JOURNAL OF SEDIMENTARY RESEARCH, VOL. 70, NO. 6, NOVEMBER, 2000, P. 1337–1340Copyright q 2000, SEPM (Society for Sedimentary Geology) 1073-130X/00/070-1337/$03.00

RESEARCH METHODS PAPERS

A SIMPLE PHOTOGRAMMETRIC METHOD TO IMPROVE QUANTITATIVE IMAGE ANALYSIS INGEOSCIENCE RESEARCH

JESUS E. CARACUEL, JAVIER CARDENAL, JORGE DELGADO-GARCIA, AND SANTIAGO GARCIA-LOPEZDepartamento de Ingenierıa Cartografica, Geodesica y Fotogrametrıa, E.P.S. Universidad de Jaen, 23071-JAEN, Spain

e-mail: caracuel@ujaen.es, jcardena@ujaen.es, jdelgado@ujaen.es and sgarcia@ujaen.es

ABSTRACT: Sedimentary field surveying uses 2D outcrop images torapidly and easily obtain quantitative information. Although photo-grammetry is capable of a complete and accurate 3D analysis, thistechnique requires great technical expertise, as well as intricate andexpensive software and hardware. Rectified digital images, instead,represent a cost-effective and easier method to obtain accurate 2D im-ages for outcrop modeling and mapping. The present methodology de-scribes a simple technique to improve quantitative image analysis foroutcrop analysis, based on widespread conventional PC software andinexpensive hardware.

The proposed methodology treats outcrop digital images with a soft-ware developed by us in order to solve for colinearity equations, whichcalculate coordinates of terrain points. Thus, the geometric correctionon the terrain-point coordinates to obtain the rectified images can bedone with some commercial and widely distributed G.I.S., remote sens-ing, or photogrammetric programs. The final rectified image representsa metrically consistent perpendicular view of the outcrop that favorsthe quantitative image analysis. This technique can also be used toimprove the photo-mosaicking of different perspective-corrected im-ages of the same outcrop, avoiding the usual misfit of the image frames.

INTRODUCTION

Geoscience field surveying often uses photographs or photomontages(overlapping image frames) of outcrops to gather information about mor-phology, spatial distribution, and linear or surface measurements of fea-tures. The simplest and least time-consuming method is taking photographswith the focal axis roughly perpendicular to the object plane (controllingthe height and tilt of the camera), and joining together the resulting papercopies, or the digital-image files with any widely used commercial soft-ware, such as Adobe Photoshopy, or Corel Photo-Painty (Arnot et al.1997). Nevertheless, difficulties arise when photographs cannot be shotwith the focal axis perpendicular to the object plane (outcrop face), or whenthe distance between the object and the camera is not constant. Digitalphotogrammetry, instead, enables a precise 3D analysis with ample possi-bilities in approaching metrically consistent images for any spatial orien-tation. Unfortunately, these techniques require great technical expertise, andan intricate non-public software and expensive hardware (Dueholm andPedersen 1992; Dueholm and Olsen 1993). The aim of the present paperis to present a cost-effective, quicker, and easier method of acquiring ac-curate images for geoscience image analysis.

Outcrop faces are usually uneven, irregularly curved, and/or oblique tothe focal axis for a ground-based shot (Fig. 1). Thus, it is frequently notpossible to take ground-based frontal photographs of an area by varyingonly the camera height and tilt. Moreover, even for vertical and planaroutcrops, ground-based shots permit only frontal views in the lower partof the outcrop (around the elevation of the camera station, generally limitedto 1–2 m above terrain level), if no natural (e.g., opposite side of a canyon)or artificial (e.g., hydraulic platform, helicopter) camera positioning isavailable. Photographs oblique to the focal axis impede the collection ofaccurate quantitative data, because the oblique perspective distorts the im-

age along the frame. Moreover, such oblique photographs result in over-lapping areas with inconsistent scale, hampering photomontage assembly.Rectified images solve this problem by rescaling the whole image to asingle scale, thereby making the focal axis of the digital image perpendic-ular to the object plane, which is considered the mean enveloping planewith respect to the outcrop surface. Thus, rectified images become metri-cally consistent views, suitable for quantitative image analysis, both in asingle image and in multiple images (photomontage).

Application of quantitative image analysis in geoscience includes mod-eling and statistical treatment of feature size and morphology, as well asthe spatial distribution of components. The data collection requires finermetric precision, because the more accurate the input data, the more con-sistent the quantitative modeling will be.

MATERIALS AND METHODS

To test the method, we selected a slightly rugose and strongly dipping(508 dip and 70 m high) outcrop face, where just the lower part was ac-cessible for measuring. The outcropping beds were subvertical rhythmiclimestones and marls, Triassic in age. Five convergent ground-based pho-tographs (film Fuji Provia 100 ISO) were taken with a conventional non-metric 6 3 6 camera (Hasselblad CM-500) with 80 mm lens (Tab 1, Fig.1; Data acquisition). Shooting distance was arbitrarily selected (around 15–20 m from the base of the talus), seeking camera stations that enabledcoverage of the entire area of interest. Cameras were stationed with height5 1.5 m (tripod height), and tilt , 108. Original images were scannedwith an Agfa Duoscan T1200 scanner, equipped with a transparency tray,at 600 dpi optical resolution and stored in compressed JPEG format. Thisresolution has proved appropriate for the case studied, determining a terrainpixel size ranging from 8 mm in the talus base to 23 mm in the upper talus(15 m and 50 m away from the camera positioning, respectively). Thewhole images were scanned without cropping. The images were treated bythe image-processing software ENVIy (the Environment for VisualizingImages, from Research System Inc.). Processing hardware was a conven-tional PC (Pentiumq II MMXy) at 350 Hz and 128 Mb RAM.

The first step in any photogrammetric work is the inner orientation ofthe images (Tab 1, Fig. 1; data reduction). This implies measurement ofthe fiducial marks (calibrated marks in the frame of the photogrammetriccameras), and analytical coordinate transformation between measured im-age (pixel coordinates; u, v system in Figure 1) and fiducial coordinates (x,y system referred to the center of the format, or principal point, in Figure1, see Ghosh 1987 for an extended treatment), which also corrects for filmdeformation. Nevertheless, because a conventional camera was used, thelack of calibrated fiducial marks forced us to measure the four corners ofthe frame, referring the measured points to the coordinate system definedby these corners. Thus, no film deformation and scanner distortion werecorrected, and error up to 0.1–0.3 mm (even higher) in the image coordinateappeared. To reduce this error, we accurately measured the camera framesize in many exposed films and averaged the results.

Other errors related to conventional cameras, in contrast to photogram-metric cameras, include, mainly: high lens distortion, which makes straightlines to appear curved; lens focal length inaccurately known; lack of film

1338 J.E. CARACUEL ET AL.

FIG. 1.—Flow chart for working methodology. DATA ACQUISITION: A) Shooting at least three convergent images (60 3 60 mm, 35 mm format, or digital cameras)of the outcrop face from arbitrary camera positioning, seeking to cover the entire area of interest in every photograph, and with one of the images (final rectified image)frontal with respect to the talus toe. B) Film development and images scanning (Desktop or photogrammetric scanner at a minimum of 400 dpi optical resolution).Alternatively, digital camera with comparable resolution can be used to avoid scanning. C) Image files stores in compressed JPEG, TIFF or RAW file format. DATAREDUCTION: D) Inner orientation changes the coordinate system for some selected points covering the entire area of interest in the three analyzed images from imagesystem (pixel coordinate; u 5 0, v 5 0) to photocoordinate system (center of the frame; x 5 0, y 5 0). The considered points were few tens of natural points easily andprecisely recognisable in all images. This coordinate change was accomplished using an affine transformation implemented in a spreadsheet. E) The photogrammetric netadjustment transforms the 2D photocoordinates into the real-world 3D coordinate system by solving the colinearity equations for the points measured in all the images.Real scale was adjusted by using field tape-measured distances in an accessible part of the outcrop. This was done using a routine programmed under IDLTM 5.1. Alternativelynon-public photogrammetric programs can do this. F) The image rectification relates the photocoordinates of the measured points in the frontal image with respect to thetalus toe, with their planimetric position in the 3D real world. This was done under ENVITM program applying a second-order polynomial transformation between the twosets of coordinates, resulting in a warping image of the original frontal photograph with respect to the talus toe. This transformation is also implemented in most of thecommercial G.I.S. and remote sensing programs. See text for extended comments.

flatness; and offset of principal point. Some of these errors can be partiallycorrected during the photogrammetric net adjustment after inner orientation(Tab 1, Fig. 1; data reduction). In the net adjustment, image coordinates(x, y) were transformed in the real-world 3D coordinate system (X, Y, Z ).In the case studied, this was achieved by the colinearity equations, whichalso correct for focal length errors and lens distortion (c, K1 coefficients,in Eq. 1). These equations state that the object 3D point, the camera station,and the image 2D point lie in the same line:

2(x 2 x ) · (1 2 K r )i 0 1

m (X 2 X ) 1 m (Y 2 Y ) 1 m (Z 2 Z )11 i 0 12 i 0 13 i 05 2c ·m (X 2 X ) 1 m (Y 2 Y ) 1 m (Z 2 Z )31 i 0 32 i 0 33 i 0

2(y 2 y ) · (1 2 K r )i 0 1

m (X 2 X ) 1 m (Y 2 Y ) 1 m (Z 2 Z )21 i 0 22 i 0 23 i 05 2c · (1)m (X 2 X ) 1 m (Y 2 Y ) 1 m (Z 2 Z )31 i 0 32 i 0 33 i 0

where (xi, yi) are image coordinates of a given point i; (x0, y0) are theprincipal point coordinates; c is the lens focal length; r is the radial distance

of image point i to principal point; K1 is the radial lens distortion coefficient;(Xi, Yi, Zi) are object coordinates of point i (in the real world); (X0, Y0, Z0)are camera station coordinates (in the real world) and m11, m12, . . . , m32,m33 are the elements of the rotation matrix (rotations around the three basiccoordinate axes); see Ghosh (1987) for an extended treatment.

Every image point measured in each image contributes two colinearityequations. An overall adjustment by least squares of all the equations solvesfor all the unknowns (spatial coordinates of points, camera stations and ro-tations elements of all cameras, focal length, principal point coordinate, andlens distortion). The adjustment is made in an arbitrary reference system (e.g.,one camera station could be taken as the origin: X0, Y0, Z0 5 0, 0, 0) andsome distances measured in the object space can help to recover the spatialcoordinates of all measured points (Atkinson 1996). This approach eliminatesthe need for a measuring survey (the classical way to give control points inphotographs), often time-consuming and costly, because it requires an ex-perienced survey crew and expensive equipment. This adjustment has beenprogrammed under IDL 5.1 (Interactive Data Language from Research Sys-tem Inc.) in order to solve the colinearity equations simultaneously for allpoints in all photographs. This program (for license-protected IDL 5.1 en-vironment) is available by request from the authors.

1339IMPROVING QUANTITATIVE IMAGE ANALYSIS FOR OUTCROP SURVEYING

TABLE 1.—Step-by-Step procedure for the case study.

Steps Procedure

Field work12

3

Select camera positioning to cover the entire area of interest.Shooting 5 convergent photographs with a conventional non-metric Hasselblad 60

3 60 mm camera, equipped with an 80 mm lens.Tape measuring reference distances in accessible outcrop areas.

Laboratory45

6

Slide-film development.Original slide-film scanning with a desktop Agfa Duoscan T1200 scanner at 600

dpi optical resolution, without cropping.Image files stores (JPEG file formats).

Workshop7a

7b

89

10

11

Inner orientation. Measurement of frame corners coordinates under ENVITM pro-gram.

Inner orientation affine transformation implemented in a spreadsheet (QuattroProIM), between measured and real corner coordinates to refer image points toprincipal point, allowing for film deformation correction.

Measurement of image points (15 points in the 5 images) under ENVIIM program.Transformation of coordinates of image points (pixel system) to photocoordinate

system trough the affine transformation parameters (computed in step 7b)Photogrammetric net adjustment through a routine programmed under IDLIM 5.1

for solving the colinearity equation (lens distortion correction is included). Spa-tial XYZ coordinates of the 15 points are computed with the real scale adjustedby means of field tape-measured distances.

Image rectification of the frontal image, with respect to the talus toe, applying asecond-order polynomial transformation under ENVIIM program. The polynomi-al transformation parameters are computed by comparing the photocoordinatesof the 15 control points and their planimetric position in real world coordinatesystem (calculated in step 10).

After the spatial coordinates of measured points in the images were cal-culated, they were transformed in order to fit the mean plane that containsthe talus. Finally, we rectified the photograph (using ENVIy), relating theimage coordinates of points in a particular photograph and their planimetricposition in the 3D real world (similar to a geometrical correction of asatellite image). This was applied through a second-order polynomial trans-formation between the two sets of coordinates:

2 2x 5 a 1 a X 1 a Y 1 a X Y 1 a X 1 a Yi 0 1 i 2 i 3 i i 4 i 5 i

2 2y 5 b 1 b X 1 b Y 1 b X Y 1 b X 1 b Y (2)i 0 1 i 2 i 3 i i 4 i 5 i

where xi, yi are image coordinates; Xi, Yi are planimetric coordinates inthe real world, and a1, a2, . . . , b5 are fitting coefficients.

This second-order polynomial transformation proved appropriate for dip-ping planar taluses, because it enabled the rotation, translation, scale changes,and nonlinear fitting coefficients for systematic error corrections, from theactual image to the rectified plane. Other alternative analytical expressionsfor rectification can be found in Novak (1992). The geometric correction canbe also made with some commercial and widely distributed G.I.S., remotesensing, and photogrammetric programs, such as Idrisiy (Clark University),ER Mappery (Earth Resource Mapping Pty Ltd.), DVPy (Digital VideoPlotter, from DVP Geomatics Systems Inc.) and others. The final rectifiedimage represents a perpendicular view of the talus.

DISCUSSION AND CONCLUSION

Figure 2 shows the final rectified image (Fig. 2D) and three selectedimages (Figs. 2A, B, C) used in the net adjustment by Eq. 1. Figure 2B isthe frontal image with respect to the talus toe from which the rectifiedimage was obtained by Eq. 2. Metric accuracy has been tested by tapemeasuring some distances in the field at accessible points of the lower partsof the outcrop. Distances measured on the outcrop and the calculated dataon the rectified image show deviations of less than 1% in metric accuracy.

The metric accuracy of the rectified image (Fig. 2D) ensures an appropriatequantitative 2D image analysis. Nonrectified images are not perspective cor-rected, and perspective distortion may be excessive for accurate metric pur-

poses. In roughly frontal views with respect to the talus toe (e.g., Fig. 2B),scale remains constant through approximately horizontal lines but decreasesupward on the talus (Fig. 2). Thus, if no reference scale (scaled rod, strati-graphic marker) can be placed in inaccessible areas, no measurements canbe made, because the scale remains unknown. Variation of scale through theframe can produce large errors if this scale variation remains unknown andcannot be calculated for each point (Figure 2B shows this scale variationclearly). Moreover, if no frontal views with respect to the talus toe can beobtained (oblique and tilted photographs, e.g., Figs. 2A and 2C), scale willvary throughout the photograph frame, making any measurement difficult totake. In addition, the analytical treatment permits correction of systematicerrors. For example, in the case of the camera used, with lens distortionerrors up to 0.5 mm (at image scale), the propagated error to the terrainranges from 80 to 300 mm at photo scales of 1/150 and 1/600, respectively.These scales are the approximate photo scales at the proximal and distal partsof the outcrop with respect to the camera positioning.

According to the photo scale (obtained from Eq. 1), rectified images favordimensional photointerpretation and metric outcrop mapping. Main applicationsare related to the quantitative analysis of feature size (e.g., bed thickness andlength), morphology (bed surfaces, component shapes, clasts, fossils, sedimen-tary structures), spatial distribution of components (within and between beds),and spatial orientation (angles between lines in the outcrop surface, apparentdips). Moreover, rectification of photographs improves the photo-mosaickingof different perspective-corrected images of the same outcrop, avoiding theusual bad fit in the overlapping areas of the image frames.

Similar to the case in which the optical axis of the rectified image wasmade perpendicular to the outcrop face, fitting coefficients in Eq. 2 can beadjusted to any other dip and tilt. This can be useful in studying obliqueviews of outcrop surfaces, which are perpendicular views with respect tosignificant features and sedimentary structures (e.g., continuous beds, chan-nels and pinch-out morphologies, slides, slumps). Other applications, as instructural geology, of tilt/dip forced images can be implemented for control-ling the deformation: measurement of 2D finite strain, study of fold profiles,or analysis of fracture array geometry.

Although the case studied is a relatively simply talus morphology (planartalus), the above methodology can be applied to other real situations. Forcases of large taluses with or without variable dip and/or orientation, thecurrent methodology can be applied, but different rectification processesmust be used in each planar part of the talus. Then, every rectified pho-tograph can easily be rescaled and merged. Because the approach is basi-cally a 2D analysis, the more the talus fits to a planar surface, the easierand more accurate the rectification. Thus, excessively complex taluses (highrugosity, too many break-lines, strongly curved surfaces) can preclude theapplication of this methodology. In these cases, more sophisticated pho-togrammetric techniques, beyond the scope of this paper, have to be applied(e.g., orthorectification combined with a detailed digital elevation model;see Novak 1992; or conventional photogrammetric techniques). Neverthe-less, the 2D mapping of relatively planar outcrop surfaces can be extendedin many selected orientations, favoring the reconstruction of 3D geologicalmodels, although it can be more easily achieved by specific photogram-metric 3D modeling software; see web page of the V Commission of theI.S.P.R.S. (International Society for Photogrammetric and Remote Sensing;V Commission: Technical Commission for Close Range Photogrammetry).

ACKNOWLEDGMENTS

This research was supported financially by the ‘‘Evolucion de los Margenes Me-sozoicos de Iberia’’ (RNM-178) and ‘‘Ingenierıa Cartografica’’ (TEP-164) groups(Junta de Andalucıa) and Projects HID98–0983, PB97–0803 (DGICYT). Reviewsby S. Bachtel (Exxon Production Research, Houston, Texas, USA) and T. Olsen(Statoil, Norway) are much appreciated. The final version was linguistically cor-rected by D. Nesbitt.

1340 J.E. CARACUEL ET AL.

FIG 2.—Selected ground-based photographs(A, B, C) used in the photogrammetric netadjustment of the area of interest (white polygonin B). Image points measured to form the Eq. 1system were natural points (around 15, coveringthe area regularly). Digital rectified image of thearea of interest (D) is a perspective correctedand scaled view.

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Received 30 September 1999; accepted 17 May 2000.