PyCoupole

GPU-accelerated Monte Carlo uncertainty quantification for SVBRDF measurements on the La Coupole setup. Companion code to the associated Optics Express paper, Supplemental Document and measured dataset.

Installation

Simply install it from PyPI:

pip install pycoupole

Quick start

Four functions are exposed, in two pairs:

• computeBRDFDeterministic / computeBRDFDistribution take the measurement geometry as explicit arguments.
• computeBRDFDeterministicFromCSV / computeBRDFDistributionFromCSV read that geometry directly from a measurement CSV (the typical entry point).

From a measurement CSV

Most of the time the inputs come from a measurement CSV, where each row is one pixel-channel sample. Rows are addressed by zero-based index (the header is not counted).

import pycoupole

# Deterministic estimate on selected rows -> list of (rowIndex, brdf in sr^-1)
# Pass a single int for one row, an iterable for several, or None for all rows
results = pycoupole.computeBRDFDeterministicFromCSV("measurements.csv", rows=[0, 1, 2])
for index, brdf in results:
    print(f"row {index}: {brdf:.6e}")

# Monte Carlo distribution on a single row.
result     = pycoupole.computeBRDFDistributionFromCSV("measurements.csv", row=0)
pdf        = result["pdf"]        # density, in sr
brdfValues = result["brdfValues"] # bin centres, in sr^-1

The distribution helper takes exactly one row: a single distribution already saturates the GPU, so for several rows you loop in Python over the row indices.

From explicit arguments

When the geometry does not come from a CSV, call the underlying functions directly.

import pycoupole

sample = dict(
    pixelID        = (1521, 915),
    channelID      = 1,
    pixelValueLSB  = 10,
    exposureTimeS  = 0.122374,
    lightCenter    = (-1.14251,   0.507025,    0.391015),
    lightNormal    = ( 0.965928,  0.00172073, -0.258806),
    triangleCenter = ( 0.490908, -0.0674868,   0.0267361),
    triangleNormal = ( 0.0135288,-0.00660755,  0.999887),
)

value  = pycoupole.computeBRDFDeterministic(**sample) # point estimate, sr^-1
result = pycoupole.computeBRDFDistribution(**sample)  # MC distribution

Both *FromCSV functions accept a device argument and forward extra keyword arguments (nbBins, batchSize, seed, ...) to the underlying estimators.

Interpreting the output

computeBRDFDistribution returns a probability density, not a histogram of counts. The density carries the inverse unit of the BRDF (sr), and integrates to 1 over its support — so its values are not bounded by 1 and will be large for a sharply peaked distribution. Recover the per-bin probability mass, then the moments and credible intervals, as:

binWidth = brdfValues[1] - brdfValues[0]
mass     = pdf * binWidth                    # sums to 1

mean   = float(np.sum(mass * brdfValues))
std    = float(np.sqrt(np.sum(mass * (brdfValues - mean) ** 2)))

cdf      = np.cumsum(mass)
median   = float(np.interp(0.50,  cdf, brdfValues))
ci95_low = float(np.interp(0.025, cdf, brdfValues))
ci95_up  = float(np.interp(0.975, cdf, brdfValues))

For a well-conditioned acquisition the deterministic value sits near the centre of the distribution and the out-of-range fraction (1 - nbAccepted / nbTotal) is negligible.

Citation

If you use this software, please cite the associated paper as below (see also CITATION.cff).

La Coupole: an SVBRDF measurement device for large and non-planar objects. Antoine Lucat, Pierre Mézières, François Margall, Louis De Oliveira, Marjorie Paillet, Arnaud Tizon, Pierre Bénard, Romain Pacanowski. Optics Express, Vol. 34, Issue 7, pp. 11695-11709 (March 2026). DOI: 10.1364/OE.587877.

@article{Lucat:26,
  author    = {Antoine Lucat and Pierre M\'{e}zi\`{e}res and Fran\c{c}ois Margall and Louis De Oliveira and Marjorie Paillet and Arnaud Tizon and Pierre B\'{e}nard and Romain Pacanowski},
  journal   = {Optics Express},
  keywords  = {Camera calibration; Imaging systems; Light sources; Physiology; Printed circuit boards; Spatial resolution},
  number    = {7},
  pages     = {11695--11709},
  publisher = {Optica Publishing Group},
  title     = {La Coupole: an SVBRDF measurement device for large and non-planar objects},
  volume    = {34},
  month     = {Apr},
  year      = {2026},
  url       = {https://opg.optica.org/oe/abstract.cfm?URI=oe-34-7-11695},
  doi       = {10.1364/OE.587877},
}

License

PyCoupole is distributed under the MIT License. See LICENSE.txt for more information.