Data Set Overview
=================

This data set represents the primary results of three dimensional
(3-D) modeling of the Mars Pathfinder landing site using data from the
Imager for Mars Pathfinder camera.  The camera system is described by
Smith et al. [SMITHETAL1997A, SMITHETAL1997B].  It consisted of a
stereo imager pair located on a pan and tilt platform. Each imager of
the pair was equipped with a filter wheel so that the camera set could
image the landscape in 15 narrow-band filters.

This data set consists of a set of tables.  Each table contains 3-D
object position information in the form of a Cartesian (x,y,z)
coordinate in units of meters corresponding to each pixel in an IMP
EDR stereo pair acquired in the 670 nm filter. The coordinates are
deduced using an automated machine vision algorithm that correlates
features between the left and right images of stereo pairs to
determine their disparity (difference in image position between the
left and right eye) then computes their 3-D object position taking
into account the camera pointing and stereo optics.  The computer
algorithm is described by Stoker et al. [STOKERETAL1999] and
summarized below.

Stereo model products (and corresponding tables) have been produced
for two IMP Pathfinder data sets acquired in stereo in the 670 nm
filter. The IMP data sets are described by Gaddis et
al. [GADDISETAL1999].  The stereo data sets that were analyzed are
called the Monster Pan and the Super Pan.  The Monster Pan was a
complete stereo panorama of the Pathfinder landing site acquired early
in the mission (sols 3-6).  The monster pan images in the 670 nm
filter were compressed using lossy JPEG compression (6:1 compression
factor) and the image to image overlap in the panoramic product was
relatively low.  The Super Pan was designed to produce a full panorama
of the landing site with low compression ratio in all 15 narrow-band
filters and the 670 nm stereo filter set was losslessly compressed
using Rice compression. It was designed with increased frame-to-frame
overlap relative to the Monster Pan to assist with automated matching
between images and insure gap-free stereo coverage.  The Super Pan
represented a large data volume and was acquired over an 8 week period
from sols 13 to 80.  It was 83% complete when the mission ended.
While incomplete, the 3-D reconstructions from the Super Pan images
are somewhat better than for the Monster Pan due to the increased
image overlap and lower image compression.


Parameters
==========

Each table entry consists of a Cartesian coordinate corresponding to
the object position computed for each pixel of the left member of a
stereo pair for which a model solution was obtained.  The origin of
the coordinate system for the values provided in these tables is at
the intersection of the camera elevation and azimuth axes.  The X axis
is aligned with north so that +X values are north of the origin, the Y
axis is aligned with west so that +Y values are west of the origin,
and the +Z direction is up.  Other parameters which enter into the
stereo reconstruction are described below along with a description of
the Stereo Pipeline algorithm.


Processing
==========

The computer program which produces the 3-D reconstruction is called
the Ames Stereo Pipeline [STOKERETAL1999].  The input to the
stereo matching algorithm consists of raw EDR images from an IMP
stereo pair.  Results are better if images are used that have not been
flat field corrected or photometrically calibrated because these
processes resample the pixel information. The first stage in the
Stereo Pipeline algorithm is called the 'preprocessing' stage and
involves preparing the input stereo pair to improve the correlation in
the later stages.  First, a linear stretch is applied to normalize the
image intensity between the left and right members of the stereo pair.
This is needed because the correlation algorithm works by matching the
intensity values between the image pairs. Then, a uni-directional
Sobel edge enhancement technique [BAXES1994] is applied.  Next
calculations are performed to correct for translational, rotational,
and pixel-scale differences between the left and right eyes.

The next stage of processing in the Stereo Pipeline is to correlate
the features in the images between the left and right cameras.  The
result of this stage is a disparity calculation for each pixel in the
image pair.  A texture-based sum-of-absolute-difference (SOAD)
correlation algorithm is used and the consistency of each match is
validated by doing both a correlation and cross-correlation. This
almost eliminates matches between wrong local figures. A small
subframe of the image surrounding a considered pixel, called the
kernel, is selected from one member of the stereo pair.  The kernel is
slid over the other image of the pair by a step of one pixel at a
time, a subtraction is performed, and the elements of the resulting
matrix are summed.  This procedure is used to find the position of the
most similar portion of the test image with the kernel. Three
correlation passes, using different sized kernels, are used to improve
both computational speed and accuracy. The same correlation algorithm,
with different parameters, is used for all three passes.  The first
pass of the correlator is used to bound the disparity range of the
image.  It uses a small kernel and searches across the complete range
of possible disparity values.  For this first pass, a relatively low
rate of correlations are found, but these are used to limit the search
space of the disparity for the next pass.  The second correlation pass
uses a larger kernel which results in a high percentage of pixels
being matched.  In the final (third) pass, the disparity search is
constrained to the neighborhood of the disparity calculated in the
previous pass. Ideally, a small kernel size is preferred for this pass
because the disparity value assigned to the pixel is the average over
the kernel.  Kernel size for the second and third pass are user
selectable.  For the models published here, kernel size was
interactively varied to minimize the amount of pixel-to-pixel variance
in computed 3-D position. High variance results from errors in the
estimate of disparity. Small errors in the estimate of disparity can
lead to large errors in the estimate of position along the camera's
line of site. The Kernel size for the second and third correlation
pass is a user defined quantity of n columns by m rows.  Values used
for this data set were 14x14 pixels (second pass) and 27x27 pixels
(third pass).  The correlation stage is followed by a filtering stage
that removes 'outliers'-- disparity values much different than those
in the nearby area.  Next, gaps in the disparity map are filled. Gaps
are places which had no match, inconsistent cross-correlations, or
outlier disparities.  Some gaps are the result of real-world
discontinuities in surface shape, such as the occluding boundaries of
rocks in the terrain.  In order to retain these boundaries in the map,
gaps occurring at large discontinuities are filled with the minimum
disparity value (corresponding to the point furthest from the camera)
in the gap neighborhood. Gaps in regions with small disparity variance
are more likely due to a smooth, texture free surface. These gaps can
be filled by interpolation or set to zero.  In the models published
here they are set to zero to avoid confusing them with values computed
by the algorithm.  The next processing stage derives 3-D position
points from disparity values. Each pixel is projected along a vector
defined by the (line, sample) coordinate of the pixel and the nodal
point of the camera to a distance consistent with its disparity. This
intersection point is the object coordinate.  Then, using the camera
pan and tilt angle, the object coordinates are rotated to the lander
coordinate system.  This computation is repeated for each pixel of the
stereo pair to get a set of object points.  These object points, in
tabular form, are the data set provided.


Ancillary Data
==============

The data are referenced to raw IMP EDR images.  These will be required
for interpretation of the 3-D model data.

Data Coverage and Quality
=========================

As discussed above, the 3-D position information is deduced matching
brightness patterns in the left and right eyes of the stereo pair.
When no match is found, or inconsistent matches found in the
correlation and cross correlation, no disparity is calculated and a
value of zero is assigned to the Cartesian coordinate (X=Y=Z=0) in
the table. Thus, zero values in the table indicate that the stereo
matching algorithm did not yield a good solution at that location.

Confidence Level and Limitations
================================

For the Mars Pathfinder IMP camera data sets, the error in the 3-D
position of an object point in the model comes from the following
sources:

1) The uncertainty in the azimuth and elevation of the camera leads to
uncertainty in the 3-D model position.  According to the IMP
calibration report [CROWEETAL1996] the pointing error acts in a plane
perpendicular to the camera optical axis.  This error is a linear
function of the camera-point distance and is within +/- 2.7% in
azimuth and +/- 1.2% in elevation of the absolute position of the
point (assuming a pan error of +/- 1.5 degrees and a tilt error of +/-
0.65 degrees.  These are worst case values due to backlash in the
camera motors.

Of the uncertainty sources, this is the largest, but the camera
pointing uncertainty affects all points from one stereo pair equally
as a solid body.  This source of error can be minimized by determining
actual camera pointing after the fact by using tiepoints between
stereo pairs. The United States Geological Survey Astrogeology Branch,
under the direction of R. Kirk, undertook a project to provide
improved camera pointing information using a control network for the
site and bundle adjustment.  This procedure is described by Kirk et
al. [KIRKETAL2001]. The values they determined were substituted for
surface based instrument azimuth and elevation for the instrument
telemetry values provided in the original EDR headers.  Inspection of
the results showed that using these values produced a noticeable
improvement in how well models from adjacent images fit together. They
also computed values for left toe-in (-13.732 radians), right toe-in
(24.63 radians) and boresight angles (1.116 radians) that are
different from those published by the IMP camera team [CROWEETAL1996].
We also used these values in our computations.

2) Uncertainty in the computed camera-point distance results from the
disparity computation method.  For any pixel, the computed disparity
represents an average over the Kernel for the final correlation
pass. Smaller Kernel sizes lead to a high percentage of false
correlations. Thus the models appear more noisy. Even though a
disparity point is assigned to each pixel, the real resolution of the
model is a function of the Kernel size in the final pass.

3) Image resolution limits stereo matching precision.  Subpixel
disparity is not computed by the algorithm.

4) The stereo images of the Monster Pan were compressed using lossy
JPEG compression.  High correlation rates are achieved even with the
compressed data of the Monster Pan but the results are clearly noisier
(defined as pixel to pixel variance in 3-D position computed by the
algorithm) than for the losslessly compressed Super Pan.  As discussed
above, this variance is due to errors in the estimated disparity.
Compression artifacts result in a higher percentage of false matches.