LU102459B1

LU102459B1 - Method for predicting building height using satellite image

Info

Publication number: LU102459B1
Application number: LU102459A
Authority: LU
Inventors: Xia Haoming; Feng Yafei; Lu Heli; Liu Guifang
Original assignee: Univ Henan
Priority date: 2020-07-22
Filing date: 2021-01-27
Publication date: 2021-08-04
Also published as: CN111721267A

Abstract

The present invention relates to a method for predicting a building height using a satellite image, and belongs to the technical field of building height measurement. In the method, heights of a small number of buildings in a target region are measured; ratios of the measured heights to corresponding shadow lengths in the satellite image are calculated; then, an average value of all ratios is taken as a ratio coefficient, which is used to solve an estimated height of each building in combination with the shadow length of each building in the satellite image; and then a determined correction model is used to correct the estimated height of each building to obtain a high-precision corrected height. The method of the present invention is simple in principle and easy to implement, without calculating the solar azimuth angle, the solar altitude angle and so on, and has a small workload. Moreover, it has high calculation accuracy and calculation efficiency, and thus has high application value.

Description

BL-5197 LU102459

METHOD FOR PREDICTING BUILDING HEIGHT USING SATELLITE IMAGE Technical field The present invention belongs to the technical field of building height measurement, and specifically relates to a method for predicting a building height using a satellite image. Technical background Buildings are main components of a city, and the increase in their heights reflects the expansion of the city's vertical space. Quickly and accurately extracting building height information in residential regions is of great significance for studying building floor area ratio, improving the living quality of urban residents and so on. In the prior art, Chinese invention patent publication No. CN108765488A proposes a shadow-based high-resolution remote sensing image building height estimation method. In the method, a shadow length is determined by performing shadow detection in an original image to be detected; then an azimuth angle of the sun is solved to further calculate a solar altitude angle; and a height of a building is estimated by using the obtained shadow length and solar altitude angle. The method has the following disadvantages: the method is complicated; the solar azimuth angle, the solar altitude angle and so on need to be solved; the workload is large; the calculation efficiency is low; and the calculation accuracy does not meet the requirements. Summary of the invention j An objective of the present invention is to provide a method for predicting a building height using a satellite image, which is used to solve the problems of complexity i and low calculation efficiency and accuracy of the existing methods. LU102459 Based on the above objective, the technical solution is as follows: A method for predicting a building height using a satellite image, comprising the following steps: (1) acquiring a satellite image of a target region, extracting a shadow of each building in the satellite image, and calculating a shadow length of each building in the target region; (2) selecting N buildings in the target region for height measurement, wherein Nz2, and a condition of selecting the N buildings is that heights of the selected buildings are different from each other; acquiring actual measured heights of the N buildings, calculating ratios between the shadow lengths and the actual measured heights of the N buildings, respectively, and calculating an average value of the N ratios to determine a ratio coefficient; (3) using the ratio coefficient to calculate an estimated height of each building in the target region in combination with the shadow length of each building in the target region; and (4) acquiring a correction model for representing a relationship between corrected heights and estimated heights of the buildings, wherein parameters of the correction model are obtained by fitting the actual measured heights and the estimated heights of the N buildings in the target region; and using the correction model to calculate the corrected height of each building in the target region in combination with the estimated height of each building in the target region.

The beneficial effects of the above technical solution are as follows: In the prediction method of the present invention, the heights of a small number of buildings in the target region are measured; ratios of the measured heights to corresponding shadow lengths in the satellite image are calculated; then, an average value of all ratios is taken as a ratio coefficient, which is used to solve an estimated height of each building in combination with the shadow length of each building in the satellite image; and then a determined correction model is used to 0102459 correct the estimated height of each building to obtain a high-precision corrected height.

The method of the present invention is simple in principle and easy to implement without calculating the solar azimuth angle, the solar altitude angle and so on, and has a small workload.

Moreover, it has high calculation accuracy and calculation efficiency, and thus has high application value.

Further, in order to reduce the calculation error, in step (1), a box plot method is used to calculate the shadow length of each building in the target region, with the following steps: 1) according to an azimuth of the sun when the satellite image is captured, intersecting simulated sun rays with a shadow plane of the building in the satellite image to determine several line segments in the shadow plane, and arranging the line segments with the values thereof from small to large to form observation samples; 2) determining an upper quartile and a lower quartile in the observation samples, calculating a difference between the upper quartile and the lower quartile, and determining outlier cutoff points Y1 and Y2 according to the difference with the following calculation formula: Y1=X075 + 1.5 x IQR Y2=X0.25 - 1.5 x IQR wherein in the formula, Y1 is a first outlier cutoff point, Y2 is a second outlier cutoff point, Xo.25 is the lower quartile, Xo 75 is the upper quartile, and IQR is the difference between the upper quartile and the lower quartile; and 3) removing line segment values greater than the outlier cutoff point Y1 and less than the outlier cutoff point Y2 in the observation samples, and averaging the remaining line segment values to obtain the shadow length of the building.

The box-plot mathematical model (i.e. box plot method) is used to automatically and quickly identify outlier values of the line segment values in each shadow plane, LU102459 and delete them, which realizes the automatic screening of the outlier values and has high detection efficiency. Further, in order to improve the accuracy of building height inversion, a calculation formula of the correction model is as follows: H, =a*H. +b*H, +c wherein in the formula, H',, is a corrected height of a building, H,,, is an estimated height of the building, and a, b, and c are all parameters in the correction model, which are obtained by fitting actual measured heights and estimated heights of known sample points in the target region.

Further, a calculation formula of the ratio coefficient in step (2) is as follows: K — YN 1Snx/ Anz n N wherein in the formula, K, is the ratio coefficient, S,, is a shadow length of an x-th building, 4, is an actual measured height of the x-th building, and N is the number of buildings.

Further, a calculation formula for the estimated height of each building in step (3) is as follows: Sys H, x =

TK wherein in the formula, H,, is the estimated height of the building.

Brief description of the drawings Fig. 1 is a flowchart of a method for predicting a building height in an embodiment 4 of the present invention; LU102459 Fig. 2 is a front view image diagram of a target region in the embodiment of the present invention; Fig. 3 is a schematic diagram of shadows of 34 buildings in the front view image in the embodiment of the present invention; and Fig. 4 is a box plot of a 28" shadow plane of shadow planes of the buildings in the embodiment of the present invention.

Detailed description of the embodiments A specific embodiment of the present invention will be further described below in conjunction with the drawings.

This embodiment proposes a method for predicting a building height using a satellite image, and its basic idea is as follows: a front view camera (nadir camera) on Ziyuan-3 satellite is used to capture several buildings in a target region to obtain a front view image of the buildings; the azimuth of the sun is used to simulate sun rays, and the simulated sun rays are intersected with a shadow plane of the building in the front view image, to determine several line segments in the shadow plane; then a box plot method is used to remove outlier values of the line segments in the shadow planes of the buildings; and thereafter, the remaining line segments are averaged to calculate shadow lengths of the buildings in the front view image, i.e. shadow lengths.

Thereafter, actual heights (i.e. actual measured heights) of a set number of buildings in the target region are measured. For example, the actual heights of three buildings are measured separately. The ratios between the shadow lengths 5 and the actual heights of the three buildings are calculated separately. An average 14102459 value of the three ratios is solved to obtain a ratio coefficient. Finally, the ratio coefficient can be used to determine an estimated height value of each building in combination with the length of the shadow plane of each building in the front view image; then a corrected height value of each building in the target region is calculated through an inversion model between estimated height values and corrected height values of the buildings to obtained accurate building heights. The overall process is as shown in Fig. 1. The steps of implementing the method are specifically set forth below: Step 1. Extract shadows of the buildings. The specific steps are as follows: According to a front view camera on the Ziyuan-3 satellite (i.e. ZY-3), a front view image of the target region as shown in Fig. 2 is captured, and according to the brightness difference of the image, the shadows of the buildings in the front view image of the residential region are extracted, wherein the shadows of 34 buildings in the front view image of Fig. 2 are as shown in Fig. 3.

Step 2. Calculate the shadow lengths according to the shadows of the buildings in Fig. 3. The specific implementation method is as follows: (1) According to the azimuth of the sun when the front view image is captured, sun rays are simulated and drawn in Fig. 3, and the simulated sun rays are intersected with the shadow plane of the buildings in the front view image to determine several line segments in the shadow plane.

(2) In order to reduce the error and improve the screening efficiency, the box plot method is used to remove the outlier values of the line segments in the shadow plane of each building. Taking an outlier value of a line segment of a shadow plane of one of the buildings as an example, the specific steps are as follows: S01. It is measured that there are a total of n line segments in the shadow plane of 6 the building, corresponding to n sample observation values. According to the order LU102459 of observation values from small to large, the sample observation values are arranged as X1, X2, X3..., Xn to form observation samples, where n is taken as 20. The arrangement is as shown in Table 1 below. Table 1 to large, unit: meter) 0389242773

5.591321954

19.69029248

19.77517983

20.58616718 2111245906

21.79398739

23.23851150 2337117369

23.58903427

23.82931407 2449323078

25.74082861

25.79608307

25.93158538

26.54006849

26.74177863

28.22438064 S02. Calculate quartiles and median of the sample observation values. The calculation formula is as follows: X({n-p}+1)» n*p is not an integer Xp=<l 5 Xap) + XD) n*p is an integer In the formula, n is the number of samples, Xp is a p-quantile of the sample (0<p<1), when p=0.25, Xo.25 represents a lower quartile; and when p=0.75, Xo.75 represents an upper quartile. „

According to the above formula, in combination with the data in Table 1, Xo.25 and LU102459 Xo.75 are calculated separately, and the calculation results are as follows: Xo.25= 1/2 * (X5 + X6)= 1/2 * (20.5861671774 + 21.1124590567)=20.84931 Xo75= 1/2 * (X15 + X16)= 1/2 * (25.7960830656 + 25.9315853827)=25.86383

S03. Calculate a difference (i.e. quantile distance) between the two quantiles Xo 25 and Xo.75: IQR=X0 75 - Xo25=5.01452 S04. Calculate two outlier cutoff points.

The calculation formula for the two outlier cutoff points is as follows: Y1=Xq75 + 1.5 x IQR=33.38561 Y2=Xg25- 1.5 x IQR=13.32153 In the formula, Y1 is a first outlier cutoff point, and Y2 is a second outlier cutoff point.

S05. Outlier value judgment: When a sample observation value Xn < Xo 25 - 1.5*IQR or Xn > Xo.75 + 1.5*IQR, it means that Xn is an outlier.

Therefore, it can be determined that the observation sample data Xi outside the interval [13.32153, 33.38561] is an outlier by judging according to the outlier cutoff points calculated in step S04. It can be seen from corresponding Table 1 that observation sample X1=0.389242773 and observation sample X2=5.591321954 are outside the range of the outlier cutoff interval [13.32153, 33.38561], so outliers X1 and X2 are removed.

Sample X3 =10.69029248 is the minimum value of the samples after removal, which automatically becomes a "lower edge" of the box plot.

Sample X20 = 28.30353732 is the maximum value of the samples after removal, which becomes an "upper edge" of the box plot.

The box plot, after the outliers are removed, is as shown in 8

Fig. 4. The abscissa "Length28" in the figure represents the line segment length of LU102459 the 28” shadow plane. (3) After the outlier values are removed, the remaining line segments (i.e. sun rays) in the shadow plane of each building are averaged to calculate the shadow length of each building in the front view image, i.e. the shadow length. 34 buildings are numbered sequentially from 0 to 33, and the shadow length of each building is calculated as shown in Table 2. Table 2 | Ne. | Shadow plane length (m)

27.754 6 1 25984 | 9 | 36.638

27.866

34.093

27.169

31.614

31.193

26.667

27.092

36.962

38.787

40.209

31.681

36.866

24.001

24.614 9

Step 3. Calculate a ratio coefficient.

The specific calculation method is as follows: First, in a study region, according to the heights of the buildings, three sample points are selected to measure actual heights (i.e. actual measured heights) of the three sample points (buildings). The ratios of the shadow lengths to the actual heights are calculated, and are used to construct a ratio coefficient K,,, as shown in Table 3. Table 3 Ho [dor tonsth (m) ual height GI] Leneth/height | pew pe Jew vo me es pew

According to the data in Table 3, the ratio coefficient K, is calculated.

The calculation formula is as follows: K, = Spi Bpy + Sus Bua + S 53 By s 3 (1) In the formula, subscripts 1, 2 and 3 represent three sample points that have obtained the actual heights of the buildings; S, + Sn2 and S,3 are lengths (i.e. shadow lengths) of front view building shadow planes of the three sample points; and hy, 1, hn2 and hy, 3 are actual measured heights of the buildings corresponding to the front view building shadow planes of the three sample points.

The relevant values of the three sample points in Table 3 are substituted into formula (1), and the calculated ratio coefficient K, is thus 0.818. In this step, a condition of selection the sample points is that the heights of the selected buildings need to be different from each other.

More preferably, the 10 greater the height difference between the selected buildings, the better, so that the LU102459 ratio coefficient of the buildings in the study region can be characterized more reasonably. The selected buildings are representative. Therefore, in this step, three buildings with large differences are selected. As other implementations, other numbers (more than two) of buildings may also be selected. As long as they are representative, the specific number is not limited. When N buildings are selected, the corresponding calculation formula of the ratio coefficient is as follows: y, — Zit Sua ne

N In the formula, K is the ratio coefficient, S,x is a shadow length of an x-th building, hnx is an actual measured height of the x-th building, and N is the number of buildings. Step 4. Calculate estimated heights of the buildings. The specific steps are as follows: According to the ratio coefficient K, in step 3, the estimated heights of the buildings are calculated in combination with the shadow lengths obtained in step 2. The calculation formula for the estimated height is as follows: 7 (2) In the formula, H,, is the estimated height of the building, S,,, is the shadow length of the building, and x is the building number, x=1, 2, ..., 34. According to the above formula (2), the estimated heights of 34 buildings in the target region are calculated separately, and the calculation results are as shown in Table 4. 1

Table 4

[4e] bunting eetimated bio |

0 | sowie

6 | 317652906968 |

9 | 447897835452 |

Step 5. Establish a correction model, and correct the heights of the buildings based on the correction model, to obtain corrected height values of the buildings.

The specific steps are as follows: 12

Taking the estimated heights H„ of the buildings as independent variables, and the corrected heights H',x of the building as a dependent variable, a correction model is established by using a quadratic equation of one variable. The correction model is expressed as follows: | akg? * H, ,=a*H, +b*H, +c (3) In the formula, H',, is the corrected building height (i.e. corrected height), H, is the estimated building height (i.e. estimated height), and a, b, and c are all parameters in the correction model, which are obtained by fitting the actual heights (i.e. actual measured heights) of the buildings at the known sample points in the study region and the estimated building heights. In this example, parameters a, b, and c are determined to be 0.0657, - 4.1246, and 96.5325, respectively, and the obtained correction model is as follows: H, =0.0657* H;, —4.1246* H,, +96.5325 After the correction model is determined, estimated height data of 34 buildings in step 4 are separately substituted into the correction model, and the corrected height values of 34 buildings in the target region can be calculated with high accuracy.

In order to verify the accuracy of the results, actual heights of 34 buildings were measured on the spot, and corrected height values of 34 buildings were calculated according to the method with step 1 to step 5 of this embodiment, as shown in Table 5. The results show that in the extracted 34 buildings, the constructed one-element quadratic correction model is used so that the calculation accuracy of 24 buildings is increased by 4.55% on average compared with the calculation 13

| accuracy when the one-element quadratic correction model is not used, and the LU102459 calculation accuracy of 10 buildings is reduced by 3.88% on average. Therefore, it is feasible to invert the building height based on the one-element quadratic correction model.

Table 5 Actual front-viewestimated Esti ted a - sTisate ccurancy height (m) height (m) Accurancy (x) height (m) (x) 0 [319 | 31911840709 9691% | 31.2999990689 100.00%

32.0917660269 994063 | 317814352422 99.63% 35 4763414059 89525 | 308354307609 97.15%

33.9285851467 94.02% | 321668060414 99.17%

33.0473877017 56.53% | 31.9266426561 99.92% 38 2165656546 81.47% | 34.7906657474 91.69% [6 [319 | 31.7652906968 99.58% | 31.7593073476 99.56%

30.9561071149 97.04% | 31.7647939645 99.58% 8 [315 | 35.1326747188 20.50% 326598155536 9767 jo (45 | 447897835452 97.12% |435000000017 16000; 34 0660152812 03.64% | 322134302060 99.03%

11.6750803154 9581% | 386699361260 3890% 332144735134 96.04% | 31.9643475516 99 80% 386476679218 88 85% | 35.1880251221 80.89% #4 7123556112 06.36% | 43 3643899252 93.46%

38.1330807213 8718% | 34.7165356881 74.81% 32 5998575672 9785% | 31 8437116986 99.82%

33.1198353178 96.32% 31 9425400825 96 57% 45 1857157946 97.38% [442057544792 95.27% 33 8966864548 94.11% | 321563336858 99.20% 34 6249938998 92.13% [324287361758 98.37% 47 .416317066 90.84% | 48 5664709647 93.04% 327029683741 70.48% | 31 2604874336 68.66%

40.1557320905 94.17% | 52.4203044950 99.58% 49 0609188998 93907, | 52.2000000192 100.009

38.7303794988 83.47% | 352670578831 76.01% 43 068242135 85.34% | 43 0042028064 84.28% 311487885819 67.13% | 31.7556887633 68.44% 29 3406661125 9198% | 320328566680 96.597, 28 8366111614 90.40% | 32.1866900189 99.11% 30 0909739976 94.33% | [31 8657577072 99 89% 31 8327183741 99.79% | 31.76273072389 99.57%

30.0845506699 94.31% | 31 2668663275 99.90% The prediction method of the present invention has the following advantages: 14

1) The method is simple and easy to implement, without calculating the solar LU102459 azimuth angle, the solar altitude angle and so on, the workload is small, and the calculation efficiency is high. 2) The prediction accuracy is high, which is mainly reflected in two aspects: On the one hand, by selecting a small number of representative buildings and measuring the height, a reasonable ratio coefficient is determined, which can accurately characterize a proportional relationship between shadow lengths of the buildings and actual measured heights. Moreover, the box plot method can be used to quickly identify the outliers of line segments in each shadow plane and delete them, which further improves the rationality of the ratio coefficient, and can determine the estimated heights of the buildings with higher accuracy. On the other hand, by constructing the correction model for representing the relationship between the corrected heights and the estimated heights of the buildings, the accuracy of inverting the heights of the buildings can be effectively improved. In summary, the method of the present invention can quickly and accurately invert the heights of buildings in residential region, and has good feasibility.

Finally, it should be noted that the above embodiment is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiment, those of ordinary skill in the art should understand that: modifications or equivalent replacements of specific implementations of the present invention without departing from the spirit and scope of the present invention shall be covered by the scope of protection of the claims of the present invention. 15

Claims

Claims LU102459

1. A method for predicting a building height using a satellite image, characterized in that it comprises the following steps: (1) acquiring a satellite image of a target region, extracting a shadow of each building in the satellite image, and calculating a shadow length of each building in the target region; (2) selecting N buildings in the target region for height measurement, wherein N>2, and a condition of selecting the N buildings is that heights of the selected buildings are different from each other; acquiring actual measured heights of the N buildings, calculating ratios between the shadow lengths and the actual measured heights of the N buildings, respectively, and calculating an average value of the N ratios to determine a ratio coefficient; (3) using the ratio coefficient to calculate an estimated height of each building in the target region in combination with the shadow length of each building in the target region; and (4) acquiring a correction model for representing a relationship between corrected heights and estimated heights of the buildings, wherein parameters of the correction model are obtained by fitting the actual measured heights and the estimated heights of the N buildings in the target region; and using the correction model to calculate the corrected height of each building in the target region in combination with the estimated height of each building in the target region.

2. The method for predicting the building height using the satellite image according to claim 1, characterized in that in step (1), a box plot method is used to calculate the shadow length of each building in the target region, with the following steps: 1) according to an azimuth of the sun when the satellite image is captured, intersecting simulated sun rays with a shadow plane of the building in the satellite image to determine several line segments in the shadow plane, and arranging the line segments with the values thereof from small to large to form observation 16 samples; LU102459 2) determining an upper quartile and a lower quartile in the observation samples, calculating a difference between the upper quartile and the lower quartile, and determining outlier cutoff points Y1 and Y2 according to the difference with the following calculation formula: Y1 = Xo 75 +15x IQR Y2=Xg25 -15x IQR wherein in the formula, Y1 is a first outlier cutoff point, Y2 is a second outlier cutoff point, Xo.25 is the lower quartile, Xo 75 is the upper quartile, and IQR is the difference between the upper quartile and the lower quartile; and 3) removing line segment values greater than the outlier cutoff point Y1 and less than the outlier cutoff point Y2 in the observation samples, and averaging the remaining line segment values to obtain the shadow length of the building.

3. The method for predicting the building height using the satellite image according to claim 1, characterized in that a calculation formula of the correction model is as follows: H, =a*H, +b*H, +c wherein in the formula, HH’, is a corrected height of a building, H,, is an estimated height of the building, and a, b, and c are all parameters in the correction model.

4. The method for predicting the building height using the satellite image according to claim 1, characterized in that a calculation formula of the ratio coefficient in step (2) is as follows: K, = Si Snx/ Anz n N 17 wherein in the formula, K, is the ratio coefficient, S,, is a shadow length of an x-th LU102459 building, 4, is an actual measured height of the x-th building, and N is the number of buildings.

5. The method for predicting the building height using the satellite image according to claim 4, characterized in that a calculation formula of the estimated height of each building in step (3) is as follows: Sax H, X = > 4 K, wherein in the formula, H,, is the estimated height of the building. 18