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# Algorithm for Detecting a Bright Spot in an Image

- Created on Saturday, 01 August 2009

### Corrections for background intensity and dark current are included.

An algorithm processes the pixel intensities of a digitized image to detect and locate a circular bright spot, the approximate size of which is known in advance. The algorithm is used to find images of the Sun in cameras aboard the Mars Exploration Rovers. (The images are used in estimating orientations of the Rovers relative to the direction to the Sun.) The algorithm can also be adapted to tracking of circular shaped bright targets in other diverse applications.

The first step in the algorithm is to calculate a dark-current ramp — a correction necessitated by the scheme that governs the readout of pixel charges in the charge-coupled-device camera in the original Mars Exploration Rover application. In this scheme, the fraction of each frame period during which dark current is accumulated in a given pixel (and, hence, the dark-current contribution to the pixel image-intensity reading) is proportional to the pixel row number. For the purpose of the algorithm, the dark-current contribution to the intensity reading from each pixel is assumed to equal the average of intensity readings from all pixels in the same row, and the factor of proportionality is estimated on the basis of this assumption. Then the product of the row number and the factor of proportionality is subtracted from the reading from each pixel to obtain a dark-current-corrected intensity reading.

The next step in the algorithm is to
determine the best location, within the
overall image, for a window of *N* × *N* pixels
(where *N* is an odd number) large
enough to contain the bright spot of
interest plus a small margin. (In the
original application, the overall image
contains 1,024 by 1,024 pixels, the image
of the Sun is about 22 pixels in diameter,
and *N* is chosen to be 29.)

The window is placed at a given position
within the overall image. A weighted
average of the intensities of the 4*N* –
4 outer pixels of the window is taken as
an estimate of background intensity
and subtracted from a weighted average
of the intensities of the remaining
inner (*N* – 2) × (*N* – 2) pixels of the
window to obtain a background-corrected
weighted sum of pixel intensities
for the window. The weighted averages
are simply pixel-intensity averages multiplied
by common denominators so as
to obviate floating-point arithmetic
operations and thereby accelerate computations.
The window is then moved
to an adjacent column position, and
weighted averages for the new position
are calculated from the previous
weighted averages by adding the appropriate
values for the new outer and
inner pixels and subtracting the corresponding
values for the pixels that have
been left behind or changed in status
between the inner and the outer. This
process is repeated until the computations
have been performed for all possible
window positions. The position that
yields the highest background-corrected
weighted sum of pixel intensities is
assumed to contain the bright spot of
interest (the image of the Sun in the
original application), and the window is
then used to locate the bright spot
more precisely as described next.

Within the inner (*N* – 2) × (*N* – 2) portion
of the window, the position of the
bright spot is determined by means of a
simple centroid calculation, using the
background-corrected pixel intensities.
Because the window position selected as
described above may not necessarily be
the optimum one, the centroid calculation
is performed twice in an iterative
process: For the second centroid calculation,
the window is re-centered on the
centroid determined by the first centroid
calculation.

*This work was done by Carl Christian
Liebe of Caltech for NASA’s Jet Propulsion
Laboratory.*

*The software used in this innovation is
available for commercial licensing. Please
contact Karina Edmonds of the California
Institute of Technology at (626) 395-2322.
Refer to NPO-41801.*

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