power. In this case, the theoretical maximum number of dwelling units that could occupy the whole grid cell at the ground level is determined empirically by placing the grid cell in a large, homogeneous residential area on the photograph, and the actual number of dwelling units is counted. This will be a realistic determination of the maximum number of dwelling units for a given area, having taken into consideration the open space and roads that are essential amenities to the residents. This method of determination is capable of taking into account different cultural requirements for living space. Once this theoretical value is obtained, it will be applied to all other grid cells on the photograph. For each grid cell, a transparent dot grid is registered on the cell, and the number of dots that fall on dwelling units is counted. By relating this to the total number of dots in the grid cell, the percentage of dwelling units actually occurring in each grid cell is then determined. Multiplying the actual percentage by the theoretical number of dwelling units for each grid cell provides an actual number of dwelling units in that grid cell. This process, however, is complicated by the fact that dwelling units can be vertically structured in multistoried buildings. In such a case, the number of stories of buildings is estimated with reference to single-storied structures in the environs from stereoscopic viewing of the aerial photographs. Multiplying the number of stories by the theoretical maximum number of dwelling units at the ground level provides a new basis for computing the actual number of dwelling units in these multistoried structures after the actual percentage has been estimated. Here an assumption has been made that for a particular grid cell the number of stories of all buildings is the same. With a large

Raster Approach to Population Estimation 61

number of grid cells being used, an error of overestimation in one grid cell is normally balanced by an error of underestimation in another. To ensure that only residential building densities are determined, the whole process is preceded by an interpretation of the use of individual buildings. Although a dichotomous classification into residential and nonresidential may have been sufficient for the present purpose, a broad Level I land use classification of each grid cell is carried out. Only the dominant land use in each grid cell is recorded. In applying this approach to space photographs, such as the Large Format Camera (LFC) photographs, the procedure of residential building density determination as described above for high-altitude aerial photographs has to be modified. This is because the spatial resolution of the space photographs is still not high enough to permit individual buildings to be discriminated, although most space photographs allow stereoscopic viewing by a mirror stereoscope to be carried out. In this case, the tonal values in each grid cell have to be relied upon to estimate the actual building densities. Buildings are observed to exhibit light tones on the space photographs so that an estimation of the percentage of light-toned areas in a grid cell will provide the percentage of buildings occupying the grid cell. This percentage can be easily estimated by means of a transparent dot grid properly registered to the grid cell. By counting the number of dots that happen to fall on the light-toned areas and dividing this by the total number of dots in the grid cell, a percentage of buildings or building density is obtained ff the area of the grid cell is known. The major problem of this approach as applied to space photographs is to determine the theoretical maximum number of dwelling units in a grid cell. The following formula is proposed: Theoretical maximum no. of dwelling units per km2 Mean no. of dwelling units per km 2 Mean percent of residential buildings per km 2 estimated from space photographs

(1) The "mean number of dwelling units per km2'' is obtained either from the existing census data or by

a sample survey. The theoretical maximum number of dwelling units per km 2 can be easily converted to conform to the area of the grid cell. The actual number of dwelling units per grid cell can be obtained by multiplying the percent of residential buildings per grid cell as estimated from the space photograph to this theoretical maximum, after having carried out an interpretation of the dominant building use in each grid cell. It is important to note that by this method the multistoried natttre of certain dwelling units has been ignored because the tonal value by itself cannot tell the number of stories of the building structure. It is clear from the discussion above that other image elements such as shape, height, pattern and size have been used to supplement tonal information in estimating the number of dwelling units from high-altitude aerial photographs. However, in the case of space photographs because of their lower spatial resolution compared with highaltitude aerial photographs, tone has been relied on as the major clue for estimating the number of dwelling units in the raster approach.

RESULTS OF APPLICATION The approach described above was applied to estimate the population of Providence, RI using 1 : 80,000 scale black-and-white National High Altitude photography (NHAP) and Large Format Camera photography enlarged to a scale of 1:50,000 from its original 1:756,000 scale. The selection of Providence was partly dictated by the availability of good quality LFC photographs and partly by the suitable size of the city which is not too large to handle but is complex enough to represent a typical American city. Use of National High Altitude Photography (NHAP) The NHAP of Providence which was acquired on 16 March 1985 is of excellent quality (Fig. 1). This black-and-white panchromatic NHAP has a ground resolution of about 5 m, and with the average dwelling unit size measured to be about 0.2 × 0.2 mm on the contact print, a grid-cell size of 0.5 x 0.5 cm which is equivalent to a ground area of 0.4 × 0.4 km or 0.16 km2 was employed. This size was found to be the smallest acceptable for visual interpreta-

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Figure 1. A National Altitude photographo| Providence,RI. tion and should not result in so many grid cells as to hamper handling ease. As explained in the previous section, the theoretical maximum number of dwelling units at ground level found within each grid cell was empiricalltt determined by putting a transparent grid of 0.5 × 0.5 cm over the single-storied residential structures of the Providence area. The actual number of dwelling units counted was 375, which provided the theoretical basis at ground level for visually determining the actual percentage of dwelling units in each grid cell. A total of 96,048 dwelling units were counted in this way. There were 1086 grids with building structures. The mean number of dwelling units per grid cell

was 88.4 and the mean building density was 552.7 building units per km2. The highest number of building units per cell was 788, thus indicating the occurrence of multistoried structures and giving the highest building density of 4925 building units per km 2. These building data by grid cells had to be aggregated into appropriate census tracts based on the census tract map of the 1980 census (Bureau of Census, 1983). Because of the irregular-shaped census tract boundaries, the grid data could only be approximately fitted. At the border between two census tracts, it was necessary to assign the building data in one whole grid cell to the census

Raster Approach to Population Estimation

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PERSONS/UNI ¢

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Figure 2. Household size distribution map of Providence by census tracts (Source: Bureau of the Census,

1983). tract which occupied more than half of the area of the grid cell. There were in total 92 census tracts in the study area (Fig. 2). It is hoped that this number was large enough to compensate for the over- and underassignment of grid cell values at the census tract boundaries. These building unit data by census tracts were compared with the housing unit data obtained by the 1980 census (Bureau of Census, 1983). It became evident that the photography-derived building unit data grossly underestimated the actual number of housing units. This was not surprising in view of the fact that the number of building units was estimated based on the percentage of a theoretical maximum. However, it was found that by taking the common logarithms of both the actual number of housing units and the photograph-derived number of building units, the two variables gave rise to a highly significant correlation of 0.742 and a double-log model in the form of Iog(NOHU) = 1.6454+0.5415(IogNOBG),

(2)

where NOHU is the number of housing units and

NOBG is the number of building units obtained from aerial photographs. Thus, by applying this model it was possible to obtain the corrected number of dwelling units, which provided the basis for population estimation. Comparing these corrected dwelling unit data with the 1980 eensus data on the number of housing units by census tracts gave a mean relative error of + 4.26%. The next question was: What would be the appropriate household size value to be used for calculating the population from these dwelling units? By analyzing the 1980 Census data for the city of Providence, it was possible to group the household size values into seven classes and to show their spatial distribution in the form of a map (Fig. 2). The midpoint value of the appropriate class of data for each census tract was employed to compute the population size from the corrected estimates of dwelling units of each census tract. This approach may be regarded as using regional estimates of household size values to compute population estimates. An alternative approach is to corn-

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Figure 3. Regression analysis of the accuracy of pop~ation estimates from: (e) National High Altitude photographs, Y = 1130.5434 + 0.6833X; ( 0 ) Large Format Camera photographys, Y = - 750.1403+ 1.1019X.

pure an overall household size value for the whole study area, irrespective of the regional variations. This figure was found to be 2.46 persons per dwelling unit. In order to examine the effect of these two different approaches, namely, regional and overall household size values, on the accuracy of population estimation, each set of figures was multiplied by the corrected number of housing units obtained from the double-log model at census tract level. Comparison was made with the estimated 1984 population figures for Providence obtained from the Bureau of the Census (1986). It was found that the resultant mean relative errors for using regional and overall household size values were respectively + 2.50 and + 6.94%. As expected, the use of an overall household size value gave a poorer result. The use of regional household size values seemed to better compensate for the overand underestimation of population. If we examine the population estimates for each census tract ob-

tained by the regional household size method, the relative errors were found to vary from a maximum of +97.7% to a minimum of +0.34%. To show the degree of variation graphically, these population estimates from NHAP were plotted against the actual population for the corresponding census tracts obtained by the Census, and a regression line was drawn (Fig. 3). The regression model was Y=1130.5434+O.6833X, the coefficient of variation was 25.77%, and the coefficient of determination was 0.58 (or 58% determined). Spatially, the inner city area suffered from an underestimation of population while the more outlying city area displayed an overestimation. This result clearly reflected the problem of multistofied structures and the greater degree of mixing of residential and nonresidential structures in the inner city area. Therefore, on the census tract basis, this method of population estimation is less reliable than the conventional dwelling unit count approach using large-scale aerial photographs, but its

Raster Approach to Population Estimation

potential for the whole procedure being incorporated into a computer-based GIS is great.

Use of Large Format Camera (LFC) Photography The next application was to apply the raster approach of population estimation to LFC photographs of the same study area acquired from the Space Shuttle Mission STS-41G on 5 October 1984 (Doyle, 1985). The LFC photography (Kodak film type 3414) exhibited excellent spatial resolution and geometric accuracy (Derenyi and Newton, 1987; Lo, 1988). The LFC photographs of the Providence study area that were selected (frames 663 and 666) provided a base-height ratio of 0.90 which allowed an enhanced vertical exaggeration of the stereomodel to be obtained when viewed through a mirror stereoscope. The Providence area occupied only a small portion of the 23 × 46 cm LFC photograph (Fig. 4). At its original scale of 1:756,000, the LFC photograph is too small for detailed population estimation by census tracts. It was therefore enlarged 15.6 times to a scale of 1:50,000 (Fig. 5). The ground resolution of the LFC system for black-and-white Kodak 3414 film is about 10 m. A transparent grid was laid on top of one photograph and the grid cell size employed was 1 × 1 cm or 0.25 km2 in ground area. These grid cells were placed in such a way that they corresponded as best as possible with the way the

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grid cells were laid out in the NHAP application. Consequently, one could make comparison with the NHAP photograph to determine how much detail was lost in the space photograph. The excellent spatial resolution of the LFC photograph compared favorably with the NHAP used before. However, individual buildings could not be distinguished under stereoscopic viewing. As already explained in an earlier section of this paper, the approach of population estimation adopted had to rely heavily on tonal information. The percentage of residential buildings which correlated with the percentage of light-toned areas within each grid cell was visually determined with reference to a dot grid with a density of 100 points per cm2. To obtain the theoretical maximum number of dwelling units per grid cell, the mean percentage of residential buildings estimated from the space photograph for the whole study area was computed on a per km 2 basis. The mean number of dwelling units per km9 for the study area was obtained from the 1980 census. These data were substituted into Eq. (1) to obtain the theoretical number of dwelling units per square kilometer. The result was 1382 dwelling units per km 2 or 346 dwelling units per 0.25 km 2 grid cell. The latter figure was multiplied by the percentage of residential buildings determined from the LFC for each grid cell to obtain the actual number of dwelling units. The overall relative error of dwelling unit

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Figure 5. An enlarged LFC photograph of Providence(originalenlargement15.6×).

determination by this method was -6.47%. In order to obtain a population estimate for each census tract, both the overall household size and regional household size values were employed as multipliers to the number of dwelling units per census tract. The overall household size method (2.32 persons per household) gave a mean relative error of -13.64% while the regional household size method gave a mean relative error of - 8.24%, thus once again confirming the superiority of the regional household size value to the overall household size value in population estimation. The population estimates obtained from the LFC photograph by the regional household size method was also plotted against the actual population for the corresponding census tracts in order to visualize the degree of variation of these population esti-

mates from their correct values (Fig. 3). The following regression model was obtained: Y = - 750.1403 + 1.1019X. The coefficient of variation was 56.25% and the coefficient of determination was 0.44 (or 44% determined). Clearly, the population estimates obtained from LFC photographs spread more widely from the regression line than those obtained from NHAP photographs. It is therefore clear that the use of LFC photographs gave much inferior results of population estimation to those for NHAP photographs. The underestimation of population in the case of the LFC photographs was obvious and could be explained by the difficulty in dealing with multistoried buildings in the process of determining the percentage of residential buildings in each grid cell based on tonal information alone.

Raster Approach to Population Estimation

THE GIS APPROACH TO POPULATION ESTIMATION The raster approach to dwelling unit count provided a convenient data format for storage by the microcomputer. In order to explore how such a new approach could be incorporated into a GIS, the dwelling unit data obtained from NHAP photographs of Providence were entered into a Zenith Z-159 personal computer with a common ASCII text editor. Three other sets of data, namely, census tract boundaries, land use, and household size by census tract were also entered into the com-

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puter. The pMAP GIS package (Berry and Reed, 1987) was employed in the analysis. The program permitted easy display of all these four sets of data as choropleth maps (Figs. 6, 7, and 8). From the land use map, the residential use could be singled out (Fig. 9), which was then combined with a dwelling unit map to produce a residential-dwelling unit map (Fig. 10). By combining household size with residential-dwelling units, one could obtain population estimates for each grid cell (Fig. 11). To obtain population estimates by census tracts, one had to identify individual census tracts using the census tract map and the population estimates map. A data file of population estimates (Table 1) for any census tract could be generated and copied into a data diskette where further analyses of the population data could be carried out. One major advantage of this GIS approach to population estimation was the flexibility with which household size data could be updated or changed,

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DISCUSSIONS AND CONCLUSIONS This paper investigated the usefulness of the raster approach to population estimation using high altitude aerial photography (NHAP) and space photography (LFC). Such an approach has the advantage of simplifying the time-consuming procedure of the conventional dwelling unit count method using large scale aerial photography. The underlying principle of this approach is the discrimination of residential building coverage by tonal changes

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C o m p u t e r residential u s e m a p of t h e P r o v i d e n e e s t u d y area.

assisted by clues on the heights and sizes of the buildings where possible. The determination of a theoretical maximum number of dwelling units per grid cell provided a means to relate the tonal data with the dwelling unit data. Although not done in this study, the whole process can be automated with the aid of a scanning densitometer and a microcomputer. The use of a raster format allows the dwelling unit data to be incorporated, along with land use, census tract, and household size data, into a microcomputer-based Geographic Information System (GIS). The commercially available pMAP package for the microcomputer has been found to be capable of integrating these data to generate population estimates by census tracts with ease. The major concern of this study, however, lies in the accuracy of the new dwelling unit count and population estimation approach, which was found to be not as good as the conventional approach using low-altitude aerial photography. In the case of application to NHAP, individual buildings could still be seen and their functions interpretable in

Raster Approach to Population Estimation 69

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Figure 10. Computer ehoropleth map of dwelling units i n residential areas only.

each grid cell. Even the number of stories of the building was visible. However, underestimation of the actual number of dwelling units inevitably occurred because the grid cell was used as the basis in aggregating data. Fortunately, this could be corrected by the application of a double-log regression model, calibrated with reference to existing census data. The resultant accuracy of population estimation by census tracts varied from + 2.50 to + 6.94% (relative error), depending on whether regional or mean household size value was used in the computation.

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The application to LFC photography was found to be feasible in generating population estimates. However, in view of the lower spatial resolution of the LFC photography compared with NHAP, individual buildings could no longer be seen. Tone was the sole image element for determining the extent of occurrence of residential building cover in each grid cell. Although stereoscopic viewing of the LFC photographs (already enlarged 15.6 times) was still possible, the presence of multistoried structures posed some difficulty in accurate estimation of dwelling units. The resultant accuracy for population estimation varied from -13.84% with the use of mean household size in the computation to - 8 . 2 4 % with the use of regional household size in the computation. The

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Table 1. A Sample Data File of Population Estimates for Each Grid Cell of a Census Tract Generated from the GIS Census Tract No.

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Grid Cell Coordinates X Y

Population

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root mean square errors (RMSE) of the estimates were also computed for each case, and it was found that there were larger RMSE for this method applied to L F C photography than that applied to NHAP photography, thus suggesting that the precision of the population estimate derived from L F C photography was poorer than that for NHAP photography. The implication clearly is that while it is possible to obtain fairly accurate population estimates for a region by the raster approach, the subregional population estimates tend to fluctuate greatly. A possible refinement at the subregional level is to develop one or more mathematical models which will correct for undercounting of dwelling units based on tonal variations. For this to be successful, good quality ground truth data on population will be required. Despite the mediocre results in population estimation, this research has demonstrated the great potential of high-altitude aerial photographs and space photographs to quickly obtain dwelling unit data in raster format as input to a GIS. The GIS approach has been shown to exhibit a high degree of flexibility, which permits mapping of population distribution and updating of population estimates on a regular basis for a city area. All this should prove to be an invaluable tool to the planners.

5730

The author wishes to thank three anonymous reviewers of this paper, who have made excellent suggestions to the author to improve the paper.

REFERENCES Berry, J. K., and Reed, K. L. (1987), Computer-assisted map analysis: a set of primitive operators for a flexible approach. Technical Papers 1987 ASPRS-ACSM Annual Convention, Vol. 1. Remote Sens/ng, Baltimore, MD, 29 March-3 April, Falls Church, VA, American Society for Photogrammetry and Remote Sensing, and American Congress on Surveyingand Mapping, pp. 206-218. Bureau of the Census (1983), 1980 Census Population and Housing Block Statistics for Providence-WarwickPawtucket, R.I.-Mass. SMSA, PHC80 1-293, U.S. Government Printing Office,Washington, DC. Bureau of the Census (1986), Northeast: 1984 population and 1983 per capita income estimates for counties and incorporated places, Current Population Reports Local Population Estimates, Series P-26, No. 84, NE-SC, U.S. Government Printing Ofliee, Washington,DC. Derenyi, E., and Newton L. (1987), Control extension utilizing Large Format Camera photography, Photogramm. Eng. Remote Sens. 53:495-499. Doyle, F. J. (1985), The Large Format Camera on Shuttle Mission 41-G, Photogramm. Eng. Remote Sens. 51:200-202.

Raster Approach to Population Estimation 71

Hsu, S. Y. (1973), Population estimation from ERTS imagery: methodology and evaluation, Proceedings of the American Society of Photogrammetry 39th Annual Meeting, Falls Church, VA, American Society of Photogrammetry, pp. 583-591.

Iisaka, J., and Hegedus, E. (1982), Population estimation from Landsat imagery, Remote Sens. Environ. 12:259-272. Lo, C. P. (1986), Accuracy of population estimation from medium-scale aerial photography, Photogramm. Eng. Remote Sons. 52:1859-1869.

Lo, C. P. (1988), Comparative evaluation of the thematic contents of Large Format Camera photography, Metric Camera photography, and Shuttle Imaging Radar-A data for topographic mapping, Photogramm. Eng. Remote Sens. 54:731-742. Watkins, J. F. (1984), The effect of residential structure variation on dwelling trait enumeration from aerial photographs, Photogramm. Eng. Remote Sens. 50:1599-1607. Watkins, J. F., and Morrow-Jones, H. A. (1985), Small area pop~dation estimates using aerial photography, Photogramm. Eng. Remote Sens. 51:1933-1935.