a computer vision based approach for 3d building modelling of airborne laser scanner dsm data

Computers, Environment and Urban Systems

30 (2006) 54–77

www.elsevier.com/locate/compenvurbsys

A computer vision based approach for 3Dbuilding modelling of airborne laser scanner

DSM data

B. BabuMadhavan a,*, C. Wang b, H. Tanahashi b, H. Hirayu b,Y. Niwa b, K. Yamamoto c, K. Tachibana a, T. Sasagawa a

a Geographic Information Systems Institute, Pasco Corporation, 1-1-2 Higashiyama,

Meguro-Ku, Tokyo 153-0043, Japanb HOIP, Softopia Japan, 4-1-7 Kagano, Ogaki City, Gifu 503-8569, Japan

c Department of Information Science, Faculty of Engineering, Gifu University, Japan

Received 16 June 2003; accepted in revised form 30 November 2004

Abstract

A computer vision based method for 3D building modelling by using stable planar regions

extracted from low-spatial-resolution airborne laser scanner (ALS) data is presented. Less

operator interaction (interactive processing) and an algorithm that automatically generates

building parameters from digital surface models (DSM) are suggested. The stable planar

region extraction approach proposed for general range data is applied to low-spatial-resolu-

tion ALS data that are resampled by a non-linear resampling method for spatial resolution

enhancement. After stable planar region extraction, the roof edges formed by adjoining planes

are computed by using the topologic relations and geometries of the extracted planar regions.

Finally, a polyhedral description of the data is derived using the geometries of the stable pla-

nar regions, line segments of jump and/or boundary edges, and roof edges. This method is

expected to be robust against noise in the DSM data.

Experimental results of 3D building models show mean differences less than 1 m in the x

and y dimensions and 2 m in height (z) values. The implemented techniques will present a

0198-9715/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compenvurbsys.2005.01.001

* Corresponding author.

E-mail address: [email protected] (B.B. Madhavan).

mailto:[email protected]

B.B. Madhavan et al. / Comput., Environ. and Urban Systems 30 (2006) 54–77 55

source of valuable automatic modelling of building structures in three-dimensions and will

permit modelling of conventional and non-conventional roof surfaces faithfully.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Stable plane extraction; Segmentation; Polyhedral model; DSM; Laser scanning; 3D modelling

1. Introduction

Researchers in the mapping and GIS industries have started to involve Digital

Surface Model (DSM) data from airborne laser scanner (ALS) systems for the devel-

opment of automatic building extraction systems (Brunn & Weidner, 1997; Haala,

Brenner, & Andres, 1998; Lemmens, Deijkers, & Looman, 1997; Maas & Vossel-

man, 1999; Wang, 1998). Laser scanners are used to measure the surface geometry

directly, especially in dense urban areas to obtain DSM, and it is possible to estimatethe parameters of planar structures accurately (elevation accuracy is 15 cm and hor-

izontal accuracy is about 1 m) with DSMs of a high-spatial resolution (Brenner,

1999). DSMs can be obtained by automatic image matching algorithms applied

on stereo aerial or high-resolution satellite imagery or can be directly captured

by airborne laser scanning systems. But in dense urban areas, the stereomatching

method poses a large problem due to occlusions and height discontinuities. There-

fore, the direct height measurement by airborne laser scanners usually provides

DSM data of a higher and more homogeneous quality especially in urban built-up areas (Haala & Brenner, 1999). Helicopter based LIDAR (LIght Detection

And Range) systems with a spatial resolution of 5 or more measurements per square

metre have been reported (Axelsson, 1998; Murakami, Nakagawa, Hasegawa,

Shibata, & Iwanami, 1999).

There are three classes of modelling methods such as volume, surface and mesh

modelling available for surface modelling of range data or 3D point data (Besl &

Jain, 1988; Fitzgibbon, Eggert, & Fisher, 1997; Hoffman & Jain, 1987; Hoover

et al., 1996; Jiang & Bunke, 1994). The representatives of volume models are super-quadrics and generalized cylinders. Mesh models provide only local geometries, and

therefore, they are not suitable for recognition tasks (Pentland & Sclaroff, 1991;

Solina & Bajcsy, 1990; Yokoya & Levine, 1990). Most of the surface modelling of

range data or 3D point data methods implement a computational paradigm that first

computes local features such as surface normals, curvatures (H and K) and/or higher

order features, and then finds the regions of points with similar features by region

growth or clustering (Besl & Jain, 1988; Fitzgibbon et al., 1997; Hoffman & Jain,

1987; Hoover et al., 1996; Trucco & Fisher, 1995; Wang, Tanahashi, Hirayu, Niwa,& Yamamoto, 2000, 2002).

A common theme of several works in 3D modelling of DSM is that no single tech-

nique can solve all of the detection and delineation problems that arise in the DSM

data generated from aerial images as well as from laser scanner data. For example, to

segment DSM data computer vision or image processing techniques such as thres-

holding, binning, morphological filtering and connected component labelling have

56 B.B. Madhavan et al. / Comput., Environ. and Urban Systems 30 (2006) 54–77

been used to achieve 3D models of buildings (Maas & Vosselman, 1999). Haala and

Brenner (1999) suggested a planar segmentation algorithm involving ground plan

data. Morphological filtering and local histogram analysis are together implemented

to segment houses (Hug & Wehr, 1997). Thus, the joint method paradigm is

adopted, where several methods are in use, and their results are combined in a prin-cipled manner. Similarly, in the present study, the use of information fusion para-

digm includes segmentation by stable planar extraction for roof plane extraction,

use of the Sobel edge detector and sequential Hough transformation for boundary

extraction and generation of walls for a complete polyhedral shape description of

DSM data.

The main focus of the present effort is to automate the 3D construction of build-

ings in dense urban areas through an efficient segmentation of DSM data implement-

ing the surface modelling methods used for range finder and structured light rangefinder data. The utility of range image segmentation knowledge has been largely

unexplored in the remote sensing and photogrammetry community. The use of stable

planar extraction and roof edge extraction techniques adopted in this study will pro-

vide additional leverage for 3D building feature extraction problems. In particular,

these techniques will provide a source of valuable automatic modelling of building

structures, and they will provide a novel idea for 3D polyhedral description of

DSM data.

In the present surface modelling approach, the DSM data from an airborne laserscanner (ALS) is first segmented into regions, which are described by a plane of a

quadric surface. Then the description of each region is obtained using geometries

of the extracted regions. The surface model not only describes the ALS DSM data

faithfully, but it also provides the global geometries of each surface. The obtained

results are evaluated for accuracy of the constructed 3D models.

2. DSM from remote sensing data

DSM data for 3D building modelling purpose are generated mostly by matching

of stereo air photos (Baillard, Schmid, Zisserman, & Fitzgibbon, 1999; Fischer

et al., 1998; Gruen, Kuebler, & Agouris, 1995; Henricsson et al., 1996) and recently

from direct measurements through airborne laser scanners (Brenner, 1999; Hug,

1997; Hug & Wehr, 1997; Kilian, Haala, & Brenner, 1996; Maas & Vosselman,

1999; Murakami et al., 1999). Both techniques have several merits and demerits

(Baltsavias, 1999a, 1999b). Laser scanner systems are alternative to an conventionaltechnologies for creating accurate and high-resolution DSM. Laser scanner gener-

ated DSM have the great advantage of representing 3D geometry of objects

directly.

2.1. DSM from air photos

A DSM that is automatically derived from a stereomodel with photogrammetric

methods always contains an amount of incorrect height values, especially at steep


slopes (e.g., building walls). 3D surface acquisition by image matching techniques

suffers from occlusion and height discontinuity problems in highly dense built-up

areas. Additionally, in urban photogrammetry, computational stereo is difficult be-

cause of two reasons: (1) presence of occlusions and (2) inaccessibility of vertical sur-

faces (building facades). The quality of the DSM mainly depends on the textureinformation of roofs and the amount of contrast between the roof and the ground

surface (Price & Huertas, 1992). Maitre and Luo (1992) utilised multiple overlapping

images and by the integration of potential roof break-lines during the matching pro-

cess, they improved the results of image matching techniques. Lotti and Giraudon

(1994) implemented an adaptive matching mask sizes and despite the achievement

of the shape of the buildings, the height discontinuities at rooflines are not depicted

well in the DSM.

2.2. DSM from airborne laser scanners

Unlike photogrammetric techniques, which are prohibitively time consuming and

expensive for performing large-area projects accurately, laser scanner technology is

faster and accurate. Moreover, the recent advancement and the use of airborne Laser

range data help us to acquire true 3D city data. The basic properties of the laser

range data appear to solve some of the problems associated with the DSM generated

from grey-level air photos. For example in a DSM generated from a laser range sen-sor, the form of the objects can be determined as objects are represented in three

dimensions, no occlusions related problems and image features could be extracted

reliably. For a coarse detection, the height information in a photogrammetrically de-

rived DSM is sufficient and detection problems occur when buildings stand close to

each other. Laser range data overcome this problem.

Advantages of laser scanners:

1. Laser scanning is an efficient method for the collection of dense digital surfacemodels (DSMs).

2. As an alternative data source, airborne laser scanning provides a DSM of high

and homogeneous quality in urban areas, which is very suitable for 3D building

reconstructions.

3. Airborne laser scanners (ALS) enable rapid acquisition of a 3D urban GIS.

4. ALS allow direct measurements of the topographic surface, including objects that

are above the ground such as trees, buildings, etc.

5. In the framework of a semi-automatic process, the manual acquisition of aground plan from a laser scanner DSM is more efficient compared to the proce-

dures that rely on 3D measurement and interaction of a human operator to pro-

vide the initial information.

6. ALS reproduce the objects� surface faithfully.

7. Surface measurement within dense urban areas is feasible (even details of chim-

neys and other smaller objects on roofs could be obtained).

8. Laser DSMs provide a better measurement at step edges.


However, laser scanning has the following demerits:

1. Presence of speckle noise in both the scanning as well as in the flyingdirections.

2. The presence of specular surfaces in the urban areas creates confusion at the

interpretation level. Laser range scanners have problems at surfaces with a

high specular reflectivity, or absorption as in the case of metals or slate

roofs.

3. Because of large volume of data, the cost of processing is high.

4. Due to the small field-of-view (FOV) techniques, more scanning is required even

for a small area and hence is not economical.5. Vertical walls or buildings� facades are not accessible.

6. Vertical building walls are not strictly vertical, and narrow streets will not be

reproduced properly (due to mixed point and interpolation effects) if the spatial

resolution is coarse.

7. The direct use of dense laser scanner data poses problems in simulation, visualisa-

tion performance and quality.

8. Even the human eyes have difficulties in understanding and interpreting the build-

ing configuration, when only the DSM data are provided, so it is very demandingto make attempts to reconstruct 3D building models from data of even a 50 cm

spatial resolution.

However, data from laser scanners have been used for 3D surface modelling, and

laser surface models are widely used because of their spatial resolution and reliabil-

ity. The construction of 3D building models mainly or solely based on laser DSM

data is limited to certain standard building primitives and combinations of those

(Haala et al., 1998; Lemmens et al., 1997) or planar roof primitives (Haala & Bren-ner, 1997). The successes of automatic building extraction and modelling of laser

scanner DSMs alone are limited and/or required some other data resources. For

example, the building outlines extracted by Wang (1998) from LIDAR data do

not have an elevation and rooftop geometry. LIDAR data are converted into grey

level images, and building outline extraction is done by image classification. Maas

and Vosselman (1999) suggested the invariant moment method to extract building

outlines from DSMs. But the intersection of two lines is strictly forced to be either

parallel or perpendicular.It has been observed that the use of previous 3D building modelling methods pos-

sibly succeeded for data of simple and isolated rectangular buildings but would pro-

vide poor results for complex shapes and closely spaced buildings (dense urban areas).

As is usually the case with image processing of DSM data, the critical step in the

whole process is the segmentation: If the entities are not well separated, there is no

high probability that the previous methods can allow a precise reconstruction. In

many of the previous research studies, the reconstruction of isolated buildings with

conventional roofs situated in the countryside is attempted. The existing urban rulesof Japan are completely different from these of other countries (Murakami et al.,

1999), and the density of houses is much higher when compared to that other Asian


countries. Closely spaced buildings would pose a problem in segmentation and

modelling.

3. ALS DSM data suitability for Japanese building modelling

In Japan, over 70% of the urban area buildings have polyhedral shapes. There-

fore, it is considered to construct a polyhedral representation of DSM data from air-

borne laser scanners. Many Japanese buildings and houses are planned based on a

unit of approximately 3 m · 3 m in the horizontal direction and a building height

is of 2 m per floor. Hence, the present airborne laser scanner data with a

50 cm · 50 cm spatial resolution on the ground acquired from the ALS of Nakani-

hon Air Service Co., Ltd. in Japan (Airborne Helicopter altitude: 200–400 m abovemean sea level; pulse length: 2000/s; scan time: 20/s; spatial resolution:

50 cm · 50 cm; 700 pixels/scan) is expected to offer enough capability for detecting

and modelling buildings in Japan. Fig. 1 shows a DSM (200 pixels · 200 pixels) of

Gifu region in the central part of Japan, used in the study for modelling. Considering

the unit size of typical Japanese buildings, the accuracies for the horizontal (1 m) and

vertical directions (10–20 cm), and ground spatial resolution (50 cm) of the DSM is

suitable for 3D building modelling. The ALS system is also capable of capturing

orthoimages by combining the position and altitude of ALS with a CCD array sen-sor mounted on the same platform (Fig. 1(c)).

4. General strategy

It is the goal of the new method to create computer vision based tools for the 3D

modelling of DSM data. It is also aimed to present the name, location and pose of

each object in the scene. The surface model, presented in the study, is at the level be-tween volume models and mesh models. Computer vision techniques such as bound-

ary detection, roof edge detection based on segmentation and plan fitting, thinning,

Fig. 1. Airborne data: (a) laser scanner DSM�s data, (b) perspective view of DSM, (c) air-photo.

Edge extraction

Polyhedral Description

Stable planar region extraction

Hierarchical Plane Extraction

Model generation by constructing

walls

Region Merging

Histogram of Local Surface Normal

Jump & Boundary Edges

Roof Edge computation

Region Closing

Hough Transform of Discontinuity Edges

3D Building Model

Pre processing

Airborne Laser Radar Data

DSM Spatial resolution

enlargement

Smoothing by Noise Removal

Fig. 2. Flow chart of vision based 3D building modelling of ALS data.


polygonisation and 3D model fitting are new to Laser DSM data processing. There-

fore, the methods adopted in the present study can be considered as new efforts for

3D building modelling of DSM data. In contrast to the previously mentioned ap-

proaches (Section 2), the present study solely utilise DSMs as a data source for

the automatic 3D modelling of buildings.

The surface modelling technique described in the previous research (Wang,

Tanahashi, Hirayu, Niwa, & Yamamoto, 2002) for range data from a Perceptron

LADAR (Light Amplitude Detection and Ranging) range finder (Perceptron,1994), and from an ABW structured light range finder from an ABW GmbH1 range

scanner (Stahs & Wahl, 1990) has been modified, and an attempt is made to extend

to the orthogonal low-spatial-resolution airborne laser scanner (ALS) data. Fig. 2

illustrates the flow of data processing and modelling based on stable planar extrac-

tion applied to compose 3D building models from ALS data.

An integrated system that generates wholly automatically building parameters

from laser scanner data with less operator interaction (interactive processing) and

algorithms is followed here. The strategy of the present approach consists of the fol-lowing steps for 3D building modelling of DSM data:

1. Pre-processing of DSM for spatial resolution enhancement.

2. Local planar fitting and stable planar region extraction (hierarchical plane

extraction).

1 ABW GmbH. 72636 Frickenhausen, Germany (Website: http://home.t-online.de/home/Wolf.ABW).

http://home.t-online.de/home/Wolf.ABW


3. Region merging.

4. Computation of the line equation of the roof edge of two neighbouring regions

(Ri,Rj) in the orthogonal image plane.

5. Detection of jump edges by applying a Sobel filter to the DSM data.

6. Thinning of binary edges and extraction of straight line segments by using asequential Hough Transform.

7. Region closing or polygonal representation of a planar region.

8. Generation of the wall.

9. Construction of 3D building models, and finally,

10. Bounding box construction for a perfect 3D model representation of buildings.

The approach described by Wang et al. (2002) is basically for modelling of per-

spective view range data in which smoothing of data for noise removal (see Section5.1) and hierarchical distribution extraction are not carried out. In the present study,

for the DSM, fitting of aX + bY + cZ + d = 0 by the minimum eigenvalue method is

implemented (see Section 5.2). For the curved surfaces, the distribution of the sur-

face normals is not Gaussian distribution, and hence, curved surfaces are extracted

piecewise which resulted in many piecewise planes, and these planes are dilated.

Boundary and roof edges are used to construct bounding boxes to characterize per-

fect 3D models.

5. DSM modelling

The spatial resolution of the DSM data is enhanced using a non-linear resampling

method, and a median_SUSAN (Smallest Univalue Segment Assimilating Nucleus)

filtering is used for smoothing the noise data (Babu Madhavan, 2001). Stable planar

regions are extracted by using the probability distributions of normal vectors of local

surfaces estimated by a least-squares method. The roof edges formed by conjunctiveplanes are computed by using the topologic relations and geometries of the extracted

planar regions. Jump and boundary edge detection, edge thinning, and construction

of edge line segments are applied to the data. Finally, together with the geometries of

planar regions, their roof edges, and jump and boundary edges, the polyhedral

description of the DSM data is accomplished. In the following sections, these

approaches are described.

5.1. Spatial resolution enlargement and filtering

The DSM data of a large range of distance and a wide field-of-view is found to be

quite noisy. Similar to large-scale range data that represent objects in 3D points, the

ALS data can also be treated like range data, except for its orthogonal representa-

tion, low-spatial resolution and high-level of noise. For example, the present ALS

data are orthogonal with a single look and has a coarse spatial resolution when

compared to range data from a Perceptron LADAR range finder or from an

ABW structured light range finder. Attempts to utilise the surface modelling method


of Wang et al. (2002) that is tailored for high-spatial resolution range data, suffered

problems pertaining to low-spatial-resolution ALS data, as the approach used a local

window with a size of 5 · 5 pixels or larger to estimate local features of noisy range

data. Therefore, for the present purpose, the ALS data is resampled and smoothed

by noise removal prior to modelling.The most difficult task in surface modelling is the segmentation, because the DSM

always contains noise. ALS data noise removal by smoothing has been accomplished

by median_SUSAN noise filters (Babu Madhavan, 2001). The SUSAN noise filtering

algorithm, like some of the existing filtering techniques, preserves the image structure

by smoothing only over those neighbours which form part of the �same region� as thecentral pixel (Smith, 1996; Smith & Brady, 1997).

With the low-spatial-resolution DSM data, the local window will contain some

border pixels of some narrow regions; hence, the local feature cannot be estimatedcorrectly in the data. Therefore, a resampling method is used to increase the spatial

resolution of the DSM. Thus, DSM(i, j) is resampled to DSMnew(2i, 2j); DSM-

new(2i + 1,2j + 1) is then computed by applying the median_SUSAN filter on

{DSMnew(2i, 2j), DSMnew(2i + 2,2j), DSMnew(2i, 2j + 2), DSMnew(2i + 2,2j + 2)}.

The median_SUSAN filter works by taking an average over all of the pixels in the

locality that lie in the USAN. It is obvious that this will give the maximal number

of suitable neighbours with which to take an average, whilst not involving any neigh-

bours from unrelated regions. As a result, all of the image structure is preserved.In the SUSAN approach (Smith & Brady, 1997), a Gaussian in the brightness do-

main has been employed for smoothing. This means that the SUSAN filter is like the

sigma filter in the brightness, and the Gaussian filter in the spatial domain. On the

contrary, the median_SUSAN smoothing algorithm has a median filter in the bright-

ness domain that removes speckle noise in the ALS data efficiently.

gði; jÞ ¼

XS

k¼�S

XS

l¼�Sexp �k2 þ l2

2r2

� �exp �ðf ði� k; j� lÞ� fmði; jÞÞ2

2T 2

!f ði� k; j� lÞ

XS

k¼�S

XS

l¼�Sexp �k2 þ l2

2r2

� �exp �ðf ði� k; j� lÞ� fmði; jÞÞ2

2T 2

!

ð1Þ

where f (i, j) is the original image and g(i, j) is the target image. S determines the win-

dow size which is 2S + 1. T is the threshold value defined in the original SUSAN filter.

The fm(i, j) is defined as the median of the neighbourhood of f(i, j):

fmði; jÞ ¼ medianff ði� k; j� lÞ; k ¼ �S; . . . ; S; l ¼ �S; . . . ; Sg ð2Þ

The f(i, j) in the SUSAN has been modified to fm(i, j) for more smoothing in themedian_SUSAN filter. Thus, DSMnew(k, l), k = 2i + 1 or l = 2j + 1 is then computed

by applying a SUSAN filter. To the resampled and noise-free DSM data, the stable

planar region extraction procedure is applied.

After smoothing of the DSM, the next process is polyhedral construction, which

includes generation of histograms of local normals, extraction of stable planar


regions, roof edge estimation, extraction of jump and boundary edges and in the end

3D model formation which are described in the following sections.

5.2. Local planar fitting and stable planar region extraction

Generally, orthogonal range data have noise distributed only along the Z-axis, so

fitting of Z = aX + bY + d is most suitable, while the sampling error is small. Perspec-

tive range data have noise distributed mostly along the view direction, as described in

a previous research (Wang et al., 2002). Experimentally, for the DSM�s data, it is ob-served that fitting of aX + bY + cZ + d = 0 by the minimum eigenvalue method used

by Wang et al. (2002) for perspective range data can achieve improved results than by

fitting Z = aX + bY + d. This is because that ALS noise is not distributed only along

the Z-axis; in fact, it is distributed in both the scanning and flight directions.In the stable planar extraction approach (Fig. 2), first histogram of local normal

vectors is computed. As the normal vectors are distributed on a sphere, for the con-

venience of computation, the local normal vectors are projected to a two-dimen-

sional (2D) space as described in Wang et al. (2000). Without loss of generality, it

is assumed that the local surface normals of a plane in the data obey a Gaussian dis-

tribution on the normal sphere whose mean is equal to the normal of the plane. Sta-

ble planar regions are obtained by extracting the Gaussian distribution in the normal

vector space. Then the largest peak is identified and projected back to the range data.If the peak stands for one or more planes, then the neighbourhoods of the peak pix-

els are most likely to belong to the same plane or planes. Using those neighbour-

hoods, the distribution of the local normal vectors of the plane or planes is

estimated. Based on the estimated distribution, the stable planar regions are ex-

tracted. By a dilation procedure, neighbourhoods are obtained, and the distribution

of the local normal vectors using those neighbourhoods is estimated. Stable planar

regions are extracted based on the estimated distribution. The pixels whose normal

vectors within one Sigma of the distribution are extracted at first, and those pixelsare dilated to their neighbourhoods if its local normal vectors are located within

the range of 4 Sigma. After the first planar region contained in the first distribution

is located and extracted, the same process is applied to the remaining data. Then next

largest peak is identified, and the planar region for this distribution is extracted. The

same process is repeated until no significant distribution existed. Here, a complete

segmentation of the DSM data is unnecessary in the present method as the polyhe-

dral description of the DSM is derived from the geometries of the extracted stable

planar regions. As a result, by examining the distributions of local normal vectorstogether with their spatial information in the 2D ALS image, stable planar regions

are extracted.

5.3. Jump and boundary edge extraction

Jump and boundary edges are extracted by applying Sobel directional filtering

and subsequent thresholding of the edge density computed on the z-images of the

data. The binary edges are then thinned out to a single pixel. A sequential Hough


Transform is applied to extract the straight line segments. In the Hough parameter

space, the largest peak is detected first and then the longest line segment, which lies

withinW pixels of the line that corresponds to the largest peak in the Hough space, is

extracted. In this approach, W = 3. These detection and extraction processes are re-

peated until no line longer than L is extracted and the L is set to 5 pixels. Then, theconnective relationship of the line segments that are extracted from the original

image is identified, and the point of intersection from each pair of connected line seg-

ments is computed. Each line segment is labelled and its endpoints and connective

relationship with other lines finally recorded.

5.4. Roof edge computation

Using the geometries of the obtained planes, the roof edge of any two adjacent re-gions can be determined. A neighbouring relationship between regions is established by

expanding each region by a certain size and testing the adjacency of the expanded re-

gions. The expansion is bounded by the jump edges, so any two regions which are close

together but separated by the jump edges are not misjudged as neighbouring regions.

Let the plane equations of Ri and Rj be a1X + b1Y + c1Z + d1 = 0 and

a2X + b2Y + c2Z + d2 = 0. The line equation of the roof edge of two neighbouring re-

gions (Ri,Rj) in the orthogonal image plane can be computed directly. By eliminating

the constant Z-items of the two plane equations of Ri and Rj, the following equationis obtained.

ða1c2 � c1a2ÞX þ ðb1c2 � c1b2ÞY þ ðd1c2 � d2c1Þ ¼ 0 ð3ÞThis line equation can be mapped to the image grid coordinate system (i, j) using the

parameters of the projection centre (i0, j0) and the scalars xscl and yscl on the X and Y

axis, as follows:

j ¼ xsclX þ j0 and i ¼ ysclY þ i0 ð4ÞFor any pair of neighbouring regions, if the roof edge computed above does not pass

through near the adjacent area of the two regions, the roof edge is judged as a false

roof edge, and the adjacent boundary is regarded as a discontinuity edge, which is

passed to the Hough transform algorithm described in Section 5.3.

Thus for two neighbouring regions, the roof edge can be computed directly from

the plane equations of the two regions. If there is a jump edge line segment at the endof the roof edge, then an endpoint can be determined by the crossing points. Other-

wise, another region is required that is neighbouring with both of the first and the

second regions to determine the endpoints. With the third region, two other roof

edges are obtained. Using either of them the endpoint is determined. The same pro-

cess is repeated for all the pairs of neighbouring regions.

5.5. Polygon description of DSM

A polyhedral description of the scene can be built easily by using the extracted line

segments of discontinuity edges and the roof edges. As the connective relations can


be detected from the edge pixels in the enlarged DSM, the cross points of the edges,

that is, the vertices of the polygons of planar surfaces, can be computed easily. Using

the plane equation of each planar region, the 3D coordinates of the vertices can be

obtained.

2D equations of the jump edge and/or boundary edges are obtained using theHough parameters of the line segments extracted by the Hough transform. The

equations of the roof edges are computed as described in Section 5.4. Cross

points of the roof edge segment and boundary edge segments are located from

the equations. Cross points of boundary line segments are also computed. The

procedure is elucidated in Fig. 3. In Fig. 3(a), LR1, LR2, LR3, and LR4 are line

segments having cross points P2, P3, P4 and P5, respectively. Lb is a roofline

segment.

The cross point of line Lb, which includes the roof edge and the lines (LR2

and LR4) that include the boundary edges is computed from the equations.

The cross point of Lb�LR1 or Lb�LR3 is computed, if Lb is not parallel to

LR1 or LR3. However, because they are not in the neighbourhood of the bound-

ary edges, they are eliminated and only the cross points which are in the neigh-

bourhood of the boundary edges (P0 and P1 in Fig. 3(a)) are extracted.

Similarly, the cross points (P2–P5) of the lines (LR(1�4)), which include boundary

edges are computed. The lines are vectorized again based on the computed cross

points (Fig. 3(b)).The final procedure followed is the generation of a 3D model based on the

cross points and the vectorized edges. Although the values (coordinates) of six

cross points obtained in the previous processing are in 2D, they have to be

transformed to 3D values using the image projection centre (i0, j0), the scale fac-

tors Xscl and Yscl of X and Y axis, and two plane equations of the roof parts.

Therefore, the 3D coordinates of the roof parts can be obtained. The cross

points (P2�5 in Fig. 3) of boundary edges, and the lines which connect the cross

points of boundary edges and the ground are computed from the plane equationof the ground. Finally, based on the obtained cross points (P0 to 5, G0 to 3), the

wall and the 3D model of the building have been generated as shown in Fig.

3(e).

Fig. 3. Polygonisation and wall construction. (a) Boundary edge and roof edge. (b) Generation of

vectorized boundary edge and roof edge. (c) Model of roof formed into 3D. (d) Projection of P2–P5 to

ground G0–G3. (e) 3D Model of building.


With the roof edges and the line segments of the jump and boundary edges, each

region is represented by a polygon similar to a building plan. Using the plane equa-

tion of the polygon region, the 3D coordinates of the vertices of the polygon regions

are determined by the image coordinates of the endpoints associated with each edge

of the region. Bounding boxes are formed for each building using the boundary androofline segments to make a perfect 3D model of buildings.

6. Results

The proposed surface modelling method is applied to the resampled DSMs and

polyhedral models of buildings are generated. Fig. 4(a) shows the estimated local

Fig. 5. Jump and boundary edges: (a) edge and (b) thin edge.

Fig. 4. (a) Local normals, (b) histogram of local normals (in pseudo-colour) obtained from the ALS image

(himg = containing all plane; himg0-2 intermediate after extracting planes), (c) stable planar regions (green

and grey colours represent ground level).

Fig. 6. Roof edge segment (red) and closed edge (blue).


surface normals and their histogram (Fig. 4(b)) in pseudo-colour as computed from

the DSM data. Since the ALS scans from a single point to the left and to the right,

only one significant distribution that resembles a Gaussian distribution can be seen

in the histogram. It can be noted that all the distributions are overlapped. As the his-

togram of local surface normals is used collectively with the spatial information inthe data, the planes from these overlapped distributions are extracted. In Fig.

4(b), img 0 to 1 illustrate the intermediate results that show larger distributions

are extracted initially and the small distributions are extracted in the following

iterations.

The final polyhedral description of the data is obtained by extracting only the sta-

ble part of the plane instead of the whole region, and thus the methods followed are

more robust to noise. Fig. 4(c) shows extracted planes. Grey and light green colours2

represent planes of non-buildings. Fig. 5 shows the results of extracted jump andboundary edges. Fig. 5(b) shows thinned edges. The roof edge segments and the

boundary edge segments are shown in Fig. 6. With the roof edges and the line seg-

ments of jump and boundary edges, each region can be represented by a polygon. By

using the plane equation of the polygon region, the 3D coordinates of the vertices of

the polygon region are determined by the image coordinates of the endpoints asso-

ciated with each edge of the region. The final polyhedral model in 3D displaying

gable roof, slant roof and flat roof buildings is shown in Fig. 7(a). Constructed

bounding boxes for perfect depiction of 3D models of buildings are shown in Fig.7(b–h). Fig. 7(b) illustrates the modelled gable roofs.

2 For interpretation of colour in figures, the reader is referred to the Web version of this article.

Fig. 7. Polyhedral city building model. (a) Polyhedral model from DSM. (b, c) 3D model of buildings

extracted showing flat roofs, gable or slant roofs. (d–h) Show perfectly extracted gable roof.



7. Model accuracy evaluation

The approaches for the reconstruction of man-made 3D objects (e.g., urban build-

ings) still do not work in acceptable quality. As the goal of the present method is to

create a sound basis for an operational tool for the automatic construction of 3Dbuilding models from DSM, the geometric accuracy of the generated 3D building

models is evaluated. For this purpose, the 3D CAD models of sixteen buildings gen-

erated from this current study are compared with a published 2D map at a 1:2500

scale (Fig. 8(a)) (Gifu City Urban Planning Base map-III A-2, 2002) to evaluate x

(width) and y (length) dimensions accuracy. Height information of buildings (z) from

original laser scanner data (DSM) (Fig. 1(a)) is referred and compared with the z val-

ues of the obtained 3D CAD models. The graphically depicted result in Fig. 9 shows

the width (x) and length (y) values as measured from the 2D map for a total of 12buildings. Similarly, the graph in Fig. 10 illustrates the z values for 28 roofs modelled

in this research.

Results in Table 1 show that the dimensions accuracy in the x and y direction is

high. There are greater geometric similarities noticed in the x and y dimensions of

buildings between the 2D published data and those of the present 3D CAD model

Fig. 8. 2D base map showing building ID. (a) 2D base map, (b) extracted buildings, (c) bounding box of

building outline.

02468

1012141618202224

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Building

Val

ues

in M

etre

x-Basemap x-Model y-Basemap y-Model

Fig. 9. x (width) and y (length) values obtained from basemap and model for 16 buildings (X direction:

Xmap, mean = 13.14, r = 5.10; Xmodel, mean = 13.08, r = 4.67, r2 = 0.987; Y direction: ymap, mean = 13.98,

r = 4.98; ymodel, mean = 14.05, r = 5.16, r2 = 0.976).

05

10152025303540455055606570

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Building Roof

Val

ues

in M

etre

z-DSM z-Model

ZDSM Mean =24.89σ = 9.37ZModel Mean =26.89 σ = 13.982

r2 = 0.976

.

Fig. 10. z-values of DSM and Model estimated for 29 roofs.


(Fig. 11). An average of 2.01m mean difference is observed in the z values of the 3D

CAD building when compared to the original Laser data (Fig. 12). The variation is

high in tall buildings, for example, building nos. 2, 3, 6, 12 and 16 (Fig. 8), which

have many smaller as well as curved structures (such as air-cooler machines and

smaller elevated structures) that are segmented as individual roofs.

For each x, y and z value from the map and the model, a parametric (t-test) test of

significance is carried out to test whether the obtained model values differ significantly

Table 1

Model evaluation by t-test

Build-ID Base map (m) Present model (m) d (m) Height from

DSM (m) z

Height from

model (m) z0dz (m)

x y x 0 y0 dx dy

1 15 10 15.58 6.19 0.58 �3.81 31 32.33 1.33

2 16.25 22.5 15.06 22.17 �1.19 �0.33 37, 41 46.6, 52.6 9.6, 11.6

3 12.5 17.5 13.68 16.91 1.18 �0.59 35, 38, 41, 53 47, 52.6, 46.8, 60.6 12, 14.6, 5.8, 7.6

4 7.5 7.5 8.15 7.9 0.65 0.4 16,18 15.6, 16.54 �0.4

5 7.5 17.5 6.88 18.08 �0.62 0.58 23 25.7 2.7

6 17.5 15 17.31 14.76 �0.19 �0.24 26, 31 31.7, 37.9 5.7, 6.9

7 22.5 15 21.56 15.48 �0.94 0.48 19, 16, 19, 19 16.7, 13.5, 17.6, 17.6 �2.3, �2.5, �1.4, �1.4

8 7.5 12.5 8.1 12.62 0.6 0.12 24 26.3 2.3

9 7.5 10 7.51 11.02 0.01 1.02 22 22.7 0.7

10 7.5 12.5 8.19 12.22 0.69 �0.28 21 22.18 1.18

11 7.5 20 8.18 20.38 0.68 0.38 17, 18 13.3, 16.7 �3.7, �1.3

12 16.5 20 16.38 20.38 �0.12 0.38 17, 18 11.8, 13.4 �5.2, �4.6

13 20 7.5 17.52 8.55 �2.48 1.05 22 26.6 4.6

14 10 7.5 9.93 8.16 �0.07 0.66 21 20.7 �0.3

15 17.5 8.75 18.11 8.92 0.61 0.17 25, 21 27.2, 19.7 2.2, �1.3

16 17.5 20 17.19 21.01 �0.31 1.01 18, 15 12.4, 16 �5.6, 1.0

Sum 210.25 223.75 209.33 224.75 �0.92 1 722 780.35 58.35

Mean 13.14 13.98 13.08 14.05 �0.06 0.062 24.89 26.89 2.01

SD 5.10 4.98 4.67 5.16 0.89 1.12 9.37 13.98 5.23

CI+ 22.94 23.74 22.23 24.15 1.69 2.23 43.26 54.31 12.27

CI� 3.34 4.22 3.92 3.9 �1.8 �2.1 6.52 �0.50 �8.25

SE 1.1 1.22 2.59

t-test x-direction = 0.0321 y-direction = 0.0337 z-direction = 0.6325

P (type 1 error) = 0.9745 P (type 1 error) = 0.9733 P (type 1error) = 0.5296

Note: SD—standard deviation; SE—standard error: CI—confidence interval.

B.B.Madhavanet

al./Comput.,

Enviro

n.andUrbanSystem

s30(2006)54–77

71

-5

-4

-3

-2

-1

0

1

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Buildings

Val

ues

in m

etre

x-delta y-delta

Mean δx = 0.05σδx

σδy

= 0.922Mean δy = 0.062

= 1.14

Fig. 11. Difference (d) in x and y values.

-7-6-5-4-3-2-10123456789

10111213141516

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Building Roofs

Val

ues

in M

etre

z-delta

Mean δz = 2.01σ δz = 5.33

Fig. 12. d z-values estimated for 28 roofs.


from the base map and ALS DSM (original) values. The x, y and z values obtained

from the model are treated as observed values. The outcome of these tests is the accep-

tance or rejection of the null hypothesis (H0). In the present case, the mean values are

the same, that is, the x, y and z values from the model contain the same percentage of


the map values and Laser data values, and the current surface modelling provided the

same analytical results. The differences observed could be due to random errors that

resulted because of the under or oversegmentation. The significance test provided re-

sults within a predefined confidence level (CL%), and it is observed that in all the

directions, the means are not different at CL 90%, 95% and 99%.There are some outliers mostly in the height (z) values of buildings 2, 3, 6, 12 and

13 (Fig. 8) that appear to be excessively high in the buildings with several non-con-

ventional structures on the rooftop or low with respect to the buildings crowded

between two tall buildings (e.g., building nos. 7 and 11). Outliers might have been

developed from small structures with a fewer number of points or sampling difficul-

ties, but may also represent problem with the segmentation.

8. Summary and conclusions

In the field of remote sensing and GIS, not many computer vision oriented tech-

niques have been used in 3D modelling of DSM from laser scanner research. In this

paper, a novel method for automatic building extraction and 3D modelling from

DSM data is presented. The ALS DSM data are robustly segmented into stable pla-

nar regions, and the geometries of the regions are used for polyhedral description.

The present method can be applied to any DSM data.The characteristics of the present surface modelling of airborne DSM data ap-

proach are as follows:

• Experimentally, for the airborne laser scanner data, it is found that fitting of

aX + bY + cZ + d = 0 by the minimum eigenvalue method, suggested in a previ-

ous study for perspective range data can obtain improved results than by fitting

Z = aX + bY + d. This is because that noise is not distributed only along the

Z-axis but it is distributed in both the scanning and flight directions.• The proposed methods are not attempted previously on 3D modelling of DSM

data.

• A complete segmentation of the data is not required, as the polyhedral description

of the data is derived from the geometries of the extracted stable planar regions.

• Jump edges are detected by a applying Sobel filter to the height image, and fol-

lowed by a fixed value threshold on the gradient of the edges obtained by the

Sobel filter. The binary edges are then thinned. A sequential Hough Transform

is adopted to extract the straight line segments.• The level of detail that is achieved by the new method corresponds to the level of

detail required for large-scale topographic mapping such as roof shapes as well as

larger roof structures such as dormers in it, roof overhangs, and small structures

such as small chimneys.

• The approaches are shown to be quite robust as they could be applied to DSM

data with noise of any region.

• As the current approach constructs a polyhedral representation of DSM, the

object models have a geographical or spatial name, location and pose.


• In Many of the previous methods for the reconstruction of buildings, the data are

representative of the countryside where the buildings are isolated and have a rect-

angular shape. Moreover, the surfaces of the locations are absolutely flat, which

makes the segmentation process easier where a fewer number of roof planes

existed. The density of houses in Japan is much higher than in other countries,and the present approach segmented the DSM�s data efficiently. Therefore, the

present approach could be applied to any data of any scene.

• One of the constraints for transferability of any segmentation approach is the spa-

tial resolution that could be overcome by the smoothing method adopted in this

research.

Differences between the approaches adopted in some recent studies, and the pres-

ent approaches for 3D building modelling from DSM are shown in Table 2. Signif-icant geometric similarities are noticed in the x (width) and y (length) values of

buildings in the 2D published map and the 3D CAD models generated from this

study (5 cm difference). An average of 2.1 m differences is observed in the z values

of the 3D CAD building when compared to the original LIDAR data. This is accept-

able with the mapping standards of Japan. Thus, an accurate and also visually effec-

tive representation of 3D building models could be constructed.

Table 2

Advantages of present method in composing 3D models from DSM

Previous methods Present method

1. Segmentation: Distinguishing

of each building structures not possible

Possible

2. Not suitable for GIS, as the resulting

polyhedrons obtained by previous methods

correspond to parts of buildings and not

necessarily to each building

Each building can be represented

3. Even large buildings cannot be distinguished

from road surfaces i.e. Buildings disappear

in the obtained 3D model

All the buildings will appear

4. Thresholding is done during the segmentation

process. Therefore another problem is that the

extracted objects are not always buildings or

houses but, for example, trees are included

Carried out as a pre-processing

method hence data relevant to

buildings only processed later

5. Roof edges are not extracted Could be possible

6. Building boundaries are extracted from the

segmented images only

Building boundaries are extracted

from edge-enhanced as well as

segmented images individually

7. Only flat roofs are represented Whereas here, even slope roofs

can be represented

8. Smoothing: An ordinary median filter is used

which over-smooth the data without preserving

the edges, which are important for building extraction

Median filter with Univalue Segment

Assimilating techniques removes

speckle noise and preserves edges

9. Polygonisation of boundary of buildings only carried out Both roof edges and boundary edges

are polygonised and combined to

represent a complete 3D building model


During the construction of wall many walls connecting diagonal corner points are

generated, which has to be improved for simple polyhedral shape description of

buildings. Although the present method can extract regions properly under a quite

hard condition of overlapping of the distribution, there may be some planes, which

are divided into several parts. In the future, each observed outlier would be evaluatedto determine whether it is a real result or it is due to a problem with planar extrac-

tion. Further it is planned to improve the z value accuracy in buildings with complex

structures. It is considered to apply the method to more complex scenes to test its

performance and also planned to extend the methods to be able to deal with curved

surfaces and some non-conventional roofs.

Acknowledgement

The work presented in this paper was performed at Softopia Japan Foundation.

The authors acknowledge the support from Japan Science and Technology for the

Human and Object Interaction Processing (HOIP) project at Softopia Japan founda-

tion. The authors are also thankful to Pasco Corporation for providing 2D data and

support to complete additional work. Helpful suggestions and comments from anon-

ymous reviewers and Dr. K.K. Mishra (Pasco corporation Tokyo) are greatly

appreciated.

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a computer vision based approach for 3d building modelling of airborne laser scanner dsm data

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