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An Evaluation and Comparison of Surface Reconstruction
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As part of our benchmark, we have included the source code for surface modeling, sampling, reconstruction,
evaluation, and plotting results. Here we provide details regarding the various executables necessary for each
of these tasks. Throughout the description, we have provided example data and instructions on how to process
the data to produce error plots.

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Compilation
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At the top-level directory (reconbench), simply type make. This will compile all libraries, and place all
executables in the bin directory. We have made an attempt to make the source as self-contained as possible,
and so it should compile fine on linux and mac; we have not tested it on windows. However, the following
libraries/executables are not included and are necessary:
- libpng12
- lapack/blas
- ffmpeg
- gnuplot
- epstopdf
These libraries/executables can easily be obtained through most linux distros, and are also easy to grab
for mac (i.e. macports).

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Surface Modeling
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We allow for the creation of polygonal MPU implicit surfaces, obtained through approximating
triangulated surface meshes:

- ./bin/mesh_to_implicit surface_mesh implicit_surface min_samples fit_epsilon covering

-- surface_mesh can be an off, obj, or ply mesh.
-- implicit_surface is the name of the output MPU surface -> needs to have .mpu as an extension, for later use.
-- min_samples specifies the minimum number of triangles necessary to fit a shape function. It also
has an effect on CSG operations. A value of 6 tends to be a good trade-off.
-- fit_epsilon specifies the quality of a fit, as a percentage of the bounding box of the input mesh ->
if satisfied, subdivision is terminated in the octree. This is largely dependent on the complexity of the
shape, and the tesselation. Typical values range from 0.005 - 0.01. Larger values result in details being
smoothed out.
-- covering specifies the radius of the sphere which occupies each octree cell, specified as a fraction of
half the bounding box diagonal. Typical values range from 1.0 - 1.25.

We note that creating MPU polygonal surfaces from triangle meshes can be a trial-and-error process, as
certain surface meshes may be difficult to fit shape functions to. Hence to facilitate this, we have
provided a marching cubes implementation so that one may quickly observe the resulting zero-set of
the implicit function:

- ./bin/isosurface implicit_surface resolution output_surface

-- implicit_surface is the aforementioned MPU surface.
-- resolution specifies the marching cubes grid resolution. This should be rather high (i.e. 256), in order to
stay within the bounds of the MPU surface definition.
-- output_surface is the resulting isosurface, either off or obj format.

Included in modeling/models is an example implicit surface, bumps, used in the "simple shapes" part
of the benchmark.

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Synthetic Scanning
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From the MPU surfaces we next allow for synthetically scanning the surfaces, simulating the process of
an optical triangulation-based scanner. We break up point cloud generation into generation of configuration
files, followed by executing the coniguration files to obtain the point cloud. To generate configuration files:

- ./bin/pc_generator implicit_surface config_base ([param value])* ([param range min_value max_value number])*

-- implicit_surface is an MPU surface file - may be specified as absolute path, or if in reconbench directory,
can specify as relative.
-- config_base represents the base file name at which the configuration, and subsequently point cloud, files
will be stored. Depending on the number of parameters set, files will be labeled config_base_0.cnf, config_base_1.cnf,
etc.. May be specified as absolute path, or if in reconbench directory, can specify as relative
-- param value: assign a scanner parameter to value. Please see sampler/pc_generator.cpp, as well as the original paper,
for further description on the parameters.
-- param range min_value max_value number: for a given parameter, assign a range of values, starting from min_value
to max_value, in uniform increments, with number being the amount generated.

It is necessary to at least supply the image resolution and number of scans. All other parameters are optional, with
defaults already at hand - see sampler/UniformSampler.cpp for default parameters.

To generate the point cloud, from within the reconbench directory:

- python scripts/RunSampler.py config_file

-- config_file is the aforementioned configuration file generated through pc_generator. The result is a .npts file,
as well as a .mov file, which is a movie of all scans and laser stripes taken through the scanning simulation.

We have provided some example config files for the bumps shape, varying in increasing resolution, found
in data/pcs/bumps. Give the above a try to produce the point clouds for these config files.

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Reconstruction
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We have provided a script to more easily run reconstruction algorithms on the generated point clouds. As
every reconstruction algorithm has its own set of parameters, we require the user to provide a script to run
their algorithm, and to modify scripts/scripts_recon.py to support their algorithm. As an example, we have included
Poisson Surface Reconstruction and its associated script, in the recon directory. Paths can be either absolute,
or relative to the reconbench directory. See data/meshes/bumps/recon_config.cnf to see how to set parameters
to your algorithm. Once all set, algorithms may be run in batch by:

- python scripts/scripts_recon.py config_file

We suggest compiling Poisson Surface Reconstruction, and running the above command on the "bumps" point clouds
produced above to get a feel for the reconstruction script and configuration.

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Evaluation
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Evaluation requires: the MPU implicit surface, a dense uniform sampling of the surface and the output
reconstructed mesh. We have provided dense uniform samplings used in our benchmark in the modeling/models
directory. However, if you have generated your own implicits, you must generate these samplings yourself.
We have provided an executable to do so:

- ./bin/implicit_uniform implicit_surface num_samples

-- implicit_surface is the MPU surface file.
-- num_samples is the number of samples to distribute on the surface. This should be a sufficiently large number
to guarantee that all surface features are covered by the sampling. Of course this depends on the shape,
so please use best judgement in determining a sufficient number of samples.

Evaluation may then be performed as follows:

- ./bin/run_evaluation reconstructed_mesh implicit_surface dense_sampling output_base write_correspondences

-- reconstructed_mesh is the mesh output from the reconstruction algorithm.
-- implicit_surface is the MPU surface file.
-- dense_sampling is the dense uniformly sampled point cloud.
-- output_base is the base file from which the reconstruction results will be written to. For instance, if
'results' is specified, then results.dist, results.recon, and optionally results.i2m and results.m2i will
be output.
-- write_correspondences is a flag indicating whether or not (1 or 0) the implicit to mesh and mesh to implicit
point correspondences are to be written out (the .i2m and .m2i files).

The .dist file contains the individual distributions of the positional and normal error metrics: min, lower quartile,
median, upper quartile, max, and mean. The .recon file contains topological information about the mesh, see
evaluator/GlobalStats.cpp for more information. The m2i and i2m files may be read in via
evaluator/ShortestDistanceMap.cpp.

We suggest running evaluation on the surfaces produced via Poisson Surface Reconstruction. Please see
modeling/models/bumps for the reference point cloud produced via the particle system.

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Plotting Results
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From the .dist file(s) generated through evaluation, we allow for two different options in plotting the results.
To generate a distribution over a single point cloud:

- ./bin/single_distribution dist_file output_base

-- dist_file is the .dist file generated through bin/run_evaluation.
-- output_base is the base file name from which two plots, in pdf, will be generated. One is a box plot of the
positional error distribution, and the other is a box plot of the normal error distribution. This is with
respect to a single point cloud.

To generate distribution plots over a collection of point clouds:

- ./bin/aggregate_distribution dist_base num_pcs output_base

-- dist_base is the base file name which the .dist files over all reconstruction evaluations reside. They must
be numbered as dist_base_0.dist, dist_base_1.dist, ... dist_base_(num_pcs-1).dist.
-- num_pcs is the number of point clouds over the distribution.
-- output_base is the base file name from which four plots, in pdf, will be generated. These are mean distance
distribution, Hausdorff distance distribution, mean normal deviation distribution, and max normal deviation distribution.

We suggest running the plotting executables on the running example, both individual and aggregate distributions,
to get a feel for the plotting.

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Contact
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Please email [email protected] for any questions, comments, suggestions, and bug reporting. Also,
please send an email if you are interested in contributing new data! We hope our reconstruction benchmark will
grow over time, in order to provide a rich amount of data for surface reconstruction researchers and practitioners.