Using the Autocorrelation Function in NIH-Image to Determine Shape-Preferred Orientations

T123-187-14

Cameron DavidsonDepartment of Geology, Carleton College

One North College Street, Northfield, Minnesota 55057cdavidso@carleton.eduIntroduction

The autocorrelation function (ACF) is a powerful, and easy to use tool that allows the user to quantify shape-preferred orientations at various scales in an image (Panozzo Heilbronner, 1992). The activity described in this poster was developed for an undergraduate level structural geology course, but can also be used as a tutorial for anyone interested in how to use the ACF to quantify shape preferred orientations.

Exploration. The first part of the activity focuses on exploration and discovery of how ACF images correspond to real images. The students are given six synthetic images with particles of known aspect ratio and shape preferred orientation (Fig. 1). They follow a detailed recipe for generating ACF’s, construct a figure comparing images and ACF’s, and are asked to write a short narrative describing the qualitative relationship between an image and ACF shape. The students then learn how to measure the ellipticity of ACF contours (Fig. 2) and plot these data to discover the relationship between shape preferred orientation and ACF ellipticity (Fig. 3).

Application. After completing the discovery part of the activity, the students apply this knowledge to images of thin sections from the Quottoon pluton near Prince Rupert, British Columbia (Fig. 4). In addition, they learn how to measure ACF grain size and plot these data and ACF ellipticity as a function of distance from the Coast shear zone, a major oblique-slip shear zone that defines the western border of the Quottoon pluton (Fig. 5). Finally, the students are asked to discuss the relationship between shape preferred orientation, ACF grain size, and the Coast shear zone.

Skills. Some of the higher-order skills this activity attempts to address include collecting and manipulating data and making decisions on what those data might mean. The activity also helps develop a student’s ability to make figures, write figure captions, and present data and interpretations in narrative form.

NIH-ImageNIH-Image is a freeware image analysis program developed and maintained by the U.S. National Institute of Health. This exercise was developed on a Macintosh running OS X with NIH-Image running on OS 9.2 emulation mode. ImageJ, a close cousin of Image, runs on Mac OS X and Windows, but does not yet have the Fast Fourier Transform macros needed for this exercise. The most recent version of Image and ImageJ can be downloaded at http://rsb.info.nih.gov/nih-image.

Goals1. Learn how to use NIH-Image to quantify shape-preferred

orientations in images.

2. Discover how autocorrelation images vary with aspect ratio of particles and the amount of preferred orientation (fabric intensity).

3. Apply this understanding to rocks (and other images).

Exploration

ACF Contours: Quantifying Shape-Preferred Orientations

Application: Quottoon Pluton, British Columbia

Application: Patterned Ground on Mars

ReferencesStudent Handout/Cookbook

Please Help Yourself

Figure 1. Synthetic images and associated ACF images.

Figure 2. 2-D and 3-D representations of the ACF of SynImage1 from Fig. 1. The 2-D ACF is similar to a topographic map, with contours marked by different grey levels.

Figure 3. ACF ellipticities from images in Fig. 1. A) Shape preferred orientations (SPO) for particles with 3:1 aspect ratio. B) Perfect shape fabrics for particles with different aspect ratios.

A)

D)

B)

E)

C)

F)

SynImage1: No SPO

Rectangles = 3:1

SynImage2: SPO after 40% shortening

Rectangles = 3:1

SynImage3: SPO after 60% shortening

Rectangles = 3:1

SynImage4: Perfect SPO

Rectangles = 3:1

SynImage5: Perfect SPO

Rectangles = 2:1

SynImage6: Perfect SPO

Rectangles = 5:1

128th Contour(1/2 peak height)

2-D ACF 3-D ACF

For greyscale images, there are 256 contours, where the ellipticity of the contours correspond to correlations (shape-preferred orientations) at different scales. Low numbered contours (light greys in Fig. 2) corresond to correlations at the scale of the image, while high numbered contours (dark greys) correspond to correlations at a much finer scale. For many geological applications, choosing the 128th contour works well.

The Quottoon pluton is a Late Cretaceous foliated biotite hornblende tonalite that intruded during dextral oblique east side up motion along the Coast shear zone near Prince Rupert, British Columbia (Ingram and Hutton, 1994; Klepeis et al., 1998, Andronicos et al., 1999). The foliation, defined by the shape-preferred orientation of biotite and hornblende, increases in intensity toward the Coast shear zone (Fig. 4). In order to quantify this change in foliation intensity, we will use the autocorrelation function to calculate the ellipticity of the ACF as a function of distance from the Coast shear zone. Important: we will only use the 96th contour for this particular application. (Why the 96th contour? This is a rhetorical question.) We will also use the 96th contour to calculate the ACF grain size. The ACF grain size is defined as:

The relationship between the ACF grain size and the grain sizes observed in thin section is not straightforward. However, it is clear that as the average grain size in thin section increases, the ACF grain size increases. Therefore, useful information might be gleaned from comparing the ACF grain sizes between samples (e.g. Davidson et al., 1996).

The ellipticity of contours is easily calculated by measuring the major and minor axes of the best fit ellipse in NIH-Image. In Figure 3, the ellipticity (major/minor) of various contours are plotted for the sythetic images shown in Figure 1.

32

Particle Aspect Ratio

Shape Fabric

64 96 128 160 192

1.0

0.0

0.0

1.0

2.0

3.0

4.0

2.0

3.0

4.0

5.0

2:1

3:1

5:1

60% Shortening

40% Shortening

Perfect SPO

Elli

ptic

ity (m

ajor

/min

or)

Elli

ptic

ity (m

ajor

/min

or)

ACF Contour

No SPO

ACF grain size (mm) = major axis*minor axis

Figure 4. Simplified geologic map of the Quottoon pluton near Prince Rupert, British Columbia. Filled circles show the locations of the samples used in this exercise. Highway 16 (dash-dot line) shown for reference. Note that deformation associated with the Coast shear zone affects a much wider area than shown by the dashed line. Photomicrographs (ppl) of the samples organized from west (upper left) to east (upper right). Each image is 2.5 cm across. ACF of each image also shown at the same scale.

3.0

3.5

2.5

2.0

1.5

1.0

0.5

0.00.0 1.0 2.0 3.0

Distance (kilometers)

ACF ellipticity ACF grain size

AC

F el

liptic

ity o

r AC

F gr

ain

size

(mm

)

4.0 5.0 6.0

Figure 5. ACF ellipticity (circles) and grain size (triangles) vs. distance from the western contact of the Quottoon pluton.

93-22

93-25

93-26

93-2193-20

93-23

93-19

96-7

Coast shear zone

16

N

Quottoonpluton Kasiks sill

Ecstallpluton

orthogneissand paragneiss

orthogneiss, paragneissand amphibolite

93-22

93-2593-2693-21

93-2093-23

96-7

0 5km

93-19

Andronicos, C., Hollister, L.S., Davidson, C., and Chardon, D., 1999, Kinematics and tectonic significance of transpressive structures within the Coast Plutonic Complex, British Columbia: Journal of Structural Geology, v. 21, p. 229-243.

Davidson, C., Rosenberg, C., and Schmid, S.M., 1996, Synmagmatic folding of the base of the Bergell pluton, Central Alps: Tectonophysics, v. 265, p. 213-238.

Davidson, C., 2004, Using the autocorrelation function in NIH-Image to determine shape-preferred orientations. On the Cutting Edge. Retreived Sept 4, 2004 from <serc.carleton.edu/NAGTWorkshops/structure04/activities /3929.html >

Ingram, G.M., and Hutton, D.H.W., 1994, The Great Tonalite Sill: emplacement into a contractional shear zone and implications for Late Cretaceous to early Eocene tectonics in Southeastern Alaska and British Columbia: Geological Society of America Bulletin, v.106, p.715-728.

Klepeis, K.A., Crawford, M.L., and Gehrels, G.E., 1998, Structural history of the crustal-scale Coast shear zone north of Portland Canal, Southeast Alaska and British Columbia: Journal of Structural Geology, v. 20, p.883-904.

Panozzo Heilbronner, R. 1992. The auto correlation function: an image processing tool for fabric analysis: Tectonophyscis, v. 212, p. 351-370.

Kanner, L., 2004, Geomorphic evidence for Martian climate change: B.A. Thesis, Carleton College, 62 p.

Figure 6. (A) Mars Orbital Camera image of patterned ground from Utopia Planitia, Mars. (B) ACF of image shown in A. (C) Enlarged center region of ACF shown in B. Note the main NNE-SSW fracture pattern is easily picked up by the ACF. See Kanner (2004) for more information on this application.

1 km 1 km

SPO = Shape Preferred Orientation