# Reflectometry from Interreflections

## Reflectometry

Reflectometry is the task for acquiring the bidirectional reflectance distribution function (BRDFs) of real-world materials. The typical reflectometry pipeline in computer vision, computer graphics, and computational imaging involves capturing images of a convex shape under multiple illumination and imaging conditions; due to the convexity of the shape, which implies that all paths from the light source to the camera perform a single reflection, the intensities in these images can subsequently be analytically mapped to BRDF values.

## Reflectometry from interreflections approach

We deviate from this pipeline by investigating the utility of higher-order light transport effects, such as the interreflections arising when illuminating and imaging a concave object, for reflectometry. We show that interreflections provide a rich set of contraints on the unknown BRDF, significantly exceeding those available in equivalent measurements of convex shapes. We develop a differentiable rendering pipeline to solve an inverse rendering problem that uses these constraints to produce high-fidelity BRDF estimates from even a single input image. Finally, we take first steps towards designing new concave shapes that maximize the amount of information about the unknown BRDF available in image measurements. We perform extensive simulations to validate the utility of this reflectometry from interreflections approach.

#### Reduced Acquisition Effort

##### More Info

Our main insight is that the intensity of light paths corresponding to interreflections (e.g., those produced when illuminating and imaging a shape with concavities) is a function of more than one samples of the BRDF—one sample for each reflection event that takes place along the path. Therefore, by capturing images of concave objects, we effectively multiplex multiple measurements of the BRDF into a smaller set of images than what would be required if we were using a convex object.

#### Differentiable Rendering

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Given the infinitely many possible interreflection paths contributing to each image pixel, and the fact that the intensity of each path is a non-linear value of the BRDF, extracting BRDF values from images containing interreflections is a challenging inverse rendering problem. We show that we can use recently-developed differentiable rendering technologies to efficiently solve this problem

#### High Fidelity

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We have demonstrated that, at the cost of increased computation, the use of concave shapes can help produce high-fidelity BRDF estimates from much fewer image measurements than what is required when using convex shapes, due to the rich set of constraints provided on the BRDF when considering the higher-order interreflection paths.

Reconstructed BRDF, rendered under the checkerboard environment map. Insets show error maps with respect to the target.

## People

#### Kfir Shem-Tov

#### Sai Praveen Bangaru

#### Anat Levin

#### IOANNIS GKIOULEKAS