Geoscience Reference
In-Depth Information
Toolbox (MathWorks 2014) contains functions that use the Hough transform
to detect lines or circular objects.
h e classic Hough transform is used to detect lines in images. At er
applying an edge detector of any kind we end up with a binary image that
has black pixels on the edges and white pixels in between. We next describe
the lines through a given black pixel by the Euklidean distance ˁ between the
line and the origin, and by the angle ʸ of the vector from the origin to the
closest point on the line (Fig. 8.11 a):
h e family of all lines passing through this particular pixel (
x
i
,
y
i
) of an edge
feature are displayed as a sinusoidal curve in the (ʸ,ˁ) parameter space
(Fig. 8.11 b). h e intersection point (ʸ',ˁ') of two such sinusoidal curves
corresponds to the line that passes through two dif erent pixels, (
x
1
,
y
1
) and
(
x
2
,
y
2
), of an edge feature. Next, we search for
n
points (
x
i
,
y
i
) in the Hough
transform where many lines intersect, since these are points dei ning the line
tracing an edge feature. Detecting circles instead of lines works in a similar
manner, using the coordinates of the center of the circle and its radius instead
of ˁ and ʸ.
For our a i rst example we use these functions to detect the thin layers of
pure white diatomite within varved sediments exposed in the Quebrada de
Cafayate of Argentina, which have already been used as examples in previous
sections (Trauth et al. 1999, 2003) (Fig. 8.12). h e quality of the image is not
perfect, which is why we can not expect optimal results. We i rst read the
cropped version of the laminated sediment from Section 8.8 and store it in
the variable
I1
. h e size of the image is 1,047-by-1,691 pixels, consisting of
three colors (red, green and blue).
clear
I1 = imread('varves_cropped.tif');
imshow(I1,'InitialMagnification',30)
We reject the color information of the image and convert
I1
to grayscale
using the function
rgb2gray
.
I2 = rgb2gray(I1);
imshow(I2,'InitialMagnification',30)
We then use
adapthisteq
to perform a contrast-limited adaptive histogram
equalization (CLAHE), in order to enhance the contrast in the image
(Zuiderveld 1994).
