Ray-Tracing Simulation Techniques for Understanding High-Resolution SAR Images

Ray-Tracing Simulation Techniques for Understanding High-Resolution SAR Images
Ray-Tracing Simulation Techniques for Understanding High-Resolution SAR Images

Ray-Tracing Simulation Techniques for Understanding High-Resolution SAR Images Stefan Auer,Member,IEEE,Stefan Hinz,Member,IEEE,and Richard Bamler,Fellow,IEEE

Abstract—In this paper,a simulation concept is presented for creating synthetic aperture radar(SAR)re?ectivity maps based on ray tracing.Three-dimensional models of man-made objects are illuminated by a virtual SAR sensor whose signal is approximated by rays sent through the model space.To this end,open-source software tools are adapted and extended to derive output data in SAR geometry followed by creating the re?ectivity map.Rays can be followed for multiple re?ections within the object scene.Signals having different multiple re?ection levels are stored in separate image layers.For evaluating the potentials and limits of the simu-lation approach,simulated re?ectivity maps and distribution maps are compared with real TerraSAR-X images for various complex man-made objects like a skyscraper in Tokyo,the Wynn Hotel in Las Vegas,and the Eiffel Tower in Paris.The results show that the simulation can provide very valuable information to interpret complex SAR images or to predict the re?ectivity of planned SAR image acquisitions.

Index Terms—Persistence of Vision Ray(POV Ray),radar scattering,ray tracing,synthetic aperture radar(SAR)simulation, TerraSAR-X,3-D modeling.

I.I NTRODUCTION

A FTER high-resolution radar satellite missions like

TerraSAR-X or COSMO-SkyMed have been launched in2007,spaceborne synthetic aperture radar(SAR)images reach spatial resolutions below1m in azimuth and range in spotlight mode[1],[2].Due to the increased resolution,only few scatterers are located within one resolution cell.Hence, new deterministic components occur particularly at man-made objects causing bright image features[3],[4],what is most apparent for strong backscattering at building walls.Texture information within the image has become more meaningful, what supports the interpretation of SAR images.Furthermore, the number of strong scatterers is increased drastically within urban areas,and extended linear or areal structures now show long-term stable scattering behavior,which can be seen as a paradigm change in persistent scatterer interferometry[5]–[7].

Manuscript received December22,2008;revised April28,2009and July3,2009.First published September15,2009;current version published February24,2010.

S.Auer is with the Remote Sensing Technology,Technische Universit?t München,80333München,Germany(e-mail:Stefan.Auer@bv.tum.de).

S.Hinz is with the Institute of Photogrammetry and Remote Sensing, Universit?t Karlsruhe(TH),76128Karlsruhe,Germany(e-mail:stefan.hinz@ ipf.uni-karlsruhe.de).

R.Bamler is with the Remote Sensing Technology Institute(IMF),German Aerospace Center(DLR),82234Oberpfaffenhofen-Wessling,Germany,and also with the Remote Sensing Technology,Technische Universit?t München, 80333München,Germany(e-mail:Richard.Bamler@dlr.de).

Color versions of one or more of the?gures in this paper are available online at https://www.360docs.net/doc/0f18891100.html,.

Digital Object Identi?er

10.1109/TGRS.2009.2029339

Fig.1.Maison de Radio France(Paris):Obvious geometry in optical image;

challenging interpretation in TerraSAR-X mean map(spotlight mode;azimuth

direction bottom up;range direction from left to right).(a)Birds eye view;

?Google Earth.(b)SAR mean map.

Although more details are distinguishable in high-resolution

SAR images,visual analysis of the geometrical distribution of

features still turns out to be challenging and time consuming.

Fig.1,showing the“Maison de Radio France”in the center of

Paris,gives an example for re?ection effects appearing in urban

areas which are dif?cult to explain:While the geometrical

structure is obvious in the optical image(left),interpretation

of the re?ection effects in the SAR mean amplitude map,

which has been created by averaging six spotlight TerraSAR-X

images,is not straightforward.Hence,creating arti?cial SAR

images or re?ectivity maps by means of simulation methods

has proven to be helpful for supporting the interpretation of

re?ection effects in the azimuth–range plane.

In the published literature,basically two groups of ap-

proaches can be found.Approaches focusing on radiometric

correctness use formulas in closed form for providing intensity

values of high quality that are comparable to real SAR images

while the level of detail of3-D models to be used is limited.For

example,Franceschetti et al.[8]developed a SAR raw signal

simulator(SARAS)and added re?ection models for describ-

ing multiple-bounce effects at buildings approximated by box

models[9],[10].The second group of simulation approaches

concentrates more on the geometrical correctness of the simula-

tion.Balz[11]used programmable graphics card units for gen-

erating single-bounce SAR images in real time.Margarit et al.

analyzed re?ection effects,multiple re?ections,and SAR po-

larimetry by illuminating detailed3-D models of vessels[12]

and buildings[13]while preserving high radiometric quality by

using a radar cross section simulator[14].Brunner et al.[15]

show how to extract features from real SAR images by

comparing them to simulated images.Hammer et al.[16] 0196-2892/$26.00?2009IEEE

compared different simulation concepts for obtaining arti?cial SAR images.

Our simulator also uses ray-tracing tools.However,in con-trast to other approaches,the core-tracing algorithms are taken from the open-source software package“Persistence of Vision Ray(POV Ray),”which was originally developed for simulat-ing optical images.This allows us to concentrate on modeling the speci?c SAR scattering effects,e.g.,tracing rays through multiple re?ecting and storing signals of different bounce levels in separated image layers.Effects caused along the synthetic aperture and during SAR focusing are approximated by using a cylindrical light source and an orthographic camera for model-ing the SAR antenna.

The motivation and novelties of this approach are outlined in Section II followed by a detailed explanation of the simulation process in Section III.Afterward,the results of the simulation are compared and assessed with real TerraSAR-X images in Section IV.Finally,potentials and limitations of the simulator are concluded,and future work to be done is summarized in Section V.

II.M OTIVATION

The aim of this work is to develop a software tool offering the possibility for simulating backscattering effects showing up in high-resolution SAR images.Furthermore,re?ection contributions of different bounce levels are to be displayed in separated image layers.Since deterministic scattering effects mostly appear at man-made objects,multibody urban scenes are of special interest.Simulated re?ectivity maps can be used for supporting the interpretation of real SAR images, for predicting backscattering effects in SAR images,and for detecting and grouping strong point scatterers[17]which are used,for instance,in persistent scatterer interferometry [18],[19].

Guida et al.[20]use closed equations to analyze deter-ministic backscattering effects appearing in high-resolution TerraSAR-X images.Hence,some restrictions have to be ac-cepted at the cost of high radiometric quality:Simulation results using meshed LIDAR data are limited to single scattering,and 3-D models of buildings are designed by parallelepipeds with-out roof structures.In our approach,for being able to analyze multiple scatterings in more complex3-D model scenes,we put more focus on the geometrical correctness of the distribution of scattering effects.Radiometric proportions between different bounce levels,as well as speckle noise,are of less importance and are only approximated.

In particular,the following requirements should be ful?lled.

1)The complexity of3-D models to be included should be

high in order to be able to detect re?ection phenomena appearing at small building features.

2)Separation of different bounce levels should be feasible

by counting the number of re?ections for each ray fol-lowed through the modeled scene.

3)Rays should be followed through the entire modeled

scene to enable geometrical analysis like location of intersection points,analysis of re?ection angles,etc.

4)Both re?ection models,specular and diffuse,as well as

the parameters for controlling the re?ectivity of surfaces, should be available.

These requirements led us to the conclusion to base the developments on an existent software tool,i.e.,POV Ray[21]–[23],a well-known ray tracer for generating virtual optical images,and modify it in such a way that it can deliver output data for generating images in SAR geometry.

In our opinion,POV Ray?tted well into the de?ned require-ment pro?le because of the following.

1)It comprises a huge variety of very fast simulation tools.

2)Basic modules are thoroughly tested and free from pro-

gramming errors.

3)Including own developments is possible due to free ac-

cess to its source code.

4)The source code has been continuously developed and

improved by a huge community since1991.

5)It uses an ef?cient concept for tracing rays,more specif-

ically backward ray tracing,which starts at the center of each image pixel and follows the ray backward on its way to the light source.

In the following section,the simulation concept is explained in more detail.Starting with the geometrical and radiometric description of objects,the process chain is continued by sam-pling the3-D model scene by means of rays and is completed by image creation for obtaining the re?ectivity map in the azimuth–range plane.

III.S IMULATION P ROCESS

The simulation process consists of three major parts:

1)Scene modeling:In the?rst step,a3-D scene model has

to be constructed and imported into the ray tracer;

2)Sampling of the model scene:By applying the ray-

tracing algorithm provided by POV Ray,the analysis for backscattering contributions is performed by tracing rays through the modeled scene.For de?ning both the origin and the direction of the rays,a virtual orthographic “camera”is used,whose optical axis is aligned with the intended viewing direction of the radar sensor.While creating the synthetic image of the scene,coordinates in azimuth and slant range,intensity values,and bounce levels are derived as output data for all intersection points detected at objects in the scene;

3)Creation of the re?ectivity map:The arti?cial re?ec-

tivity map is generated by assigning all the intensity contributions—according to their azimuth and slant range coordinates—to the elements of a regular grid in radar coordinates imposed onto the irregularly distributed data points derived during the prior sampling step.

A.Scene Modeling

A model scene to be used by a ray tracer has to contain the following elements:3-D scene objects to be illuminated, surface properties like re?ectivity factors or the strength of diffuse/specular re?ection for each object face,a camera at the position of the observer,and at least one light source.The

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quality of the images derived by ray-tracing methods depends,in particular,on the quality of the modeled scene.While simple surfaces and standard objects like triangles,spheres,boxes,cylinders,etc.,are easily created,complex objects can be formed by means of constructive solid geometry (CSG)[24]including set operations like “union,”“difference,”or “intersec-tion”for composing complex objects from simple primitives.Moreover,besides some other formats which still have to be tested,the following 3-D model formats have been successfully imported into POV Ray:object format (.obj),3DS max (.3ds),and sketchup (.skp).

To generate a synthetic backscatter image of the scene,the virtual sensor is modeled by means of two components:1)a cylindrical light source emitting parallel light rays for simulating the azimuth-focused SAR signal and 2)an ortho-graphic sensor for modeling the receiver antenna,both at the same position and with coinciding viewing https://www.360docs.net/doc/0f18891100.html,ing an orthographic sensor offers the possibility to determine the phase center position of each scattering contribution in the azimuth and range direction.As the simulator scans the modeled scene by means of rays,the density of the sampling process depends on the geometrical resolution of the sensor,i.e.,the synthetic image.

Considering the radiometric model for the simulation,we rely on standard models since our focus is on geometrical quality of the result.Intensity values are evaluated at object surfaces by means of a combination of a diffuse and a specular re?ection model.

For estimating the diffuse intensity contribution I d ,the fol-lowing equation is applied:

I d =k ·I ·(?→N ·?→

L )b (1)where k is a diffuse re?ection factor and I is the intensity

of the incoming https://www.360docs.net/doc/0f18891100.html,mbertian re?ectance is considered

by the scalar product of the normalized vector ?

→L pointing in the direction to the light source and the normalized surface

normal ?→N ,which is one in the case of ?→L =?→

N .Parameter b can be adapted for approximating the backscattering behavior of metallic surfaces.

The re?ection model for evaluating the specular re?ected intensity I s is de?ned as follows:

I s =s ·(?→N ·?→H )1

r (2)where s represents the re?ectivity coef?cient of the surface

and r is a roughness factor de?ning the sharpness of specular

highlights.The normalized vector ?

→H is the bisection vector

[25]between the vector ?

→L pointing in the direction to the

light source and the direction vector ?

→V of the re?ected ray whose intensity contributions have to be estimated.Eventually,diffuse and specular intensities are summed up for each signal re?ection detected within the 3-D model scene.

Both the specular and the diffuse re?ection models have been originally developed for optical light [26],[27].Hence,for improving the radiometric quality of the result in the future,both re?ection models could be replaced by more appropriate models adapted to the wavelength of SAR signals,e.g.,the

Fig.2.Simulation concept:Scene imaged by an orthographic camera while two objects are illuminated by a cylindrical light source.a o ,a p :Coordinates to be used for the calculation of the phase center in the azimuth;r 1,r 2,r 3:Depth values for the determination of the slant range coordinate;slant range coordinate of double-bounce contribution determined by (r 1+r 2+r 3)/2.

However,replacing the re?ection models currently used for simulation of the simulator.B.Sampling A SAR imaging system maps the 3-D world into a cylin-drical coordinate system.It employs central perspective in the elevation direction and orthographic scanning in the azimuth.For spatially limited areas,e.g.,individual buildings,and space-borne geometry,the central perspective in elevation can be well approximated by orthographic projection.This has several advantages:First,a 2-D orthographic camera type is readily available in POV Ray,and,second,having a constant incidence angle offers the possibility of zooming into the 3-D model scene in order to analyze signal backscattering from features of interest like roofs,balconies,or facades.The modeling of shadow is solved by including a cylindrical light source emitting parallel light.Thereby,a shadow test can be performed along all scan positions in the azimuth.Moreover,equal signal intensities are guaranteed for all objects illuminated in the local area of interest.

The intensity contributions of the synthetic image are ac-quired by backward ray tracing [25]and shall be explained in the case of the model scene shown in Fig.2.The term “backward”refers to the fact that tracing starts at the receiving sensor and continues until the light source is reached or is aborted due to geometrical or radiometric constraints.Starting at the center of each image pixel,one ray,commonly called “primary ray,”is constructed.Since the camera type is “or-thographic,”the direction of the ray is perpendicular to the image plane of the camera.Simultaneously,two default values are necessary for capturing the characteristics of the re?ection process to be analyzed.First,the re?ection level—which is referred to as “bounce level”in the following parts of this paper—for counting the number of bounces along the ray’s path is set to one.Moreover,in order to scale all the intensity contributions derived throughout the modeled scene,a weight factor is introduced for the ray having a weight of one.

The search for contributions is started at the center of each image pixel by following the ray along its path and seeking for

1448IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.48,NO.3,MARCH2010 intersections with the modeled scene.If the ray hits more than

one object,the intersected surface having the smallest spatial

distance to the pixel center is treated as“visible”and checked

for color contributions,i.e.,the intensity backscattered at the

surface of object1is evaluated by calculating the specular and

diffuse re?ection component caused by the illumination of the

light source,i.e.,the virtual azimuth-focused SAR signal.

Afterward,using both the intersection point and the surface

normal at object1,a secondary ray is created in the specular

direction,and the bounce level is increased to two.In this

context,all rays constructed for trace levels that are higher than

one are referred to as“secondary rays.”The weight factor of the

ray decreases according to the re?ectivity factor of the surface

of object1,i.e.,all further intensity contributions will be scaled by a value that is smaller than one.

Tracing rays for the current pixel ends if the ray to be fol-lowed does not hit any further object,if the maximum bounce level is reached,or if the weight factor of the ray falls below a de?ned threshold.Both limits,namely,bounce level and weight threshold,can be chosen by the operator.Eventually, all contributions are summed up for determining the intensity hitting the image pixel.

Concerning the calculating time,the duration of the simu-lation process highly depends on the number of pixels of the orthographic camera chosen for sampling the object scene,e.g., doubling the number of n pixels on each axis of the image plane requires the analysis of4?n rays,which all can?nally reach a bounce level of?ve.The in?uence of the complexity of the imported3-D models on the processing time was remarkable but turned out to be much weaker than the in?uence of the image size.

C.Coordinates in Range and Azimuth

For computing the slant range coordinates,we have extended POV Ray’s source code for extracting necessary depth informa-tion from the ray-tracing process.In the case of single bounce, the slant range distance R s is directly given by the depth value of the?rst intersection point,i.e.,

R s=r1.(3) If a double bounce appears,the slant range coordinate is derived by tracing the ray throughout the scene until it hits the second face—in our example,at object2.Then,an additional ray has to be constructed,which is parallel to the primary ray and?xed at the second intersection point.By intersecting this ray with the image plane of the orthographic camera, the origin of the ray at the virtual antenna is determined. Finally,according to Fig.2,the slant range coordinate R d for double bounce is evaluated by half the sum over all three rays,i.e.,

R d=(r1+r2+r3)/2.(4) For multiple bounces,the procedure is easily extended since only the number of rays between the objects and the corre-sponding intersection points increases.

Triangular trihedral corner re?ectors appear as a point in SAR images even if the physical size of the re?ector is larger Fig.3.Image creation:A regular grid is imposed on the(red points)detected re?ection contributions followed by interpolation within each resolution cell. than the spatial resolution of the SAR system[29].This effect is accommodated in the simulator by averaging the azimuth coordinates a o of the ray’s origin at the antenna and the azimuth coordinate of the pixel center a p where the primary ray was constructed(see Fig.2),i.e.,

A=(a p+a o)/2.(5) Compared to the real SAR system,our simulator does not have to deal with ambiguities in the azimuth and range.Both range and azimuth coordinates are obtained conserving the best resolution.

Finally,as output data,the simulator stores one azimuth coordinate,one slant range coordinate,one intensity value,and the bounce level for re?ection effect detected along the path traveled by a ray.

Potential enhancements for the3-D analysis of the re?ection effects[30]–[32]will have to be investigated in the future by including the elevation direction as third dimension(Fig.2). D.Creation of the Re?ectivity Map

The preceding steps showed how to derive the necessary output data by means of our simulator.At this point,all the intensity contributions are irregularly distributed in the azimuth–range plane since scanning of the scene in the SAR geometry yields areas with high point densities(caused by small angles between ray and object surfaces),lower point densities(caused by increased angles between ray and object surface),and also shadowed areas without any contributions. Hence,for obtaining the re?ectivity map,a regular grid has to be imposed onto the illuminated area(see Fig.3).For each bounce level appearing in the scene,one empty image layer is created,whose resolution in the azimuth and range is chosen by the operator.As for the range direction,the operator can decide,in favor of slant range or ground range,what requires the speci?cation of the radar incidence angle.After starting a loop over all the contributions,the subpixel coordinates are cal-culated for each intensity contribution whose intensity is added to the appropriate image layer by using the available bounce level information.For each bounce level requested by the operator,separate re?ectivity maps are prepared and displayed. Moreover,since imposing a regular grid over an irregular point

AUER et al.:RAY-TRACING SIMULATION TECHNIQUES1449 Fig.4.Google Earth data3-D model.Level of detail:Moderate,?ynakamura.

Google3-D gallery;optical image:?Google Earth.(a)Google Earth Model.

(b)Birds eye view:pipe structures on one side of the roof.

cloud may cause aliasing effects,the possibility of smoothing the image layers by means of a bilinear?lter has been included.

IV.A PPLICATIONS

In the following section,as all modeling and processing steps have been explained now,the potentials and limitations of the simulator are shown by comparing the simulated re?ectivity maps with the TerraSAR-X images.To this end,the following three locations with different kinds of complex objects have been chosen:

1)a skyscraper in Tokyo for detecting deterministic double-

bounce effects;

2)the Wynn Hotel in Las Vegas as an example for support-

ing the detailed interpretation of multiple-bounce effects;

3)the Eiffel Tower in Paris for detailed SAR simulation.

In each case,an available3-D model has been imported and sampled in POV Ray followed by creating the re?ectivity map.

A.Skyscraper

High-resolution SAR sensors like TerraSAR-X or COSMO-SkyMed provide images having a geometrical resolution of https://www.360docs.net/doc/0f18891100.html,pared to the Envisat or ERS SAR data,fewer scatterers are located within one resolution cell,causing less random interference between scattering contributions.Hence, more deterministic re?ection effects become visible,particu-larly in urban areas containing many man-made objects.In the following,this is exempli?ed for a TerraSAR-X image showing a skyscraper in Tokyo(Japan).

Within the Chuo-ku district of Tokyo,several skyscrapers are located next to the Aioi-bashi Bridge crossing the Sumida River.For one of these,the distribution of scattering effects has been analyzed by means of a Google Earth3-D model processed by our simulator.Both the rotation angle of the building and the incidence angle of the signal have been roughly estimated from the TerraSAR-X data,and re?ection properties have been assigned to all surfaces.Fig.4(a)shows a perspective Fig.5.(a)TerraSAR-X image versus(b)simulation.(Points1–6)Corre-sponding features.Feature7not obtained by simulation.Azimuth direction: Left to right.Slant range direction:Top down.

view onto the building as seen by a spectator located at the position of the SAR sensor.In order to model the double-bounce effects caused by the surrounding ground,a?at plane with low diffuse scattering characteristics has been introduced into the model scene.Since single-bounce contributions show weak appearance at walls,the facades are modeled by closed surfaces showing strong specular re?ection and low diffuse re?ection.

Although the level of detail of the skyscraper model is only moderate,several similarities are clearly visible in the SAR im-age[Fig.5(a)]and the simulation result[Fig.5(b)].All double-bounce contributions caused on the roof(feature4),at wall corners,oriented in the direction to the sensor,either on the in-side of the building(feature3)or on the outside of the building (feature6),or by the interaction of the walls and the surround-ing ground(features2and5)appear as linear structures and are much stronger than the single-bounce contributions.Lines of this kind appearing at the building’s headwall are of special interest since their length depends on the following:1)on the building height and2)on the rotation angle of the building with respect to the line of sight of the sensor.Signals hitting higher regions of the rotated skyscraper’s wall are re?ected farther into the background of the building,increasing the distance covered by the SAR signal back to the sensor.Consequences arising due to double-bounce lines reaching beyond the ends of building walls should be taken into account in the case of feature extraction in high-resolution SAR images even if this effect shows little occurrence for low buildings.For instance, Thiele et al.[33],whose approach for building reconstruction in SAR images is based on the analysis of double-bounce lines, report of a slight overestimation of building footprints extracted from multiaspect high-resolution SAR images.

In contrast to its long appearance in the re?ectivity map, the double-bounce line in the right part of the SAR image

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Fig.6.Separated layers for different bounce levels.Azimuth direction:Left to right.Slant range direction:Top down.(a)Single Bounce.(b)Double Bounce. (feature5)is much shorter since it is cut off by an adjacent building which has not been included in the POV Ray model scene[Fig.4(a)].Re?ection contributions caused at roof fea-tures(feature4)are clearly visible in both images,while the gap in one of the horizontal double-bounce lines(feature1)is only hinted in the real SAR https://www.360docs.net/doc/0f18891100.html,pared to the SAR image,linear feature7[Fig.5(a)]does not show up in the simulation result. This re?ection contribution is likely to be caused by a strong re?ection effect at a step on the roof or by nearby metallic pipe structures which are shown in Fig.4(b).A closer look at the skyscraper model in Fig.4(a)reveals that the step,as well as the metallic pipes,is not modeled in3-D since it has only been mapped as2-D textures on the?at roof surface. Moreover,a vertical line of points(feature8)is visible in the SAR image at the left end of the building which might appear due to backscattering at building edges or due to trihedrals at the facade of the building.For instance,Soergel et al.[34] analyzed edge scattering effects at urban buildings in the case of high-resolution airborne SAR images.Contributions of tri-hedrals at the skyscraper’s wall facing the SAR sensor can clearly be distinguished as focused points in the SAR image. However,these effects are missing in the re?ectivity map since all building walls have been modeled by?at surfaces.

In addition to the re?ectivity map,different bounce levels are displayed in separated layers for supporting the interpretation in more detail(see Fig.6).Concerning the comparability of intensities,the radiometric quality of the result is as limited as it was expected in advance.Even if the available re?ection parameters had been optimized for all surfaces,radiometric errors would have appeared because of the discrete sampling of the3-D model scene,the simpli?ed re?ection models for evaluating the backscattered intensity contributions,and the separated treatment of each bounce along the ray’s

path.Fig.7.Perspective view onto the Wynn Hotel,Las Vegas(USA).“Lake of Dreams”situated in front of the building.?Google

Earth.

Fig.8.“Lake of Dreams”:(Left)Water surface in front of the waterfall, Google Panoramio,?Pete&Sarah.(Right)Concave model used for the simulation derived by subtracting a sphere from a cube.

B.Wynn Hotel

The second simulated re?ectivity map uses a3-D model of the Wynn Hotel located in the center of Las Vegas,USA.By means of this example,it shall be shown that,also,3-D models of low quality can be used for supporting image interpretation even if the SAR geometry is coarsely approximated.

A perspective view onto the curved building,which has been captured in Google Earth,is shown in Fig.7and approximately indicates the line of sight of the sensor with respect to the hotel complex.A small lake called“Lake of Dreams”is visible in front of the hotel with a surface area of approximately 12000m2.At one end of the lake,an arti?cial waterfall is installed at a concave wall whose curvature is oriented in the direction to the hotel(left part of Fig.8).This is done because, at the beginning of the afternoon,both lake and waterfall are illuminated for showing spectacular image sequences and color effects.The wall is curved so that the same visual quality can be provided to all guests watching the show through the window of their hotel rooms.

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Fig.9.TerraSAR-X image of the hotel complex captured in spotlight mode. (A–F)Features to be compared with the simulation.Azimuth direction:Left to right.Range direction:Top down.

By coincidence,the concave surface of the building is ori-ented perpendicular to the?ight path of TerraSAR-X.In Fig.9, a spotlight image containing the hotel area is shown with range direction pointing top down.First,strong re?ection effects oriented in the azimuth direction shall be considered from near to far range.The?rst eye-catching feature looks like a curved rectangle whose transparent area seems to be framed by a bright border(feature A).This re?ection effect is assumed to be caused by the roof of the hotel.Afterward,several lines are visible in the right part of the image,showing strong contrast to the background(feature B).Moving on in the range direction, a long transparent part ends at a bright arc which is assumed to contain double-bounce contributions derived by the interaction between the hotel wall and the surrounding ground(feature C). Finally,after a region showing smeared features(feature D) and a broad line oriented in the azimuth direction(feature E), a short shadow region starts.Furthermore,considering the features oriented in the range direction,three dashed lines are oriented in the range direction(features F1,F2,and F3). Google’s3-D gallery provides a3-D model of the Wynn Hotel in sketchup format(?concept3D).Hence,in addition to visual interpretation of the image,the geometrical interpretation of these scattering effects can be supported by means of a simulated re?ectivity map.To this end,the model is imported into our simulator,where the geometrical model is completed by de?ning the surface parameters,introducing a virtual sensor, and constructing a?at plane beneath the building.The walls of the hotel are characterized by strong specular scattering combined with weak diffuse re?ection and a high re?ection coef?cient.In the case of a detailed representation of the roof structures in the3-D model,specular re?ection characteristics would be more reasonable for roof parts since only the roof outline is visible in the SAR image.Here,strong diffuse scat-tering is assigned to the plane roof of the current3-D model

for Fig.10.(Left)Result of simulation.(Right)Distribution of re?ection effects.

(Blue)Single bounce.(Green)Double bounce.(Red)Triple bounce.(Magenta) Fourfold bounce.Azimuth direction:Left to right.Range direction:Top

down. Fig.11.Cross section through lake and hotel wall:Fourfold bounce caused

by the interaction between walls and water surface.

emphasizing the extension of the building and the shape of the roof.In order to be able to capture the re?ection effects caused by the waterfall,a simple concave wall model is shifted into the segment of the circle de?ned by the curved wall of the hotel. The concave appearance of the wall model has been designed by CSG by subtracting a sphere from a cube(see model on the right part of Fig.8).Like for the walls of the hotel,the waterfall model is assumed to show strong specular re?ection behavior. The simulated re?ectivity map,including the intensity values of bounce level1–4,is shown on the left part of Fig.10.A map displaying the distribution of single or multiple scatterings is shown in the right part of Fig.10,where colors blue,green,red, and magenta correspond to single,double,triple,and fourfold bounce,respectively.

At?rst,re?ection effects showing up in both SAR image and re?ectivity map are to be exempli?ed.Feature(A)is also included in the simulated image and is caused by the roof https://www.360docs.net/doc/0f18891100.html,pared to the real SAR image,the area of the

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Fig.12.Three-dimensional model of Eiffel Tower,Paris,France;?SETE (http:www.tour-eiffel.fr).

curved rectangle is not transparent in the arti?cial map since a high diffuse re?ection component has been chosen for all parts of the roof.The assumption of feature(C)to be caused by double bounce between the hotel and the surrounding ground is con?rmed by the simulator.Moreover,two additional lines showing up at both ends of feature(C)in the re?ectivity map can also be identi?ed in the real SAR image.

While the outline of the shadow zone is quite similar in both images,linear feature(E)is only hinted by the simulator and marked with bounce level4.Fig.11indicates how the fourfold signals might be derived at the Wynn Hotel complex, more speci?cally,by the interaction of the signal with the hotel facade,the surface of the lake,and the waterfall.As both the curvature of the building and the curvature of the wall are oriented contrarily,spatial distances traveled by the rays following the path“sensor–building–water surface–waterfall–building–sensor”within the POV Ray scene are almost similar.

A complex multibody3-D model of the area,which might be available in the future,could be used to further support the identi?cation of objects causing fourfold-bounce signals backscattered from the Wynn Hotel complex.

By using the distribution map(see Fig.10),two of the three vertical dashed lines are classi?ed as the combination of double-and triple-bounce re?ections at the wall of the hotel. The dashed line in the center of the hotel wall likely occurs due to double-bounce effects caused by battens at almost all?oors of the building.It is not possible to obtain this effect in the simulated image as all walls of the hotel have been modeled by means of?at surfaces.Contributions of the surrounding buildings,vegetation,or terrain are not visible since they have not been designed in the model scene.

In the case of low-quality Wynn Hotel model,the information derived is not suf?cient for interpreting all the re?ection effects in the SAR image because most of them are caused by objects not included in the POV Ray model scene,e.g.,features(B) and(D)do not appear in the simulation result.Nevertheless, arti?cial re?ectivity maps can support the process of opinion making while observing and analyzing features in SAR images. Users of radar data should be aware of an increased number of deterministic re?ection effects particularly showing up in urban areas.

In the subsequent section,an example for the integration of 3-D models of increased quality into the simulation process is given.

C.Eiffel Tower

As the geometrical quality of the simulated re?ectivity map mainly depends on the quality of the3-D model scene used for the simulation process,also models of high quality are to be illuminated by the virtual SAR sensor for analyzing further the potentials and limits of our simulator.

A highly interesting example is,for instance,the Eiffel Tower(Paris)in order to compare the images derived from the simulator to the TerraSAR-X images.In this example, an amplitude mean map of six TerraSAR-X spotlight images (incidence angle:34?,6?)has been generated to suppress speckle.The3-D model,which is shown in Fig.12,can be downloaded on www.tour-eiffel.fr)for noncommercial pur-poses.It is composed of9.488facets and is offered in formats .obj(object format)and.dxf(AutoCAD format).

According to the SAR geometry given for the TerraSAR-X images,the tower was rotated and illuminated by the virtual sensor using the same signal incidence angle as for the real SAR images.The number of rays to be followed was chosen to1.000 in azimuth times4.000in elevation,yielding a sampling density of0.2m×0.2m in the model scene.Afterward,the re?ectivity map was created whose pixel spacing was adapted to the TerraSAR-X sampling,i.e.,0.43m×0.4m in the azimuth and ground range.The maximum number of bounces to be traced was?xed to?ve which was the maximum number for the Eiffel Tower case as detected by the simulator[Fig.14(a)].With re-gard to processing time in the case of the complex Eiffel Tower model,both steps,namely,sampling and image creation,took 5min and14s on a standard computer(2-GHz dual core,4-GB RAM).Concerning the radiometry,a strong specular re?ection behavior,a low amount of diffuse scattering,and a high re?ec-tivity factor were assigned to all surfaces of the tower.Since double-bounce contributions caused by the interaction between the tower and the ground were to be considered,a?at plane was introduced into the model scene,showing low diffuse re?ec-tion but strong re?ectivity.Strong backscattering at crossbeam structures was derived by means of strong specular re?ection behavior for surfaces combined with mean diffuse re?ection for considering local double-bounce effects at the tower and signals backscattered by small features like nivets which have not been considered in the3-D model.Both the mean map obtained by averaging six spotlight TerraSAR-X images and the simulation result are shown in Fig.13.The pixel spacing in the SAR mean

AUER et al.:RAY-TRACING SIMULATION TECHNIQUES

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https://www.360docs.net/doc/0f18891100.html,parison:(Left)Mean map obtained by averaging six spotlight TerraSAR-X images;(right)re?ectivity map.(A)Pinnacle.(B)Crossbeam structures.

(C and D)Platforms.(E,F,and G)Feet.(H)Shadow zone.(I,J,and K)Double-bounce contributions between the tower and the surrounding ground.Azimuth direction:Left to right.Ground range direction:Top down.

map is0.86m×0.8m in the azimuth and ground range due to a multilooking factor of https://www.360docs.net/doc/0f18891100.html,pared to the SAR image,many features are also clearly visible in the re?ectivity map derived by the3-D model scene of the tower.The shortest distance with respect to the SAR sensor is obtained for the pinnacle(A),fol-lowed by the crossbeam structures(B)in higher regions of the tower,two main platforms(C,D),three visible feet of the tower (E,F,G),and the shadow zone(H).Obviously,during the SAR simulation,a higher amount of signal power was able to pene-trate the crossbeam structures,causing stronger single-bounce

1454IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.48,NO.3,MARCH

2010

Fig.14.Separation of bounce levels.(Left)Distribution of re?ection effects.(Blue)Single bounce.(Green)Double bounce.(Red)Triple bounce.(Magenta) Fourfold bounce.(Cyan)Fivefold bounce.(Center and right)Re?ectivity maps of single and double bounce.Azimuth direction:Left to right.Ground range direction:Top down.

backscattering in the background of the tower.By contrast,this region is almost completely shadowed in the SAR image,where it appears black.This might appear due to signal diffraction at the tower crossbeams,which is not considered in the sim-ulation https://www.360docs.net/doc/0f18891100.html,pared to the real SAR case,objects in the neighborhood of the tower are neglected since the ground underneath the tower only has been modeled by means of a?at plane.Hence,overlay effects with other objects are not obtained in the simulation but clearly visible in the real SAR image, where features C–G are overlaid with diffuse backscattering contributions caused by vegetation in the park surrounding the tower.Furthermore,double-bounce effects caused by the interaction between the tower and the surrounding ground show up at the bottom(I)and at both sides of the tower(J,K).While effect(I)is also apparent in the SAR image,effects(J)and(K) likely disappear because of buildings that are adjacent to the tower,avoiding any backscattering to the sensor.Geometrical and radiometric interpretation is supported by using the bounce level information in order to display the different bounce levels in the separated image layers[Fig.14(b)and(c)].While single bounce and double bounce cause strong intensities and,hence, clear structures in the re?ectivity map,contributions of higher bounce levels are weakened by the decreasing weight factor of the ray followed through the modeled scene(see Section III-B). For this reason,three-,four-,and?vefold bounces are not displayed since their contributions show too little contrast to the background.

V.C ONCLUSION AND O UTLOOK

In this paper,a new approach for simulating SAR re?ectivity maps has been presented.It extends the open-source ray-tracing software POV Ray.The imaging SAR system is approximated by both a cylindrical light source and an orthographic camera. Re?ection contributions are evaluated by following rays in reverse direction,i.e.,starting at the center of each image

AUER et al.:RAY-TRACING SIMULATION TECHNIQUES1455

pixel.Arti?cial images are derived by a processing chain con-taining three major steps:modeling of a virtual3-D object scene,sampling of the scene by rays,and image creation in the azimuth–range plane.The simulation results created by means of3-D models of moderate and high quality have been shown for different purposes:1)for detection of deterministic double-bounce effects;2)for fast classi?cation of multiple-bounce effects;and3)for creating high-resolution re?ectiv-ity maps.

Generally,the geometrical quality of the resulting re?ectivity maps is limited both by the level of detail of the3-D models and the sampling density chosen by the operator,i.e.,the area cov-ered per pixel in the image plane of the orthographic camera. The radiometric quality is constrained by relying purely on the specular and diffuse re?ection models.Moreover,it has to be considered that discrete rays are sent through the model scene instead of continuous waves.

Despite of these limits of the ray-tracing approach,it has been shown that the simulation of the geometrical distribution of the scattering effects is helpful for supporting the inter-pretation of high-resolution SAR images.Three-dimensional models of high complexity can be handled in our simulator to provide arti?cial re?ectivity maps of high geometrical quality for comparison to real spaceborne SAR images.Most common model formats can be processed while the computing time is low because of the optimized source code.Most importantly, different bounce levels can be assigned to separated layers for further geometrical analysis.Future work will concentrate on additional case studies at very detailed3-D models for detecting backscattered signals caused by small building features.Strong re?ection zones that are visible in the re?ectivity map are to be mapped back into the3-D model for identifying areas causing strong double-or multiple-bounce effects.Future developments will focus on evaluating potentials for tomographic analysis of re?ection effects in3-D since,so far,information along the elevation direction has not been included in the backscattering analysis.

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1456IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.48,NO.3,MARCH

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Stefan Auer(M’07)was born in Bad Reichenhall,

Germany,on April17,1980.He received the Dipl.-

Ing.(Univ.)degree in geodesy and geoinformation

from the Technische Universit?t München(TUM),

München,Germany,in2005.

Since December2006,he has been a Full-Time

Scienti?c Collaborator with the Remote Sensing

Technology,TUM,and pursues his Ph.D.degree on

the simulation of radar re?ection effects by means

of3-D models of high quality.His work is part of

the project team“Dynamic Earth”which was estab-lished in the International Graduate School of Science and Engineering,TUM, as a result of the German excellence initiative in2007.In February/March2008 and2009,he spent nine weeks with the Department of Electronic and Telecom-munication Engineering(DIET),University of Naples“Federico II,”Naples, Italy,where he busied himself with the theory of electromagnetic?eld propaga-tion at man-made objects.His main interest is in supporting the interpretation of high-resolution synthetic aperture radar images by generating re?ectivity maps

and separating deterministic re?ection effects of different bounce

levels.

Stefan Hinz(M’03)was born in1972.He received

the Dipl.-Ing.degree in geodesy and geoinformation,

the Dr.-Ing.degree(summa cum laude)for his Ph.D.

work on automatic extraction of urban road networks

from aerial images,and the venia legendi(“habilita-

tion”)for his work on moving object detection and

monitoring in remote sensing data from the Tech-

nische Universit?t München,München,Germany,in

1998,2003,and2008,respectively.

In1999,he was a Guest Researcher with the

Institute of Robotics and Intelligent Systems(IRIS), University of Southern California,Los Angeles.The research conducted at IRIS was funded by the German Academic Exchange Service by a grant.Since December2008,he has been a Full Professor for remote sensing and computer vision and the Head of the Institute of Photogrammetry and Remote Sensing, Universit?t Karlsruhe(TH),Karlsruhe,Germany.His research interests include various aspects of computer vision and image understanding,particularly the-ory and methods for the automatic extraction,characterization,and monitoring of natural and infrastructural objects in optical,infrared,lidar,and radar remote sensing

data.

Richard Bamler(M’95–SM’00–F’05)received the

Diploma degree in electrical engineering,the Doc-

tor of Engineering degree,and the“habilitation”

in the?eld of signal and systems theory from the

Technische Universit?t München(TUM),München,

Germany,in1980,1986,and1988,respectively.

During1981–1989,he worked with TUM on opti-

cal signal processing,holography,wave propagation,

and tomography.In1989,he joined the German

Aerospace Center(DLR),Wessling,Germany,where

he is currently the Director of the Remote Sensing Technology Institute(IMF).Since then,he and his team have been working on synthetic aperture radar(SAR)signal processing algorithms(ERS,SIR-C/ X-SAR,RADARSAT,SRTM,ASAR,TerraSAR-X,and TanDEM-X),SAR calibration and product validation,SAR interferometry,phase unwrapping, estimation theory and model-based inversion methods for atmospheric sound-ing(GOME,SCIAMACHY,MIPAS,and GOME-2),and oceanography.In early1994,he was a Visiting Scientist with the Jet Propulsion Laboratory in preparation of the SIC-C/X-SAR missions,and,in1996,he was a Guest Professor with the University of Innsbruck,Innsbruck,Austria.Since2003, he has been holding a full professorship in remote sensing technology with TUM.He is the author of more than150scienti?c publications,among them about35journal papers,a book on multidimensional linear systems theory, and several patents on SAR signal processing.His current research interests are in algorithms for optimum information extraction from remote sensing data with emphasis on SAR,SAR interferometry,persistent scatterer interferometry, SAR tomography,and ground moving target indication(GMTI)for traf?c monitoring.He and his team have recently developed and are currently de-veloping operational processor systems for the German missions TerraSAR-X, TanDEM-X,EnMAP,and MetOp/GOME-2.

圆梦2015·高三年级理科数学仿真模拟试题(3)精美word版

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