low‐altitude terrestrial spectroscopy from a pushbroom sensor

rob21624 W3G-rob.cls September 19, 2015 18:8

Author ProofLow-altitude Terrestrial Spectroscopy from a PushbroomQ1

Q2 Sensor

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

Q3 Juan-Pablo Ramirez-ParedesDepartment of Electrical Engineering, University of Texas at Dallas, 800 West Campbell Road, Richardson, Texas 75080e-mail: [email protected] LaryDepartment of Physics, The University of Texas at Dallas, 800 West Campbell Road, Richardson, Texas 75080e-mail: [email protected] GansDepartment of Electrical Engineering, University of Texas at Dallas, 800 West Campbell Road, Richardson, Texas 75080

Received 23 January 2015; accepted 23 July 2015

Hyperspectral cameras sample many different spectral bands at each pixel, enabling advanced detection andclassification algorithms. However, their limited spatial resolution and the need to measure the camera motion tocreate hyperspectral images makes them unsuitable for nonsmooth moving platforms such as unmanned aerialvehicles (UAVs). We present a procedure to build hyperspectral images from line sensor data without cameramotion information or extraneous sensors. Our approach relies on an accompanying conventional camera toexploit the homographies between images for mosaic construction. We provide experimental results from alow-altitude UAV, achieving high-resolution spectroscopy with our system. C© 2015 Wiley Periodicals, Inc.

1. INTRODUCTION

While digital cameras are useful as airborne sensors forterrestrial surveying, the spectral information contained intheir images is limited to a few broad bands, typically onefor grayscale imaging or three-color imaging. Multispectralcameras partially overcome this limitation, but they are alsorestricted in the quantity and breadth of the frequency bandsthey make available per picture element. In contrast, hyper-spectral cameras provide potentially hundreds of differentspectral bands per pixel. Since the 1970s, when field mea-surements were made supporting the analysis of Landsat-1observations, imaging spectroscopy via hyperspectral cam-eras has steadily progressed (Goetz, 2009).

There have been many applications of hyperspectralsensors in imaging of land, ocean, and atmospheric com-position. In precision farming, it is possible to model theresponse of plants to factors such as drought, disease, orpollution by analyzing the reflectance and absorption ofspecific spectral wavelengths (Smith, Steven, & Colls, 2004).There have also been successful studies of mineral identi-fication by processing hyperspectral data from instrumentssuch as the Airborne Visible/Infrared Imaging Spectrom-eter (AVIRIS) (Kruse, Boardman, & Huntington, 2003). Oilspills such as the Deepwater Horizon incident of 2010 can

Direct correspondence to: Nicholas Gans, e-mail: [email protected]

also be precisely delimited by spectroscopy (Sidike, Khan,Alam, & Bhuiyan, 2012). There have been attempts at char-acterizing human skin from hyperspectral data to get anaccurate identification of pedestrians, setting a precedentfor surveillance or search-and-rescue applications (Herweg,Kerekes, & Eismann, 2012).

To enable imaging at hundreds of distinct frequencybands, the optics of hyperspectral sensors are significantlydifferent from a typical digital camera. Hyperspectral cam-eras are typically line-scanning and record the spectrum atall channels corresponding to a single image line in space.An example of a hyperspectral image is seen in Figure 1.Given the narrow collimation slit of the optics, a singlehyperspectral image is often of limited use since it has avery small field of view in one direction. Hyperspectral sen-sor technology has progressed toward solutions that allowtwo-dimensional (2D) frame capture, where each pixel hasan associated set of frequency responses. Recent develop-ments, such as the Fabry-Perot interferometer camera, havethe potential to replace line-scanning cameras (Honkavaaraet al., 2013). However, the line-scan variety is reliable, com-mercially available, has no moving parts, and remains thelowest in cost and complexity (Vagni, 2007). Line-scan hy-perspectral cameras typically have finer spectral resolutionthan their full-frame counterparts, and generally cover awider spectrum in each capture. Therefore, line-scan cam-eras still address the widest range of useful data analysisand applications.

Journal of Field Robotics 00(0), 1–16 (2015) C© 2015 Wiley Periodicals, Inc.View this article online at wileyonlinelibrary.com • DOI: 10.1002/rob.21624


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2 • Journal of Field Robotics—2015

Figure 1. Comparison of a hyperspectral image line with a section of a visible light, conventional camera image. The cameras arepositioned side by side, and the dashed line corresponds to the line captured by the hyperspectral camera.

If the hyperspectral camera is moved at a precise speedorthogonal to the scan line and consistent with the cameraframe rate, the scan lines can be compiled and processedinto a single image. Ideally, the imaging line moves onepixel per sample time in a direction perpendicular to theline, and the collected data are a proper image. Therefore,this is often referred to as “pushbroom imaging” and “push-broom camera.”1 Typically, interpolation is performed tocompensate for imprecise motion. This approach generallyQ4requires high altitude aircraft or Earth-orbiting instruments.Relevant examples with aircraft include that in Asmat,Milton, & Atkinson (2011), which imaged 32 spectral bandsover farmland from an aircraft flying steadily at 1,900 m,and that in Schechner & Nayar (2002), which involved acamera imaging 21 spectral bands, moving precisely in acontrolled lab environment. An example of a pushbroomhyperspectral camera not mounted on aircraft is presentedin Monteiro, Minekawa, Kosugi, Akazawa, & Oda (2007), inwhich a crane was used as a platform to mount the sensor. Inall cases, the pushbroom camera must be moved smoothlyand at a constant speed.

There are many advantages to using unmanned aerialvehicles (UAVs) in place of or in conjunction with satel-lites. Due to their low flight altitude, better resolution canbe achieved from the instruments they carry in terms of thenumber of “pixels on target.” Data capture for a given area

1While we present a method to generate hyperspectral imageswhile not sweeping in a straight line, we will maintain the commonconvention of calling such cameras “pushbroom” cameras.

can be scheduled on demand, and the cost of the wholeplatform is considerably lower when compared with largeraircraft or Earth-orbiting equipment. The payload is alsoeasily changed or upgraded according to application de-mands. However, using a line-scan sensor to perform push-broom imaging on a non-smoothly-moving platform suchas a UAV is a nontrivial task, given the difficulty of recover-ing the exact motion of the camera over time. There are dif-ferent classes of UAVs, the main two being helicopters andairplanes. The helicopter class, including multirotor UAVs,is the most challenging for pushbroom imaging due to thefact that they have to tilt in order to move. They are alsosubject to vibration from their motors. Airplane UAVs canachieve steadier flight, but those with smaller wingspansare more prone to suffer from disturbances such aswind.

The precision and accuracy of localization sensorsneeds to be higher for a small UAV, since it is subjected toabrupt motions from internal and external sources, with anassociated increase in cost. Spectroscopy has been achievedon these platforms by fusing inertial measurements anddata from the global positioning system (Hruska, Mitchell,Anderson, & Glenn, 2012; Lucieer, Malenovsky, Veness, &Wallace, 2014; Zarco-Tejada, Gonzalez-Dugo, & Berni, 2012).In each of these works, the main problem is the level of ac-curacy of the inertial sensors of the UAVs. A workaroundfor this limitation is to complement the onboard sensordata with ground control points captured by a cameraand to apply computer vision techniques to match pixelsacross images (Turner, Lucieer, & Watson, 2012). This is a

Journal of Field Robotics DOI 10.1002/rob


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Ramirez-Paredes et al.: Low-Altitude Terrestrial Spectroscopy • 3

successful way to georeference data from frame imagers,but it does not apply to line-scanning sensors.

We propose a novel approach to enable a pushbroomhyperspectral camera to be used from a UAV, despite theaforementioned challenges. Furthermore, we do not requirethe addition of inertial sensors or external measurementsof the camera pose. This is accomplished by using a con-ventional digital camera2 rigidly attached close to the hy-perspectral camera to provide additional information withwhich to build the hyperspectral image.

We focus on computer vision techniques, providing adirect map between the hyperspectral scanlines and theconventional camera images. With conventional cameras,it is possible to stitch together different views of a sceneby means of the image homography. This process is typi-cally called image mosaicing (Caballero, Merino, Ferruz, &Ollero, 2009; Szeliski, 1996). Computation of the homogra-phy requires point correspondences from two views of aplanar object or scene and relates point projections in bothcamera views. The homography contains information aboutthe rotation and translation of one camera view relativeto the other, and by exploiting this our approach buildsa hyperspectral image from a collection of hyperspectrallines mapped to a mosaic created from conventional cam-era images. Recent work focused on correlation-based align-ment of pushbroom camera images (Moroni, Dacquino, &Cenedese, 2012). The ability of such a technique to copewith perspective transformations is limited, so its perfor-mance would be compromised in the presence of pitch orroll motions from the aircraft. As we show in the results,our approach can deal with a wide set of camera motions.

The work presented herein is an extension of that ofRamirez-Paredes, Lary, & Gans (2013), in which the con-cepts of this paper were introduced, accompanied by ex-perimental results retrieved by hand-held operation of thesensor array. This paper presents new results from theuse of a low-altitude UAV in conjunction with the sen-sor array to capture long image sequences exceeding 200frames.

The rest of this paper is organized as follows: Section 2explains how the intrinsic parameters of the hyperspectralcamera are computed. Section 3 deals with the necessaryaspects of designing a rig to mount the hyperspectral andconventional cameras, detailing restrictions on positioningthe cameras and the method for aligning them. Section 4explains how to map the pixels captured by the hyper-spectral camera to their corresponding line in the conven-tional camera frame. Section 5 describes the constructionof an image mosaic for the conventional camera and lever-aging that mosaic, along with the results of the previous

2By “conventional digital camera” we mean a two-dimensionalsensor with a rectangular grid as its image plane, where each ele-ment is sensitive to light in a broad band of frequencies hundredsof nanometers wide.

sections, to obtain a hyperspectral image. Experimental re-sults are shown in Section 6, followed by a discussion inSection 7.

2. HYPERSPECTRAL CAMERA GEOMETRICCALIBRATION

The typical approach to geometrically calibrate line sen-sors, such as hyperspectral cameras, is to attach them toa mechanical platform able to perform precise movementsin a direction perpendicular to the scan line (Drareni, Roy,& Sturm, 2011; Gupta & Hartley, 1997). If the line sensormoves at a constant speed while imaging a known calibra-tion target, stacking the image lines results in a full image.With this approach, the calibration procedure is similar toconventional camera techniques.

Our approach to geometrical calibration is mathemat-ically similar to that in Gupta & Hartley (1997). However,their calibration method requires a moving camera (or amoving known target) with accurate measurements of ve-locity. Our method does not require any such motions, soit simplifies ex situ calibration. We model the hyperspectralcamera as a conventional camera with one row of pixels, andevery pixel is capable of measuring the intensity of severalspectral bands. This approximation simplifies the cameramodel, yet it provides precise results.

We perform geometric calibration by capturing imagesof a special target. This provides a correspondence betweenworld points with known coordinates and their projectionson the pushbroom camera scanline, allowing for the recov-ery of parameters such as the field of view and the principalpoint. This same target is also used to align the hyperspec-tral and conventional cameras in our array, as will be de-tailed in the next section.

Consider a Cartesian frame Fh attached to the hyper-spectral camera, with the origin at the camera focal point,the X axis parallel to the spatial pixels direction, the Y axisperpendicular to the spatial pixels direction, and the Z axisaligned with the line going from the focal point to the imageline center and normal to the image line. Another Cartesianframe Ft is associated with the target. The target has a spe-cial pattern on the surface, containing a number of high con-trast features we call control points with known coordinatesin Ft . It is essential that all control points not be collinearin 3D Cartesian space. For such a configuration there is anambiguity, and a certain image of the points can arise froman infinite number of camera poses. Therefore, we suggesta target consisting of control points on two intersecting per-pendicular lines.

In this work, we designed a target consisting of a thin,rigid, planar plastic sheet approximately 3 mm thick with atriangular shape. There is an alternating pattern of black andwhite bars on two edges that provides easily detectable tran-sitions in the hyperspectral image, which constitute the con-trol points. The separation between these points is 30 mm.



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Figure 2. Left: the geometric calibration target used for the hyperspectral camera. Right: the calibration target along with thehyperspectral camera. The pyramid (Ch) represents the hyperspectral camera as in the pinhole model, with its scan line in red.

The target consists of two pieces of acrylonitrile-butadiede-styrene (ABS) plastic built from a 3D printer with a resolu-tion of 0.254 mm. The target frame Ft has its X and Z axesas the intersecting lines containing the control points. Weassume that the collimation slit of the hyperspectral cam-era is aligned with the pixel rows of its imaging sensor. Ifthe target is currently aligned with the slit, the dark andwhite bands can detected in the hyperspectral image andthe control points extracted.

The calibration target is shown in Figure 2, along with adiagram of the hyperspectral camera and the control pointson a target. Any rotation of the target along the X or Y axeswith respect to Fh will result in one or more control pointsnot being projected into the scan line. Figure 3 simulates thedifference between a correctly aligned target and a rotatedone. A rotation of 1 degree on both the X and Y axes ofFh is shown. When the hyperspectral camera and the targetare properly aligned, the projected control points (crosses)lie on the camera line, and they can all be detected. Therotations cause the projected points (squares) to fall outsideof this line, making them not detectable.

Let us assume that no points are outside of the XZ

plane of Fh, since they could not be imaged otherwise. Forsimplicity, and without loss of generality, assume the targetframe Ft is the world/inertial frame Fw . The homogeneouscoordinates of a point in Fw are M = [X 0 Z 1]T , and thehomogeneous transformation from the world frame to theFh camera frame is denoted by T h

w ∈ SE(3) (i.e., the space ofrigid body motions). A projection model from the world tothe hyperspectral camera is given by

λu = K�0Thw M. (1)

The projection of the point is λu = λ[u 1]T , with λ being anunknown scale factor. K is a calibration matrix given by

K =[f u0

0 1

]

with f being the horizontal focal length of the camera andu0 its principal point in the horizontal direction. The matrix�0 is a projection given by

�0 =[

1 0 0 00 0 1 0

].

Following the developments for conventional cameras, it ispossible to adapt the direct linear transform (DLT) (Abdel-Aziz, 1971) approach to the pushbroom camera. Just as theoriginal DLT inverts a map P2 : P

3 → P2, the pushbroom

case requires an inversion of a map P1 : P2 → P. Choosing

the control points of the calibration target to be on the sameplane as the hyperspectral camera line and focal point, it ispossible to discard the Y coordinate of the points by settingit to zero.

As the frames Fw and Fh must have their Y -axesaligned, the rotation in T h

w must have the form

T hw =

⎡⎢⎢⎣

cos θ 0 sin θ tx0 1 0 0

− sin θ 0 cos θ tz0 0 0 1

⎤⎥⎥⎦ ,

where θ is the angle between the X axes of Fh and Fw .Considering that Y = 0 for every point, let us multiply

�0Thw and discard the Y dimension in our computations, as

it does not contribute to the projection. This gives rise to the



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Figure 3. Calibration target points projected on the hyperspectral camera. Only when the control points lie over the scan line arethey visible to the camera.

simplified projection equation

λu =[f u0

0 1

] [cos θ sin θ tx

− sin θ cos θ tz

] ⎡⎣X

Z

1

⎤⎦ = K

[R t

]X,

(2)

where R ∈ SO(2) and t ∈ R2. The intrinsic parameters of the

camera are f and u0 and determine the relationship betweenpixel and image plane coordinates. The extrinsic parametersdefine the pose of the camera with respect to the knownworld frame, Fw . The intrinsic and extrinsic parameters canbe combined to give a camera matrix that has six unknownsas

λu =[a1 a2 a3

a4 a5 a6

] ⎡⎣X

Z

1

⎤⎦ = AX. (3)

To cancel the scaling factor λ and rewrite the equations as ahomogeneous linear system, we multiply both sides of Eq.(3) by uT Q, where Q is a skew-symmetric matrix given by

Q =[

0 −11 0

],

thus getting

uT QAX = 0. (4)

Arranging the terms, the resulting equation gives

Xa1 + Za2 + a3 − uXa4 − uZa5 − ua6 = 0.

Stacking equations for five or more point matches betweenthe control points in Ft and their projection on the hyper-spectral camera line gives the homogeneous system

⎡⎢⎢⎢⎣

X1 Z1 1 −u1X1 −u1Z1 −u1

X2 Z2 1 −u2X2 −u2Z2 −u2...

......

......

...Xn Zn 1 −unXn −unZn −un

⎤⎥⎥⎥⎦

⎡⎢⎢⎢⎣

a1

a2...a6

⎤⎥⎥⎥⎦ = 0. (5)

SAs = 0. (6)

The matrix S can be at most of rank 5, so As can besolved up to a scale factor by finding the nullspace of thematrix S. From Eq. (2), we see that a2

4 + a25 = 1, so the proper

scale α can be recovered up to a sign ambiguity as

α = ± 1√a2

4 + a25

.

Once the matrix S has been properly scaled, the intrinsicand extrinsic parameters can be recovered as

u0 = a1a4 + a2a5,

f = [a2

1 + a22 − u2

0

]1/2.



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Either choice of sign for α results in the same parametersf and u0. However, the different sign choice leads to twosolutions for R and t. Picking either α, the recovered posesare

R1 =[a5 −a4

a4 a5

],

R2 = RT1 ,

t1 =[

(a3 − u0a6)/fa6

],

t2 = −t1.

One solution will have a negative value for tz. Sincethis would correspond to the control points being behindthe camera, we can discard this translation and consider thepositive tz. Likewise, one rotation would be equivalent tothe camera facing a direction opposite to the target.

We also address the issues of radial distortion and im-age noise. Radial distortion is a lens-induced phenomenonthat causes deviation from rectilinear projection. It is typ-ically modeled as a polynomial of even degree, where theonly nonzero coefficients are those of even powers (Brown,1966; Salvi, Armangue, & Batlle, 2002). For the case of thepushbroom camera, radial distortion can be modeled as

ud = u + κ1(u − u0)2 + κ2(u − u0)4 + H.O.T . (7)

The distorted point projection is ud , while the projectionpredicted by the pinhole model is given by u, and κ1, κ2, . . .

are distortion coefficients. The number of coefficients to usedepends on the degree of precision required. One coeffi-cient provides acceptable results for our application. Thedistortion coefficient can be determined, and the camera pa-rameters refined, by using convex nonlinear optimization,with the results obtained from the DLT part of the calibra-tion as initialization values for the Levenberg-Marquardtalgorithm (Zhang, 2000). Taking m images of the calibrationtarget and locating the n control points in each, the measureto be minimized is the point reprojection error,

Jd (up, u′p, κ1) =

n∑i=1

m∑j=1

||uji − u

ji

′||2. (8)

The vector up ∈ Rnm contains the projections of the cali-

bration points as predicted by our model using the hyper-spectral camera parameters, while u′

p ∈ Rnm are the actual

projections of the calibration points. The point uji represents

the ith point of the j th calibration target image.Another important procedure related to the hyperspec-

tral camera is the precise determination of its spectral sensi-tivities. This procedure is known as radiometric calibration.This type of calibration generally requires measurements ofspecial light sources for different integration times by thehyperspectral camera, under precise laboratory conditions(Zarco-Tejada et al., 2012). A related approach is to use afield spectroradiometer, which is a calibrated instrument

that measures the reflectance of a particular object underfield conditions (Al-Moustafa, Armitage, & Danson, 2012;Stratoulias, Balzter, Zlinszky, & Toth, 2015). The light re-flectance of the target objects is measured under outdoorlighting and then compared to the spectral response of thesame targets as seen by the hyperspectral camera. This isdone prior to the data collection flights. Our laboratory isnot equipped to perform the radiometric calibration of thehyperspectral camera, so we relied on spectral sensitivitydata from the camera manufacturer. This is sufficient todemonstrate and assess the hyperspectral imagery that ourapproach is able to create, but more precise calibration willneed to be performed before application in dedicated stud-ies of the environment.

3. CAMERA ARRAY ALIGNMENT

Our approach requires an accurate mapping between thepixels in the pushbroom line and the pixels in the conven-tional camera. Given the projection of a world point on oneof the cameras, it is generally not possible to predict its pro-jection on the other camera without knowing the depth ofthe point with respect to either of the cameras. However,under certain alignment conditions, epipolar geometry al-lows us to predict the line along which that point will befound (Hartley & Zisserman, 2003). This is a line-to-line mapthat generally depends on the depth of the world pointsin the camera frames. However, the correspondence canbe uniquely determined if the hyperspectral line coincideswith an epipolar line.

In projective geometry, using the pinhole cameramodel, elements of R

3 can be used as homogeneous co-ordinates to represent both lines and points on the imageplane. For points, the vector p = [u v 1]T represents the co-ordinates of a point in the image plane; typically this de-notes the intersection of the image plane and a ray of lightfrom a 3D point through the focal point of the camera. Theimplicit equation for a line au + bv + c = 0 leads to a linerepresentation l = [a b c]T . A given point p is part of a linel iff pT l = 0. Thus, the hyperspectral camera line can beexpressed as lh = [0 1 0]T in homogeneous coordinates inFh, since only points p = [u 0 1]T belong to it. By our hy-perspectral camera model in Eq. (1), only points with 3Dhomogeneous coordinates X = [X 0 Z 1]T in Fh frame canhave a projection in the hyperspectral image. The projec-tions of these points to the hyperspectral imaging surfacelie on lh.

Consider the hyperspectral camera focal center Ch andthe conventional camera focal center Cc. The epipole eh isthe point at which the line from Ch to Cc intersects theline lh. The epipole ec is the point where the line from Cc

to Ch crosses the image plane of the conventional camera.This is illustrated in Figure 4. By making the epipole eh lieon lh such that eT

h lh = 0, lh becomes an epipolar line. Fromepipolar geometry, it is known that each of the epipolar lines



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Figure 4. Effect of the world point depth over the projectionof the hyperspectral camera line onto the conventional camera,with different alignments between cameras. Top: The worldpoints lie on the same plane and are projected on a line onthe conventional camera, but the position of this line dependson the point depths. The projections of these points wouldbe part of a different line if their depths changed. Bottom: Thehyperspectral line is an epipolar line, i.e., ec and lh are coplanar.The points project over the same line in the conventional cameraregardless of their depth.

in one camera plane has a corresponding epipolar line inthe other. To find the line lc in the conventional image planethat corresponds to lh, consider a line k in the hyperspectralcamera plane not crossing eh. The point where lh and kintersect is x = k × lh. Then lc = Ex, where E is the Essentialmatrix between both cameras (Huang & Faugeras, 1989).

Any nonzero p ∈ R3 can represent either a line or a

point in projective geometry, and the line expressed by p issuch that p as a point does not belong to the line. This canbe verified easily since pT p �= 0. We need a line k that willnever go through eh. Thus, the line with coordinates givenby the epipole eh is a good choice for k. Then the epipolarline in the conventional camera plane corresponding to lhcan be found as

lc = E[eh × lh]. (9)

From the constraints placed on eh, the only translationbetween cameras that is allowed is T = [X 0 Z 1]T in thehyperspectral camera frame. Rotation is only restricted bythe need to have the points within the field of view of thecamera. It is only when the hyperspectral line becomes anepipolar line that the points projected onto the hyperspectralcamera frame can be found on a corresponding epipolar linein the conventional camera regardless of the 3D world pointdepths.

With the conditions for a line-to-line mapping betweencameras established, the next step is to formulate a way toalign the cameras such that Eq. (9) holds. The calibrationtarget from Section 2 can be used as an alignment aid. Thealignment procedure we suggest is as follows:

� Affix the hyperspectral camera to the carrying rig.� Position the calibration target such that every control

point is visible to the hyperspectral camera.� Translate and rotate the conventional camera until every

control point of the calibration target lies on the same linein the image plane.

4. HYPERSPECTRAL LINE-TO-IMAGE MAPPING

We propose an optimization task that finds the mappingbetween cameras for any scene. With the camera arrayaligned as in Section 3, the world points projected onto thehyperspectral camera line can be found over a single linein the conventional camera image plane. From Eq. (9), weknow the line-to-line mapping between the hyperspectraland conventional cameras. However, the data in the hyper-spectral image are a line segment in lh, which corresponds toa line segment in lc. While it is known that the world pointsprojected onto lh are also projected onto lc, the precise map-ping between line segments is not known if the depth andorientation of the plane π1 with respect to Fh and Fc areunknown. Finding a map between line segments involvesfinding a scale factor s and displacement d that scale thelength and shift the position of the pixels.

The conventional camera captures grayscale intensityimages, so every pixel performs an integration of the lightintensity over the pass band of the sensor. In the case of thehyperspectral camera, an intensity image can be approxi-mated at each spatial pixel by summing the responses atevery frequency band. This allows a comparison betweenintensity values from both cameras after they are normal-ized, even though they may differ by some unknown scalarfactor and offset.

Consider a sequence of n simultaneously captured hy-perspectral and conventional images. The kth hyperspectralimage can be considered as a real f × c matrix Gk , whereeach element gk

i,j corresponds to the ith frequency band andthe j th spatial component. There are f frequency bands, c

spatial components, and k = 1, . . . , n such matrices for an n



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image sequence. Consider the n × c matrix V, where eachelement vk,j is given by

vk,j =f∑

i=1

gki,j . (10)

That is, each row of V is the intensity response of the hy-perspectral camera in image k. Similarly, consider an n × m

matrix W where the kth row is the pixel values of the line lcthat correspond to the kth lh.

To match each conventional image line segment to thecorresponding hyperspectral line segment, we minimize thecost function

Jm(d, s, V, W) =n∑

k=1

∑mi=1 vk,i · wk,�(i−dk )sk�

||vk||√∑m

i=1

[wk,�(i−dk )sk�

]2. (11)

The vector vk is the kth row of V. The n-element vectors dand s are the displacements and the scale factors that defineeach line correspondence, and their elements are denotedas dk and sk , respectively. The cost function is based onthe cosine similarity between signals. The locally optimalscaling and displacement vectors satisfy

{dopt, sopt} = arg mind,sJm(d, s, V, W). (12)

This optimization task is nonlinear in nature, and wehave obtained our best results by applying the Nelder-Meadalgorithm (Nelder & Mead, 1965). For initialization, we es-timate an initial displacement by using normalized correla-tion between the scaled hyperspectral lines and their con-ventional camera equivalents. The initial scaling factor isthe ratio between the conventional camera focal length andthat of the hyperspectral camera.

5. IMAGE REGISTRATION

We have detailed a procedure to obtain a mapping betweenthe hyperspectral camera data and the images captured bythe conventional camera. These correspondences alone arenot sufficient to create a hyperspectral image of the capturedscene. It is still necessary to recover the motion of the hy-perspectral camera over time in order to organize the data,i.e., to properly order and align the line segments imagedby the hyperspectral camera. To achieve this, we leverageapproaches to combine multiple overlapping images, form-ing a single depiction of the captured scene from the con-ventional camera. Forming an image mosaic with the con-ventional camera images also provides a mapping betweenthe relative positions of the camera when each image wascaptured. This, along with the mapping from points in thehyperspectral image to the conventional image described inSection 4, can enable spectroscopy of a given region.

5.1. Correlation-based Matching

One approach to mosaicing that has been applied to formhyperspectral images is to use correlation to find a simi-larity transform (Moroni et al., 2012). This approach workswell when the motion of the camera is primarily translationover the X and/or Y axes. Since it can be a costly opera-tion, correlation is often replaced with frequency-domainmultiplication via fast Fourier transform.

The correlation between two images can provide infor-mation about the location of maximum similarity to overlaptwo images, but not about the degree of rotation or the dif-ference in scale between them. To determine these parame-ters, it is necessary to perform the correlation operation formultiple Z-axis rotations and/or scalings. This adds to thecomputational cost of the operation, but it can provide accu-rate results for aircraft-mounted cameras following straightflight paths.

When the straight-path assumption is not satisfied, itis still possible to find the similarity transform that mostclosely matches the subsequent frames. However, as weshow further below, the resulting imagery may not preservethe geometry of the original scene.

5.2. Feature-based Matching

When the imaged scenes are far away from the camera, wecan approximate every world point as lying on a commonplane. This assumption is of special interest while perform-ing aerial or satellite photography. The points mapping be-tween different images of such scenes can be characterizedwith a homography, which can then be used to create im-age mosaics. Let there be a set of 3D points restricted to liein a plane π1 ⊂ R

3, and let two cameras capture images ofthe points. There exists a homography matrix H ∈ R

3×3 thatrelates the projection p1 of each point in the second camera,p2. This relationship is given by

p2 ∼ Hp1. (13)

The homography matrix between two conventionalcamera views can be recovered by the four-point algorithmfrom point correspondences (Faugeras & Lustman, 1988;Ma, Soatto, Kosecka, & Sastry, 2004). Coupling the four-point algorithm with random sample consensus (RANSAC)delivers an accurate homography matrix solution in thepresence of noise and mismatches (Torr & Zisserman, 1999).This is useful if the correspondences are obtained usingregion features such as scale-invariant feature transform(SIFT) or speeded-up robust features (SURF). In our ap-proach, we make use of SURF (Bay, Ess, Tuytelaars, & VanGool, 2008). Its performance is comparable to SIFT for theclass of motions considered here, while being computation-ally less expensive (Bauer, Sunderhauf, & Protzel, 2007).

The number of SURF features per image to retrievewas not set in advance, but more that 1,000 were extractedin every frame. A higher number of matches between SURF



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points in different images is not the only factor related tothe quality of the registration. Matching SURF features be-tween image pairs requires a metric to evaluate the cor-respondences. The sum of squared differences (SSD) for aneighborhood of pixels around the candidate points pro-vide a good indication of the match quality. The SSD can becoupled with a distance threshold to discard unreasonablematches, under the standard assumptions of optical flowfor features (constant intensity and smooth motion acrossframes).

The quality of the registration is also greatly affected bythe residual error after computing H . The RANSAC algo-rithm provides a good estimate in the presence of outliers,even if some incorrect point matches are not properly dis-carded with the SSD and distance metric. The resulting H

matrix will still need to be refined by the application ofnonlinear optimization (e.g., the Levenberg-Marquardt al-gorithm) to minimize the reprojection error. At the end ofthe optimization, the homography matrix for a single imagepair is obtained.

One approach to construct a mosaic from several im-ages of a planar scene is to find the homographies for ev-ery image pair. Then the images are warped to register toa reference image chosen among them. The problem withthis approach is that errors accumulate, resulting in distor-tion effects. To avoid this, we use the approach of Shum &Szeliski (2000). Consider a set of n images I = I1, . . . , In ofa planar scene, with enough overlap and matching featurepairs to successfully recover the homographies. In image Ik ,let there be m feature points. The homogeneous coordinatesfor the feature points in Ik can be combined to form a matrixP ∈ R

3×m. Let H denote the set of n2 homographies, witheach element H

ji being the homography between images Ii

and Ij that satisfies Pj = Hji Pi . These relationships can be

exploited in an optimization scheme to reduce registrationerrors in building the mosaic. Consider a cost function tominimize given by

Jh(H, P1, . . . , Pn) =n∑

i=1

n∑j=1

||Pj − Hji Pi ||2 (14)

with the optimum being the solution to

Hopt = arg minH

Jh(H, P1, . . . , Pn). (15)

We favor using the feature-based matching approachsince it better preserves the underlying geometry of theimaged scene. To illustrate this point, consider Figure 5.It first shows a visible-light orthophoto from the GoogleMaps satellite image collection. We highlighted two featuresconnected by a dashed line, and a rectangle emphasizes acreek. Note that the rectangle lies mostly to the right of thedashed line. The two images below compare the position ofthese features for the frequency-based and the feature-basedapproaches, respectively. The frequency-based mosaic on

Figure 5. Comparison of the relative placement of some scenefeatures between a reference orthophoto and the image mosaicsfrom experimental data. The bottom left image is a mosaic builtusing frequency-based matching, while the bottom right imagewas assembled using feature-based matches. Only the latterpreserves the geometry of the orthophoto.

the left does not preserve the geometry of the orthophoto,as the dashed line crosses over the creek. The feature-basedmosaic, on the right, does preserve the relationship.

5.3. Hyperspectral Image Assembly

At this stage, there is enough information to constructthe hyperspectral image. Using the line-to-line correspon-dences described in Section 3 and the scaling factors andthe displacements between the hyperspectral and the con-ventional camera pixels described in Section 4, the positionsof the hyperspectral camera points projected onto the con-ventional camera images can be recovered. Using these newpoint coordinates for the hyperspectral data and applying



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the homographies from Eq. (15), a single hyperspectral im-age with all the frequency bands as layers is recovered.

The application of the homographies results in sparsedata consisting of triplets of the form {x, y, F1,...,f }, wherex, y are image coordinates and F1,...,f is the set of all theintensity values for each of the frequency bands from thehyperspectral sensor. An interpolation procedure is neededto obtain a dense data set. The choice of interpolation algo-rithm is up to the specific application for the images. Thereare nonuniform interpolation techniques that can then beapplied to the data, including linear interpolation, inversedistance weighting, nearest neighbors, kriging, etc. (Oliver& Webster, 1990; Ruprecht, Nagel, & Muller, 1995). The in-terpolated result is also known as a data cube.

Qualitatively, the proposed approach results in mo-saics that better fit orthorectified image databases thancorrelation-based approaches. Validating the geometric ac-curacy generally requires reference orthorectified imageryto match the hyperspectral image (Laliberte, Winters, &Rango, 2008) or georeferenced ground control points in-dicated by reflective markers on a surveyed area (Rocchini& Di Rita, 2005). It also requires additional data, such asthe external orientation of the aircraft and camera array, thecamera position as determined from GPS points, and a digi-tal elevation model. This work demonstrated hyperspectralimage creation using only image data, but quantitative anal-ysis will be performed prior to any application in remotesensing.

6. RESULTS

We present experiments conducted with a low-altitudeUAV. We employed a Sony XCG-V60E monochrome con-ventional camera and a custom-made hyperspectral cameramanufactured by Surface Optics, based on the AVT Prosil-ica GC 655. Both cameras have 640 pixels of horizontal res-olution. The conventional camera has 480 pixels of verti-cal resolution, while the hyperspectral vertical informationcontains the frequency response in 120 different bands, withwavelengths covering a range of 400–1,000 nm. The rate ofacquisition for the system is 90 frames per second for bothcameras. Our camera array is mounted on an aluminumrail, shown in Figure 6. The radiometric calibration of thesensor was based on manufacturer spectral sensitivity data.

We used a piloted, radio-controlled airplane to performthe data collection. The plane, pictured in Figure 7, is capa-ble of carrying a 2.5 kg payload with its electric motor. Itis equipped with a micro-ATX PC and GigE interface tothe cameras. The airplane was flown over a designated RCfield. The imaged area included grassland and ponds forlivestock. The airplane height above ground was set below100 m, with an average of 60 m, and the wind was blowingat an average of 30 km/h from the south.

The hyperspectral camera has many applications invegetation studies, such as precision agriculture, by as-

Figure 6. Experimental camera array. The hyperspectral cam-era has a cylindrical shape and it is shown in the middle, withthe smaller conventional camera to its left.

Figure 7. Low-altitude airplane used to carry the camera array.

sessing plant health using narrowband indices. A studyof the application of various narrowband indices for planthealth and stress assessment can be found in Zarco-Tejadaet al. (2005). One useful quantity that can be computedfrom hyperspectral data is the Normalized Difference Veg-etation Index (NDVI) (Tucker, 1979). The NDVI combinesthe reflectance of objects to visible and near-infrared lightwavelengths to estimate the vegetation content of a region.Healthy vegetation absorbs most of the visible light thatreaches it, while reflecting most of the infrared radiation.Unhealthy or dormant vegetation reflects more visible lightwith respect to near-infrared. For each imaged point, theNDVI is computed as

NDVI = NIR − VISNIR + VIS

,

where NIR stands for near-infrared intensity and VIS is thevisible light intensity. The range of values for the NDVI is[−1, 1], where 1 represents healthy, dense vegetation. Values



Author Proof


Figure 8. These images show some spectral bands that can be retrieved from the hyperspectral data. From left to right: R670,related to the chlorophyll absorption in plants; R725, in the edge of the red band; and R800, within the near-infrared.

near 0 may represent concrete, dirt, or otherwise vegetation-depleted regions, and values near −1 typically correspondto deep water or clear sky. Let us refer to individual narrow-band images as Rn, where n is the wavelength of the band.There are narrowband versions of the NDVI, such as

NDVIn = R774 − R677

R774 + R677.

A sample of the constructed hyperspectral datacubecan be seen in Figure 8. These are some narrowbands as-sociated with remote sensing of vegetation: R670 is relatedto the chlorophyll absorption of the plants, R725 is the edgeof the red portion of the spectrum and has been associatedwith chlorophyll content as well, and R800 is at the beginningof the near-infrared. The airplane flew a horizontal distanceof 200 m while capturing this particular set of images.

For each image sequence, we show three results. Thefirst image shows the mosaic assembled from the conven-tional camera data, with an overlay of the intensity imagederived from the hyperspectral data. This intensity image iscomposed by the sum of every hyperspectral channel. Thesecond image shows the mosaic from the conventional cam-era with the NDVIn data overlayed. We used a color mapwhere blue tones correspond to areas with no vegetationand healthy plants begin to appear as red tones, with darkred being the most dense and healthy. Finally, the third im-age is a pseudocolor representation of the scene, on top ofthe conventional camera mosaic. To build the pseudocolorimage, we took R700, R550, and R490 to represent the colorsred, green, and blue, respectively.

We selected a few regions of interest from the avail-able imagery in order to present a variety of objects, as wellas to emphasize some aircraft motions that would makehyperspectral imaging impossible without the approachdescribed here. The compiled scenes include grass, water,

trees with and without foliage, bale sheds, fences, dirt roads,etc. The flights were carried out over the month of Febru-ary 2014 near Dallas, Texas, at a time of year when mostvegetation was dormant. The first sequence, pictured inFigure 9, covers a region over a pond approximately 200 mlong. The water had a green hue, as visible in the last image,but as expected it appeared to have low NDVIn values. Like-wise, the roof from the shed covered by the hyperspectralimagery appears in a dark blue hue due to it being highlyreflective in the visible frequency bands but absorptive inthe NIR bands. This fact is also evident from depictions ofthe shed in Figure 8, which correspond to the same imagesequence. The amount of detail preserved is notable, con-sidering the sparseness of the original data and the absenceof pose information of the plane with respect to the scenery.

Figure 10 illustrates a more difficult imaging scenario.Here the airplane was banking during a turning motion. Theperspective effect is noticeable. A mixture of small pondsand some trees over mostly dormant grass comprises thescene. The buildings shown near the top give an indica-tion of the banking angle of the airplane, and yet the imagemosaic and the hyperspectral image match seamlessly. Thestraight-line flight distance for this sequence was 350 m.A last example is shown in Figure 11. This area includedmostly grass in different health conditions, from dry togreen. The airplane was pushed by a wind gust while com-pleting a turn, giving rise to the shape shown for the hyper-spectral data. Even under these motions, there are no severemismatches or gaps in the resulting images. The flight dis-tance for this image set was 150 m.

As can be seen from the results, our approach achievesa precise alignment between the hyperspectral data andthe conventional camera mosaic. This remains true evenin the presence of large disturbances due to external fac-tors such as wind gusts or vibrations from the UAV motor.



Author Proof


Figure 9. Hyperspectral imaging of a rural landscape. Top image: sum of every spectral channel from the HS image, overlaid ontop of the visible camera mosaic. Middle image: Normalized Difference Vegetation Index. Bottom image: pseudocolor from red,green, and blue channels.



Author Proof


Figure 10. Severe perspective effect due to the aircraft banking while turning. The top image corresponds to intensity, followedby the NDVIn and pseudocolor images.



Author Proof


Figure 11. An scene that shows the effect of wind on the airplane while it was banking. Intensity, NDVIn, and pseudocolor imagesare shown.



Author Proof


The hyperspectral images retain a level of detail on a parwith the conventional camera images, with little blurring ordistortion.

7. CONCLUSION

Based on an auxiliary conventional camera, we have pre-sented a method to acquire images with a pushbroom hy-perspectral sensor. Our approach maps each hyperspectralline to a line in the conventional camera image plane. Weshowed that this can only be achieved for arbitrary worldpoint depths when the hyperspectral line is an epipolar linetoo. Two variables that need to be determined given thisline-to-line mapping are the scale of each hyperspectral linesegment and its displacement with respect to the conven-tional camera line segment over which it is mapped. Nonlin-ear optimization through direct search methods yields thebest results when dealing with such a task. We have testedparallel implementations of these optimization algorithmsthat resulted in promising reductions in computation time,making hyperspectral image creation more practical.

The final assembly of a hyperspectral image involvesfinding the homographies between conventional cameraimage pairs. This is done to create an image mosaic andat the same time the hyperspectral image. The data cubesproduced by the application of our technique show remark-able alignment with the conventional camera mosaics, de-livering high-resolution spectroscopy from a low-cost UAV.We must stress the inexpensiveness of the equipment weused when compared to other solutions. Other than the hy-perspectral camera, the rest of the platform, including theairplane, the secondary camera, and the onboard computer,has a lower cost than some software packages.

Several challenges can to be addressed by our method,including the absence of pose information for the cameraswhile they captured the images, and the presence of externaldisturbances such as wind gusts. We showed that assum-ing that the scene is planar works in practice, even if theterrain is not flat. Future research will focus on extendingthe techniques described to cover wider areas with multi-ple flight lines. Furthermore, we plan to apply this researchto specific field studies in remote sensing. An importanttask to perform during these studies will be to combine ourtechnique with the placement of ground control points sothat the perspective transformation between the generatedhyperspectral images and the ground surface enables thecreation of a fully georeferenced data set.

ACKNOWLEDGMENTS

This work was supported by the Mexican National Councilfor Science and Technology (CONACyT) through scholar-ship grant number 215161. The authors would like to thankDavid Schaefer and William A. Harrison for their help in de-veloping the experimental platform and piloting the UAV

during data collection. The authors are also indebted to theanonymous reviewers for their valuable comments.

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